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-rw-r--r--graphics/asymptote/base/plain_arrows.asy18
-rw-r--r--graphics/asymptote/base/plain_strings.asy10
-rw-r--r--graphics/asymptote/base/rational.asy10
-rw-r--r--graphics/asymptote/base/rationalSimplex.asy152
-rw-r--r--graphics/asymptote/base/simplex.asy156
-rw-r--r--graphics/asymptote/base/solids.asy31
-rw-r--r--graphics/asymptote/base/webgl/asygl.js2
7 files changed, 219 insertions, 160 deletions
diff --git a/graphics/asymptote/base/plain_arrows.asy b/graphics/asymptote/base/plain_arrows.asy
index d7d79217dd..96a33dd5a4 100644
--- a/graphics/asymptote/base/plain_arrows.asy
+++ b/graphics/asymptote/base/plain_arrows.asy
@@ -629,3 +629,21 @@ frame[] fit(string prefix="", picture[] pictures, string format="",
return fit2(pictures,all);
}
+
+// Pad a picture to a specified size
+frame pad(picture pic=currentpicture, real xsize=pic.xsize,
+ real ysize=pic.ysize, filltype filltype=NoFill)
+{
+ picture P;
+ size(P,xsize,ysize,IgnoreAspect);
+ draw(P,(0,0),invisible+thin());
+ draw(P,(xsize,ysize),invisible+thin());
+ add(P,pic.fit(xsize,ysize),(xsize,ysize)/2);
+ frame f=P.fit();
+ if(filltype != NoFill) {
+ frame F;
+ filltype.fill(F,box(min(f),max(f)),invisible);
+ prepend(f,F);
+ }
+ return f;
+}
diff --git a/graphics/asymptote/base/plain_strings.asy b/graphics/asymptote/base/plain_strings.asy
index 8d1fd41bd0..a515861493 100644
--- a/graphics/asymptote/base/plain_strings.asy
+++ b/graphics/asymptote/base/plain_strings.asy
@@ -184,18 +184,10 @@ string jobname(string name)
string graphic(string name, string options="")
{
- if(settings.xasy)
- name=stripdirectory(name);
-
if(latex()) {
if(options != "") options="["+options+"]";
string includegraphics="\includegraphics"+options;
- if(settings.inlinetex)
- return includegraphics+"{"+jobname(name)+"}";
- else
- return includegraphics+
- (find(name," ") < 0 ? "{"+name+"}" :
- (pdf() ? "{\""+stripextension(name)+"\".pdf}" : "{\""+name+"\"}"));
+ return includegraphics+"{"+(settings.inlinetex ? jobname(name) : name)+"}";
}
if(settings.tex != "context")
notimplemented("graphic");
diff --git a/graphics/asymptote/base/rational.asy b/graphics/asymptote/base/rational.asy
index d24da0d664..a120c14123 100644
--- a/graphics/asymptote/base/rational.asy
+++ b/graphics/asymptote/base/rational.asy
@@ -176,15 +176,21 @@ string texstring(rational r)
return s+"\frac{"+string(abs(r.p))+"}{"+string(r.q)+"}";
}
-void write(file fout=stdout, string s="", rational r, suffix suffix=none)
+
+void write(file fout, string s="", rational r, suffix suffix=none)
{
write(fout,s+string(r),suffix);
}
+void write(string s="", rational r, suffix suffix=endl)
+{
+ write(stdout,s,r,suffix);
+}
+
void write(file fout=stdout, string s="", rational[] a, suffix suffix=none)
{
if(s != "")
- write(fout,s);
+ write(fout,s,endl);
for(int i=0; i < a.length; ++i) {
write(fout,i,none);
write(fout,':\t',a[i],endl);
diff --git a/graphics/asymptote/base/rationalSimplex.asy b/graphics/asymptote/base/rationalSimplex.asy
index 5175b87ba7..d694843289 100644
--- a/graphics/asymptote/base/rationalSimplex.asy
+++ b/graphics/asymptote/base/rationalSimplex.asy
@@ -2,21 +2,23 @@
import rational;
void simplexTableau(rational[][] E, int[] Bindices, int I=-1, int J=-1) {}
+void simplexPhase1(rational[] c, rational[][] A, rational[] b,
+ int[] Bindices) {}
void simplexPhase2() {}
-void simplexWrite(rational[][] E, int[] Bindicies, int, int)
+void simplexWrite(rational[][] E, int[] Bindices, int, int)
{
int m=E.length-1;
int n=E[0].length-1;
- write(E[m][n],tab);
- for(int j=0; j < n; ++j)
+ write(E[m][0],tab);
+ for(int j=1; j <= n; ++j)
write(E[m][j],tab);
write();
for(int i=0; i < m; ++i) {
- write(E[i][n],tab);
- for(int j=0; j < n; ++j) {
+ write(E[i][0],tab);
+ for(int j=1; j <= n; ++j) {
write(E[i][j],tab);
}
write();
@@ -68,10 +70,10 @@ struct simplex {
while(true) {
// Find first negative entry in bottom (reduced cost) row
rational[] Em=E[m];
- for(J=0; J < N; ++J)
+ for(J=1; J <= N; ++J)
if(Em[J] < 0) break;
- if(J == N)
+ if(J > N)
break;
int I=-1;
@@ -79,7 +81,7 @@ struct simplex {
for(int i=0; i < m; ++i) {
rational e=E[i][J];
if(e > 0) {
- M=E[i][N]/e;
+ M=E[i][0]/e;
I=i;
break;
}
@@ -87,7 +89,7 @@ struct simplex {
for(int i=I+1; i < m; ++i) {
rational e=E[i][J];
if(e > 0) {
- rational v=E[i][N]/e;
+ rational v=E[i][0]/e;
if(v < M) {M=v; I=i;} // Bland's rule: choose smallest argmin
}
}
@@ -105,19 +107,19 @@ struct simplex {
int iterateDual(rational[][] E, int N, int[] Bindices) {
while(true) {
- // Find first negative entry in right (basic variable) column
+ // Find first negative entry in zeroth (basic variable) column
rational[] Em=E[m];
int I;
for(I=0; I < m; ++I) {
- if(E[I][N] < 0) break;
+ if(E[I][0] < 0) break;
}
if(I == m)
break;
- int J=-1;
+ int J=0;
rational M;
- for(int j=0; j < N; ++j) {
+ for(int j=1; j <= N; ++j) {
rational e=E[I][j];
if(e < 0) {
M=-E[m][j]/e;
@@ -125,14 +127,14 @@ struct simplex {
break;
}
}
- for(int j=J+1; j < N; ++j) {
+ for(int j=J+1; j <= N; ++j) {
rational e=E[I][j];
if(e < 0) {
rational v=-E[m][j]/e;
if(v < M) {M=v; J=j;} // Bland's rule: choose smallest argmin
}
}
- if(J == -1)
+ if(J == 0)
return INFEASIBLE; // Can only happen in Phase 2.
simplexTableau(E,Bindices,I,J);
@@ -157,66 +159,94 @@ struct simplex {
n=A[0].length;
if(n == 0) {case=INFEASIBLE; return;}
- int N=phase1 ? n+m : n;
- rational[][] E=new rational[m+1][N+1];
+ rational[][] E=new rational[m+1][n+1];
rational[] Em=E[m];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Em[j]=0;
for(int i=0; i < m; ++i) {
rational[] Ai=A[i];
rational[] Ei=E[i];
if(b[i] >= 0 || dual) {
- for(int j=0; j < n; ++j) {
- rational Aij=Ai[j];
+ for(int j=1; j <= n; ++j) {
+ rational Aij=Ai[j-1];
Ei[j]=Aij;
Em[j] -= Aij;
}
} else {
- for(int j=0; j < n; ++j) {
- rational Aij=-Ai[j];
+ for(int j=1; j <= n; ++j) {
+ rational Aij=-Ai[j-1];
Ei[j]=Aij;
Em[j] -= Aij;
}
}
}
- if(phase1) {
- for(int i=0; i < m; ++i) {
- rational[] Ei=E[i];
- for(int j=0; j < i; ++j)
- Ei[n+j]=0;
- Ei[n+i]=1;
- for(int j=i+1; j < m; ++j)
- Ei[n+j]=0;
+ void basicValues() {
+ rational sum=0;
+ for(int i=0; i < m; ++i) {
+ rational B=dual ? b[i] : abs(b[i]);
+ E[i][0]=B;
+ sum -= B;
}
+ Em[0]=sum;
}
- rational sum=0;
- for(int i=0; i < m; ++i) {
- rational B=dual ? b[i] : abs(b[i]);
- E[i][N]=B;
- sum -= B;
- }
- Em[N]=sum;
-
- if(phase1)
- for(int j=0; j < m; ++j)
- Em[n+j]=0;
-
int[] Bindices;
if(phase1) {
- Bindices=sequence(new int(int x){return x;},m)+n;
- iterate(E,N,Bindices);
+ Bindices=new int[m];
+ int p=0;
+
+ // Check for redundant basis vectors.
+ bool checkBasis(int j) {
+ for(int i=0; i < m; ++i) {
+ rational[] Ei=E[i];
+ if(i != p ? Ei[j] != 0 : Ei[j] <= 0) return false;
+ }
+ return true;
+ }
+
+ int checkTableau() {
+ for(int j=1; j <= n; ++j)
+ if(checkBasis(j)) return j;
+ return 0;
+ }
+
+ int k=0;
+ while(p < m) {
+ int j=checkTableau();
+ if(j > 0)
+ Bindices[p]=j;
+ else { // Add an artificial variable
+ Bindices[p]=n+1+k;
+ for(int i=0; i < p; ++i)
+ E[i].push(0);
+ E[p].push(1);
+ for(int i=p+1; i < m; ++i)
+ E[i].push(0);
+ E[m].push(0);
+ ++k;
+ }
+ ++p;
+ }
+
+ basicValues();
+
+ simplexPhase1(c,A,b,Bindices);
+
+ iterate(E,n+k,Bindices);
- if(Em[J] != 0) {
+ if(Em[0] != 0) {
simplexTableau(E,Bindices);
case=INFEASIBLE;
return;
}
- } else Bindices=sequence(new int(int x){return x;},m)+n-m;
+ } else {
+ Bindices=sequence(new int(int x){return x;},m)+n-m+1;
+ basicValues();
+ }
rational[] cB=phase1 ? new rational[m] : c[n-m:n];
rational[][] D=phase1 ? new rational[m+1][n+1] : E;
@@ -225,12 +255,12 @@ struct simplex {
// Drive artificial variables out of basis.
for(int i=0; i < m; ++i) {
int k=Bindices[i];
- if(k >= n) {
+ if(k > n) {
rational[] Ei=E[i];
int j;
- for(j=0; j < n; ++j)
+ for(j=1; j <= n; ++j)
if(Ei[j] != 0) break;
- if(j == n) continue;
+ if(j > n) continue;
output=false;
simplexTableau(E,Bindices,i,j);
Bindices[i]=j;
@@ -241,22 +271,22 @@ struct simplex {
int ip=0; // reduced i
for(int i=0; i < m; ++i) {
int k=Bindices[i];
- if(k >= n) continue;
+ if(k > n) continue;
Bindices[ip]=k;
- cB[ip]=c[k];
+ cB[ip]=c[k-1];
rational[] Dip=D[ip];
rational[] Ei=E[i];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Dip[j]=Ei[j];
- Dip[n]=Ei[N];
+ Dip[0]=Ei[0];
++ip;
}
rational[] Dip=D[ip];
rational[] Em=E[m];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Dip[j]=Em[j];
- Dip[n]=Em[N];
+ Dip[0]=Em[0];
if(m > ip) {
Bindices.delete(ip,m-1);
@@ -267,17 +297,17 @@ struct simplex {
}
rational[] Dm=D[m];
- for(int j=0; j < n; ++j) {
+ for(int j=1; j <= n; ++j) {
rational sum=0;
for(int k=0; k < m; ++k)
sum += cB[k]*D[k][j];
- Dm[j]=c[j]-sum;
+ Dm[j]=c[j-1]-sum;
}
rational sum=0;
for(int k=0; k < m; ++k)
- sum += cB[k]*D[k][n];
- Dm[n]=-sum;
+ sum += cB[k]*D[k][0];
+ Dm[0]=-sum;
simplexPhase2();
@@ -290,9 +320,9 @@ struct simplex {
x[j]=0;
for(int k=0; k < m; ++k)
- x[Bindices[k]]=D[k][n];
+ x[Bindices[k]-1]=D[k][0];
- cost=-Dm[n];
+ cost=-Dm[0];
}
// Try to find a solution x to sgn(Ax-b)=sgn(s) that minimizes the cost
diff --git a/graphics/asymptote/base/simplex.asy b/graphics/asymptote/base/simplex.asy
index 040621dd90..b9ff172077 100644
--- a/graphics/asymptote/base/simplex.asy
+++ b/graphics/asymptote/base/simplex.asy
@@ -11,7 +11,7 @@ struct simplex {
int m,n;
int J;
- real epsilonA;
+ real EpsilonA;
// Row reduce based on pivot E[I][J]
void rowreduce(real[][] E, int N, int I, int J) {
@@ -45,26 +45,26 @@ struct simplex {
while(true) {
// Find first negative entry in bottom (reduced cost) row
real[] Em=E[m];
- for(J=0; J < N; ++J)
+ for(J=1; J <= N; ++J)
if(Em[J] < 0) break;
- if(J == N)
+ if(J > N)
break;
int I=-1;
real M;
for(int i=0; i < m; ++i) {
real e=E[i][J];
- if(e > epsilonA) {
- M=E[i][N]/e;
+ if(e > EpsilonA) {
+ M=E[i][0]/e;
I=i;
break;
}
}
for(int i=I+1; i < m; ++i) {
real e=E[i][J];
- if(e > epsilonA) {
- real v=E[i][N]/e;
+ if(e > EpsilonA) {
+ real v=E[i][0]/e;
if(v < M) {M=v; I=i;} // Bland's rule: choose smallest argmin
}
}
@@ -80,34 +80,34 @@ struct simplex {
int iterateDual(real[][] E, int N, int[] Bindices) {
while(true) {
- // Find first negative entry in right (basic variable) column
+ // Find first negative entry in zeroth (basic variable) column
real[] Em=E[m];
int I;
for(I=0; I < m; ++I) {
- if(E[I][N] < 0) break;
+ if(E[I][0] < 0) break;
}
if(I == m)
break;
- int J=-1;
+ int J=0;
real M;
- for(int j=0; j < N; ++j) {
+ for(int j=1; j <= N; ++j) {
real e=E[I][j];
- if(e < epsilonA) {
+ if(e < -EpsilonA) {
M=-E[m][j]/e;
J=j;
break;
}
}
- for(int j=J+1; j < N; ++j) {
+ for(int j=J+1; j <= N; ++j) {
real e=E[I][j];
- if(e < epsilonA) {
+ if(e < -EpsilonA) {
real v=-E[m][j]/e;
if(v < M) {M=v; J=j;} // Bland's rule: choose smallest argmin
}
}
- if(J == -1)
+ if(J == 0)
return INFEASIBLE; // Can only happen in Phase 2.
// Generate new tableau
@@ -125,7 +125,9 @@ struct simplex {
bool dual=false) {
if(dual) phase1=false;
static real epsilon=sqrt(realEpsilon);
- epsilonA=epsilon*norm(A);
+ real normA=norm(A);
+ real epsilonA=100.0*realEpsilon*normA;
+ EpsilonA=epsilon*normA;
// Phase 1
m=A.length;
@@ -133,78 +135,103 @@ struct simplex {
n=A[0].length;
if(n == 0) {case=INFEASIBLE; return;}
- int N=phase1 ? n+m : n;
- real[][] E=new real[m+1][N+1];
+ real[][] E=new real[m+1][n+1];
real[] Em=E[m];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Em[j]=0;
for(int i=0; i < m; ++i) {
real[] Ai=A[i];
real[] Ei=E[i];
if(b[i] >= 0 || dual) {
- for(int j=0; j < n; ++j) {
- real Aij=Ai[j];
+ for(int j=1; j <= n; ++j) {
+ real Aij=Ai[j-1];
Ei[j]=Aij;
Em[j] -= Aij;
}
} else {
- for(int j=0; j < n; ++j) {
- real Aij=-Ai[j];
+ for(int j=1; j <= n; ++j) {
+ real Aij=-Ai[j-1];
Ei[j]=Aij;
Em[j] -= Aij;
}
}
}
- if(phase1) {
- for(int i=0; i < m; ++i) {
- real[] Ei=E[i];
- for(int j=0; j < i; ++j)
- Ei[n+j]=0.0;
- Ei[n+i]=1.0;
- for(int j=i+1; j < m; ++j)
- Ei[n+j]=0.0;
+ void basicValues() {
+ real sum=0;
+ for(int i=0; i < m; ++i) {
+ real B=dual ? b[i] : abs(b[i]);
+ E[i][0]=B;
+ sum -= B;
}
+ Em[0]=sum;
}
- real sum=0;
- for(int i=0; i < m; ++i) {
- real B=dual ? b[i] : abs(b[i]);
- E[i][N]=B;
- sum -= B;
- }
- Em[N]=sum;
-
- if(phase1)
- for(int j=0; j < m; ++j)
- Em[n+j]=0.0;
-
int[] Bindices;
if(phase1) {
- Bindices=sequence(new int(int x){return x;},m)+n;
- iterate(E,N,Bindices);
+ Bindices=new int[m];
+ int p=0;
+
+ // Check for redundant basis vectors.
+ bool checkBasis(int j) {
+ for(int i=0; i < m; ++i) {
+ real[] Ei=E[i];
+ if(i != p ? abs(Ei[j]) >= epsilonA : Ei[j] <= epsilonA) return false;
+ }
+ return true;
+ }
+
+ int checkTableau() {
+ for(int j=1; j <= n; ++j)
+ if(checkBasis(j)) return j;
+ return 0;
+ }
+
+ int k=0;
+ while(p < m) {
+ int j=checkTableau();
+ if(j > 0)
+ Bindices[p]=j;
+ else { // Add an artificial variable
+ Bindices[p]=n+1+k;
+ for(int i=0; i < p; ++i)
+ E[i].push(0.0);
+ E[p].push(1.0);
+ for(int i=p+1; i < m; ++i)
+ E[i].push(0.0);
+ E[m].push(0.0);
+ ++k;
+ }
+ ++p;
+ }
+
+ basicValues();
+ iterate(E,n+k,Bindices);
- if(abs(Em[J]) > epsilonA) {
+ if(abs(Em[0]) > EpsilonA) {
case=INFEASIBLE;
return;
}
- } else Bindices=sequence(new int(int x){return x;},m)+n-m;
-
+ } else {
+ Bindices=sequence(new int(int x){return x;},m)+n-m+1;
+ basicValues();
+ }
+
real[] cB=phase1 ? new real[m] : c[n-m:n];
real[][] D=phase1 ? new real[m+1][n+1] : E;
if(phase1) {
// Drive artificial variables out of basis.
for(int i=0; i < m; ++i) {
int k=Bindices[i];
- if(k >= n) {
+ if(k > n) {
real[] Ei=E[i];
int j;
- for(j=0; j < n; ++j)
- if(Ei[j] != 0) break;
- if(j == n) continue;
+ for(j=1; j <= n; ++j)
+ if(abs(Ei[j]) > EpsilonA) break;
+ if(j > n) continue;
Bindices[i]=j;
rowreduce(E,n,i,j);
}
@@ -212,22 +239,22 @@ struct simplex {
int ip=0; // reduced i
for(int i=0; i < m; ++i) {
int k=Bindices[i];
- if(k >= n) continue;
+ if(k > n) continue;
Bindices[ip]=k;
- cB[ip]=c[k];
+ cB[ip]=c[k-1];
real[] Dip=D[ip];
real[] Ei=E[i];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Dip[j]=Ei[j];
- Dip[n]=Ei[N];
+ Dip[0]=Ei[0];
++ip;
}
real[] Dip=D[ip];
real[] Em=E[m];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Dip[j]=Em[j];
- Dip[n]=Em[N];
+ Dip[0]=Em[0];
if(m > ip) {
Bindices.delete(ip,m-1);
@@ -237,17 +264,17 @@ struct simplex {
}
real[] Dm=D[m];
- for(int j=0; j < n; ++j) {
+ for(int j=1; j <= n; ++j) {
real sum=0;
for(int k=0; k < m; ++k)
sum += cB[k]*D[k][j];
- Dm[j]=c[j]-sum;
+ Dm[j]=c[j-1]-sum;
}
real sum=0;
for(int k=0; k < m; ++k)
- sum += cB[k]*D[k][n];
- Dm[n]=-sum;
+ sum += cB[k]*D[k][0];
+ Dm[0]=-sum;
case=(dual ? iterateDual : iterate)(D,n,Bindices);
if(case != OPTIMAL)
@@ -257,9 +284,8 @@ struct simplex {
x[j]=0;
for(int k=0; k < m; ++k)
- x[Bindices[k]]=D[k][n];
-
- cost=-Dm[n];
+ x[Bindices[k]-1]=D[k][0];
+ cost=-Dm[0];
}
// Try to find a solution x to sgn(Ax-b)=sgn(s) that minimizes the cost
diff --git a/graphics/asymptote/base/solids.asy b/graphics/asymptote/base/solids.asy
index 942a7fe233..2f0a13f4b5 100644
--- a/graphics/asymptote/base/solids.asy
+++ b/graphics/asymptote/base/solids.asy
@@ -115,23 +115,13 @@ struct revolution {
return (angle2-angle1) % 360 == 0 ? p&cycle : p;
}
- triple camera(projection P) {
- triple camera=P.camera;
- if(P.infinity) {
- real s=abs(M-m)+abs(m-P.target);
- camera=P.target+camerafactor*s*unit(P.vector());
- }
- return camera;
- }
-
// add transverse slice to skeleton s;
void transverse(skeleton s, real t, int n=nslice, projection P) {
skeleton.curve s=s.transverse;
path3 S=slice(t,n);
- triple camera=camera(P);
int L=length(g);
real midtime=0.5*L;
- real sign=sgn(dot(axis,camera-P.target))*sgn(dot(axis,dir(g,midtime)));
+ real sign=sgn(dot(axis,P.camera-c))*sgn(dot(axis,dir(g,midtime)));
if(dot(M-m,axis) == 0 || (t <= epsilon && sign < 0) ||
(t >= L-epsilon && sign > 0))
s.front.push(S);
@@ -154,7 +144,7 @@ struct revolution {
path3 p1=subpath(S,t1,t2);
path3 p2=subpath(S,t2,len);
path3 P2=subpath(S,0,t1);
- if(abs(midpoint(p1)-camera) <= abs(midpoint(p2)-camera)) {
+ if(abs(midpoint(p1)-P.camera) <= abs(midpoint(p2)-P.camera)) {
s.front.push(p1);
if(cyclic(S))
s.back.push(p2 & P2);
@@ -212,7 +202,6 @@ struct revolution {
for(int i=0; i < M; ++i) {
real t=(m == 0) ? i : reltime(g,i*factor);
path3 S=slice(t,n);
- triple camera=camera(P);
path3 Sp=slice(t+epsilon,n);
path3 Sm=slice(t-epsilon,n);
path sp=project(Sp,P);
@@ -232,8 +221,7 @@ struct revolution {
}
int L=length(g);
real midtime=0.5*L;
- triple camera=camera(P);
- real sign=sgn(dot(axis,camera-P.target))*sgn(dot(axis,dir(g,midtime)));
+ real sign=sgn(dot(axis,P.camera-c))*sgn(dot(axis,dir(g,midtime)));
skeleton sfirst;
transverse(sfirst,tfirst,n,P);
@@ -293,7 +281,6 @@ struct revolution {
real Longitude(triple v) {return longitude(T*(v-c),warn=false);}
real ref=Longitude(point(g,t));
real angle(real t) {return Longitude(point(S,t/P.ninterpolate))-ref;}
- triple camera=camera(P);
void push(real[] T) {
if(T.length > 1) {
path3 p=rotate(angle(T[0]),c,c+axis)*g;
@@ -301,7 +288,7 @@ struct revolution {
path3 p2=subpath(p,t,length(p));
if(length(p1) > 0 &&
(length(p2) == 0 ||
- abs(midpoint(p1)-camera) <= abs(midpoint(p2)-camera))) {
+ abs(midpoint(p1)-P.camera) <= abs(midpoint(p2)-P.camera))) {
s.longitudinal.front.push(p1);
s.longitudinal.back.push(p2);
} else {
@@ -346,15 +333,15 @@ void draw(picture pic=currentpicture, revolution r, int m=0, int n=nslice,
if(is3D()) {
pen thin=thin();
void drawskeleton(frame f, transform3 t, projection P) {
- skeleton s=(t*r).skeleton(m,n,P);
+ skeleton s=r.skeleton(m,n,inverse(t)*P);
if(frontpen != nullpen) {
- draw(f,s.transverse.back,thin+defaultbackpen+backpen,light);
- draw(f,s.transverse.front,thin+frontpen,light);
+ draw(f,t*s.transverse.back,thin+defaultbackpen+backpen,light);
+ draw(f,t*s.transverse.front,thin+frontpen,light);
}
if(longitudinalpen != nullpen) {
- draw(f,s.longitudinal.back,thin+defaultbackpen+longitudinalbackpen,
+ draw(f,t*s.longitudinal.back,thin+defaultbackpen+longitudinalbackpen,
light);
- draw(f,s.longitudinal.front,thin+longitudinalpen,light);
+ draw(f,t*s.longitudinal.front,thin+longitudinalpen,light);
}
}
diff --git a/graphics/asymptote/base/webgl/asygl.js b/graphics/asymptote/base/webgl/asygl.js
index 9b7abe5b84..75c97ad695 100644
--- a/graphics/asymptote/base/webgl/asygl.js
+++ b/graphics/asymptote/base/webgl/asygl.js
@@ -36,4 +36,4 @@ AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.*/
-let vertex="\nattribute vec3 position;\n#ifdef WIDTH\nattribute float width;\n#endif\n#ifdef NORMAL\nattribute vec3 normal;\n#endif\nattribute float materialIndex;\n#ifdef COLOR\nattribute vec4 color;\n#endif\n\nuniform mat3 normMat;\nuniform mat4 viewMat;\nuniform mat4 projViewMat;\n\n#ifdef NORMAL\n#ifndef ORTHOGRAPHIC\nvarying vec3 ViewPosition;\n#endif\nvarying vec3 Normal;\n#endif\nvarying vec4 diffuse;\nvarying vec3 specular;\nvarying float roughness,metallic,fresnel0;\nvarying vec4 emissive;\n\nstruct Material {\n vec4 diffuse,emissive,specular;\n vec4 parameters;\n};\n\nuniform Material Materials[Nmaterials];\n\nvoid main(void)\n{\n vec4 v=vec4(position,1.0);\n gl_Position=projViewMat*v;\n#ifdef NORMAL\n#ifndef ORTHOGRAPHIC\n ViewPosition=(viewMat*v).xyz;\n#endif \n Normal=normal*normMat;\n \n Material m;\n#ifdef TRANSPARENT\n m=Materials[int(abs(materialIndex))-1];\n if(materialIndex >= 0.0) {\n diffuse=m.diffuse;\n emissive=m.emissive;\n } else {\n diffuse=color;\n#if nlights > 0\n emissive=vec4(0.0);\n#else\n emissive=color;\n#endif\n }\n#else\n m=Materials[int(materialIndex)];\n#ifdef COLOR\n diffuse=color;\n#if nlights > 0\n emissive=vec4(0.0);\n#else\n emissive=color;\n#endif\n#else\n diffuse=m.diffuse;\n emissive=m.emissive;\n#endif\n#endif\n specular=m.specular.rgb;\n vec4 parameters=m.parameters;\n roughness=1.0-parameters[0];\n metallic=parameters[1];\n fresnel0=parameters[2];\n#else\n emissive=Materials[int(materialIndex)].emissive;\n#endif\n#ifdef WIDTH\n gl_PointSize=width;\n#endif\n}\n",fragment="\n#ifdef NORMAL\n#ifndef ORTHOGRAPHIC\nvarying vec3 ViewPosition;\n#endif\nvarying vec3 Normal;\nvarying vec4 diffuse;\nvarying vec3 specular;\nvarying float roughness,metallic,fresnel0;\n\nfloat Roughness2;\nvec3 normal;\n\nstruct Light {\n vec3 direction;\n vec3 color;\n};\n\nuniform Light Lights[Nlights];\n\nfloat NDF_TRG(vec3 h)\n{\n float ndoth=max(dot(normal,h),0.0);\n float alpha2=Roughness2*Roughness2;\n float denom=ndoth*ndoth*(alpha2-1.0)+1.0;\n return denom != 0.0 ? alpha2/(denom*denom) : 0.0;\n}\n \nfloat GGX_Geom(vec3 v)\n{\n float ndotv=max(dot(v,normal),0.0);\n float ap=1.0+Roughness2;\n float k=0.125*ap*ap;\n return ndotv/((ndotv*(1.0-k))+k);\n}\n \nfloat Geom(vec3 v, vec3 l)\n{\n return GGX_Geom(v)*GGX_Geom(l);\n}\n \nfloat Fresnel(vec3 h, vec3 v, float fresnel0)\n{\n float a=1.0-max(dot(h,v),0.0);\n float b=a*a;\n return fresnel0+(1.0-fresnel0)*b*b*a;\n}\n \n// physical based shading using UE4 model.\nvec3 BRDF(vec3 viewDirection, vec3 lightDirection)\n{\n vec3 lambertian=diffuse.rgb;\n vec3 h=normalize(lightDirection+viewDirection);\n \n float omegain=max(dot(viewDirection,normal),0.0);\n float omegali=max(dot(lightDirection,normal),0.0);\n \n float D=NDF_TRG(h);\n float G=Geom(viewDirection,lightDirection);\n float F=Fresnel(h,viewDirection,fresnel0);\n \n float denom=4.0*omegain*omegali;\n float rawReflectance=denom > 0.0 ? (D*G)/denom : 0.0;\n \n vec3 dielectric=mix(lambertian,rawReflectance*specular,F);\n vec3 metal=rawReflectance*diffuse.rgb;\n \n return mix(dielectric,metal,metallic);\n}\n#endif\nvarying vec4 emissive;\n \nvoid main(void)\n{\n#if defined(NORMAL) && nlights > 0\n normal=normalize(Normal);\n normal=gl_FrontFacing ? normal : -normal;\n#ifdef ORTHOGRAPHIC\n vec3 viewDir=vec3(0.0,0.0,1.0);\n#else\n vec3 viewDir=-normalize(ViewPosition);\n#endif\n Roughness2=roughness*roughness;\n vec3 color=emissive.rgb;\n for(int i=0; i < nlights; ++i) {\n Light Li=Lights[i];\n vec3 L=Li.direction;\n float cosTheta=max(dot(normal,L),0.0);\n vec3 radiance=cosTheta*Li.color;\n color += BRDF(viewDir,L)*radiance;\n }\n gl_FragColor=vec4(color,diffuse.a);\n#else\n gl_FragColor=emissive;\n#endif\n}\n";!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var i=t();for(var a in i)("object"==typeof exports?exports:e)[a]=i[a]}}("undefined"!=typeof self?self:this,function(){return function(e){var t={};function i(a){if(t[a])return t[a].exports;var r=t[a]={i:a,l:!1,exports:{}};return e[a].call(r.exports,r,r.exports,i),r.l=!0,r.exports}return i.m=e,i.c=t,i.d=function(e,t,a){i.o(e,t)||Object.defineProperty(e,t,{configurable:!1,enumerable:!0,get:a})},i.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return i.d(t,"a",t),t},i.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)},i.p="",i(i.s=1)}([function(e,t,i){"use strict";Object.defineProperty(t,"__esModule",{value:!0}),t.setMatrixArrayType=function(e){t.ARRAY_TYPE=e},t.toRadian=function(e){return e*r},t.equals=function(e,t){return Math.abs(e-t)<=a*Math.max(1,Math.abs(e),Math.abs(t))};var a=t.EPSILON=1e-6;t.ARRAY_TYPE="undefined"!=typeof Float32Array?Float32Array:Array,t.RANDOM=Math.random;var r=Math.PI/180},function(e,t,i){"use 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a=function(e){if(e&&e.__esModule)return e;var t={};if(null!=e)for(var i in e)Object.prototype.hasOwnProperty.call(e,i)&&(t[i]=e[i]);return t.default=e,t}(i(0));function r(e,t,i){var a=t[0],r=t[1],n=t[2],s=t[3],o=t[4],l=t[5],h=t[6],c=t[7],d=t[8],m=t[9],f=t[10],u=t[11],v=t[12],g=t[13],p=t[14],x=t[15],M=i[0],w=i[1],A=i[2],b=i[3];return e[0]=M*a+w*o+A*d+b*v,e[1]=M*r+w*l+A*m+b*g,e[2]=M*n+w*h+A*f+b*p,e[3]=M*s+w*c+A*u+b*x,M=i[4],w=i[5],A=i[6],b=i[7],e[4]=M*a+w*o+A*d+b*v,e[5]=M*r+w*l+A*m+b*g,e[6]=M*n+w*h+A*f+b*p,e[7]=M*s+w*c+A*u+b*x,M=i[8],w=i[9],A=i[10],b=i[11],e[8]=M*a+w*o+A*d+b*v,e[9]=M*r+w*l+A*m+b*g,e[10]=M*n+w*h+A*f+b*p,e[11]=M*s+w*c+A*u+b*x,M=i[12],w=i[13],A=i[14],b=i[15],e[12]=M*a+w*o+A*d+b*v,e[13]=M*r+w*l+A*m+b*g,e[14]=M*n+w*h+A*f+b*p,e[15]=M*s+w*c+A*u+b*x,e}}])});let canvasWidth,canvasHeight,b,B,angle,Zoom0,viewportmargin,zoomFactor,zoomPinchFactor,zoomPinchCap,zoomStep,shiftHoldDistance,shiftWaitTime,vibrateTime,embedded,canvas,gl,alpha,offscreen,context,maxMaterials,halfCanvasWidth,halfCanvasHeight,Zoom,P=[],Materials=[],Lights=[],Centers=[],Background=[1,1,1,1],absolute=!1,viewportshift=[0,0],nlights=0,Nmaterials=1,materials=[],pixel=.75,BezierFactor=.4,FillFactor=.1,maxViewportWidth=window.innerWidth,maxViewportHeight=window.innerHeight;const windowTrim=10;let lastzoom,H,zmin,zmax,size2,ArcballFactor,positionBuffer,materialBuffer,colorBuffer,indexBuffer,resizeStep=1.2,Fuzz2=1e3*Number.EPSILON,Fuzz4=Fuzz2*Fuzz2,third=1/3,rotMat=mat4.create(),projMat=mat4.create(),viewMat=mat4.create(),projViewMat=mat4.create(),normMat=mat3.create(),viewMat3=mat3.create(),rotMats=mat4.create(),cjMatInv=mat4.create(),translMat=mat4.create(),center={x:0,y:0,z:0},shift={x:0,y:0},viewParam={xmin:0,xmax:0,ymin:0,ymax:0,zmin:0,zmax:0},redraw=!0,remesh=!0,mouseDownOrTouchActive=!1,lastMouseX=null,lastMouseY=null,touchID=null,Positions=[],Normals=[],Colors=[],Indices=[];class Material{constructor(e,t,i,a,r,n){this.diffuse=e,this.emissive=t,this.specular=i,this.shininess=a,this.metallic=r,this.fresnel0=n}setUniform(e,t){let i=i=>gl.getUniformLocation(e,"Materials["+t+"]."+i);gl.uniform4fv(i("diffuse"),new Float32Array(this.diffuse)),gl.uniform4fv(i("emissive"),new Float32Array(this.emissive)),gl.uniform4fv(i("specular"),new Float32Array(this.specular)),gl.uniform4f(i("parameters"),this.shininess,this.metallic,this.fresnel0,0)}}let indexExt,enumPointLight=1,enumDirectionalLight=2;class Light{constructor(e,t){this.direction=e,this.color=t}setUniform(e,t){let i=i=>gl.getUniformLocation(e,"Lights["+t+"]."+i);gl.uniform3fv(i("direction"),new Float32Array(this.direction)),gl.uniform3fv(i("color"),new Float32Array(this.color))}}function initShaders(){let e=gl.getParameter(gl.MAX_VERTEX_UNIFORM_VECTORS);maxMaterials=Math.floor((e-14)/4),Nmaterials=Math.min(Math.max(Nmaterials,Materials.length),maxMaterials),noNormalShader=initShader(),pixelShader=initShader(["WIDTH"]),materialShader=initShader(["NORMAL"]),colorShader=initShader(["NORMAL","COLOR"]),transparentShader=initShader(["NORMAL","COLOR","TRANSPARENT"])}function setBuffers(){positionBuffer=gl.createBuffer(),materialBuffer=gl.createBuffer(),colorBuffer=gl.createBuffer(),indexBuffer=gl.createBuffer()}function noGL(){gl||alert("Could not initialize WebGL")}function saveAttributes(){let e=window.parent.document.asygl[alpha];e.gl=gl,e.nlights=Lights.length,e.Nmaterials=Nmaterials,e.maxMaterials=maxMaterials,e.noNormalShader=noNormalShader,e.pixelShader=pixelShader,e.materialShader=materialShader,e.colorShader=colorShader,e.transparentShader=transparentShader}function restoreAttributes(){let e=window.parent.document.asygl[alpha];gl=e.gl,nlights=e.nlights,Nmaterials=e.Nmaterials,maxMaterials=e.maxMaterials,noNormalShader=e.noNormalShader,pixelShader=e.pixelShader,materialShader=e.materialShader,colorShader=e.colorShader,transparentShader=e.transparentShader}function initGL(){if(alpha=Background[3]<1,embedded){let e=window.parent.document;null==e.asygl&&(e.asygl=Array(2)),context=canvas.getContext("2d"),(offscreen=e.offscreen)||(offscreen=e.createElement("canvas"),e.offscreen=offscreen),e.asygl[alpha]&&e.asygl[alpha].gl?(restoreAttributes(),(Lights.length!=nlights||Math.min(Materials.length,maxMaterials)>Nmaterials)&&(initShaders(),saveAttributes())):((gl=offscreen.getContext("webgl",{alpha:alpha}))||noGL(),initShaders(),e.asygl[alpha]={},saveAttributes())}else(gl=canvas.getContext("webgl",{alpha:alpha}))||noGL(),initShaders();setBuffers(),indexExt=gl.getExtension("OES_element_index_uint")}function getShader(e,t,i,a=[]){let r=`#version 100\n#ifdef GL_FRAGMENT_PRECISION_HIGH\n precision highp float;\n#else\n precision mediump float;\n#endif\n #define nlights ${Lights.length}\n\n const int Nlights=${Math.max(Lights.length,1)};\n\n #define Nmaterials ${Nmaterials}\n`;orthographic&&(r+="#define ORTHOGRAPHIC\n"),a.forEach(e=>r+="#define "+e+"\n");let n=e.createShader(i);return e.shaderSource(n,r+t),e.compileShader(n),e.getShaderParameter(n,e.COMPILE_STATUS)?n:(alert(e.getShaderInfoLog(n)),null)}function drawBuffer(e,t,i=e.indices){if(0==e.indices.length)return;let a=t==pixelShader,r=t!=noNormalShader&&!a;setUniforms(e,t),gl.bindBuffer(gl.ARRAY_BUFFER,positionBuffer),gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(e.vertices),gl.STATIC_DRAW),gl.vertexAttribPointer(t.vertexPositionAttribute,3,gl.FLOAT,!1,r?24:a?16:12,0),r&&Lights.length>0?gl.vertexAttribPointer(t.vertexNormalAttribute,3,gl.FLOAT,!1,24,12):a&&gl.vertexAttribPointer(t.vertexWidthAttribute,1,gl.FLOAT,!1,16,12),-1!=t.vertexMaterialAttribute&&(gl.bindBuffer(gl.ARRAY_BUFFER,materialBuffer),gl.bufferData(gl.ARRAY_BUFFER,new Int16Array(e.materialIndices),gl.STATIC_DRAW),gl.vertexAttribPointer(t.vertexMaterialAttribute,1,gl.SHORT,!1,2,0)),t!=colorShader&&t!=transparentShader||(gl.bindBuffer(gl.ARRAY_BUFFER,colorBuffer),gl.bufferData(gl.ARRAY_BUFFER,new Uint8Array(e.colors),gl.STATIC_DRAW),gl.vertexAttribPointer(t.vertexColorAttribute,4,gl.UNSIGNED_BYTE,!0,0,0)),gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER,indexBuffer),gl.bufferData(gl.ELEMENT_ARRAY_BUFFER,indexExt?new Uint32Array(i):new Uint16Array(i),gl.STATIC_DRAW),gl.drawElements(r?gl.TRIANGLES:a?gl.POINTS:gl.LINES,i.length,indexExt?gl.UNSIGNED_INT:gl.UNSIGNED_SHORT,0),embedded&&context.drawImage(offscreen,0,0)}class vertexBuffer{constructor(){this.clear()}clear(){this.vertices=[],this.materialIndices=[],this.colors=[],this.indices=[],this.nvertices=0,this.materials=[],this.materialTable=[]}vertex(e,t){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.vertices.push(t[0]),this.vertices.push(t[1]),this.vertices.push(t[2]),this.materialIndices.push(materialIndex),this.nvertices++}Vertex(e,t,i=[0,0,0,0]){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.vertices.push(t[0]),this.vertices.push(t[1]),this.vertices.push(t[2]),this.materialIndices.push(materialIndex),this.colors.push(i[0]),this.colors.push(i[1]),this.colors.push(i[2]),this.colors.push(i[3]),this.nvertices++}vertex1(e){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.materialIndices.push(materialIndex),this.nvertices++}vertex0(e,t){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.vertices.push(t),this.materialIndices.push(materialIndex),this.nvertices++}iVertex(e,t,i,a=[0,0,0,0]){let r=6*e;this.vertices[r]=t[0],this.vertices[r+1]=t[1],this.vertices[r+2]=t[2],this.vertices[r+3]=i[0],this.vertices[r+4]=i[1],this.vertices[r+5]=i[2],this.materialIndices[e]=materialIndex;let n=4*e;this.colors[n]=a[0],this.colors[n+1]=a[1],this.colors[n+2]=a[2],this.colors[n+3]=a[3],this.indices.push(e)}append(e){append(this.vertices,e.vertices),append(this.materialIndices,e.materialIndices),append(this.colors,e.colors),appendOffset(this.indices,e.indices,this.nvertices),this.nvertices+=e.nvertices}}let materialIndex,material0Data=new vertexBuffer,material1Data=new vertexBuffer,materialData=new vertexBuffer,colorData=new vertexBuffer,transparentData=new vertexBuffer,triangleData=new vertexBuffer;function append(e,t){let i=e.length,a=t.length;e.length+=a;for(let r=0;r<a;++r)e[i+r]=t[r]}function appendOffset(e,t,i){let a=e.length,r=t.length;e.length+=t.length;for(let n=0;n<r;++n)e[a+n]=t[n]+i}class Geometry{constructor(){this.data=new vertexBuffer,this.Onscreen=!1,this.m=[]}offscreen(e){let t=projViewMat,i=e[0],a=i[0],r=i[1],n=i[2],s=1/(t[3]*a+t[7]*r+t[11]*n+t[15]);this.x=this.X=(t[0]*a+t[4]*r+t[8]*n+t[12])*s,this.y=this.Y=(t[1]*a+t[5]*r+t[9]*n+t[13])*s;for(let i=1,a=e.length;i<a;++i){let a=e[i],r=a[0],n=a[1],s=a[2],o=1/(t[3]*r+t[7]*n+t[11]*s+t[15]),l=(t[0]*r+t[4]*n+t[8]*s+t[12])*o,h=(t[1]*r+t[5]*n+t[9]*s+t[13])*o;l<this.x?this.x=l:l>this.X&&(this.X=l),h<this.y?this.y=h:h>this.Y&&(this.Y=h)}return(this.X<-1.01||this.x>1.01||this.Y<-1.01||this.y>1.01)&&(this.Onscreen=!1,!0)}T(e){let t=this.c[0],i=this.c[1],a=this.c[2],r=e[0]-t,n=e[1]-i,s=e[2]-a;return[r*normMat[0]+n*normMat[3]+s*normMat[6]+t,r*normMat[1]+n*normMat[4]+s*normMat[7]+i,r*normMat[2]+n*normMat[5]+s*normMat[8]+a]}Tcorners(e,t){return[this.T(e),this.T([e[0],e[1],t[2]]),this.T([e[0],t[1],e[2]]),this.T([e[0],t[1],t[2]]),this.T([t[0],e[1],e[2]]),this.T([t[0],e[1],t[2]]),this.T([t[0],t[1],e[2]]),this.T(t)]}setMaterial(e,t){null==e.materialTable[this.MaterialIndex]&&(e.materials.length>=Nmaterials&&t(),e.materialTable[this.MaterialIndex]=e.materials.length,e.materials.push(Materials[this.MaterialIndex])),materialIndex=e.materialTable[this.MaterialIndex]}render(){let e;if(this.setMaterialIndex(),0==this.CenterIndex?e=corners(this.Min,this.Max):(this.c=Centers[this.CenterIndex-1],e=this.Tcorners(this.Min,this.Max)),this.offscreen(e))return void this.data.clear();let t,i=this.controlpoints;if(0==this.CenterIndex){if(!remesh&&this.Onscreen)return void this.append();t=i}else{let e=i.length;t=Array(e);for(let a=0;a<e;++a)t[a]=this.T(i[a])}let a=orthographic?1:this.Min[2]/B[2],r=pixel*Math.hypot(a*(viewParam.xmax-viewParam.xmin),a*(viewParam.ymax-viewParam.ymin))/size2;this.res2=r*r,this.Epsilon=FillFactor*r,this.data.clear(),this.Onscreen=!0,this.process(t)}}class BezierPatch extends Geometry{constructor(e,t,i,a,r,n){super(),this.controlpoints=e,this.Min=a,this.Max=r,this.color=n,this.CenterIndex=t;let s=e.length;if(n){let e=n[0][3]+n[1][3]+n[2][3];this.transparent=16==s||4==s?e+n[3][3]<1020:e<765}else this.transparent=Materials[i].diffuse[3]<1;this.MaterialIndex=i,this.vertex=this.transparent?this.data.Vertex.bind(this.data):this.data.vertex.bind(this.data),this.L2norm(this.controlpoints)}setMaterialIndex(){this.transparent?this.setMaterial(transparentData,drawTransparent):this.color?this.setMaterial(colorData,drawColor):this.setMaterial(materialData,drawMaterial)}L2norm(e){let t=e[0];this.epsilon=0;let i=e.length;for(let a=1;a<i;++a)this.epsilon=Math.max(this.epsilon,abs2([e[a][0]-t[0],e[a][1]-t[1],e[a][2]-t[2]]));this.epsilon*=Fuzz4}processTriangle(e){let t=e[0],i=e[1],a=e[2],r=unit(cross([i[0]-t[0],i[1]-t[1],i[2]-t[2]],[a[0]-t[0],a[1]-t[1],a[2]-t[2]]));this.offscreen([t,i,a])||(this.color?(this.data.indices.push(this.data.Vertex(t,r,this.color[0])),this.data.indices.push(this.data.Vertex(i,r,this.color[1])),this.data.indices.push(this.data.Vertex(a,r,this.color[2]))):(this.data.indices.push(this.vertex(t,r)),this.data.indices.push(this.vertex(i,r)),this.data.indices.push(this.vertex(a,r))),this.append())}processQuad(e){let t=e[0],i=e[1],a=e[2],r=e[3],n=cross([i[0]-t[0],i[1]-t[1],i[2]-t[2]],[a[0]-i[0],a[1]-i[1],a[2]-i[2]]),s=cross([a[0]-r[0],a[1]-r[1],a[2]-r[2]],[r[0]-t[0],r[1]-t[1],r[2]-t[2]]),o=unit([n[0]+s[0],n[1]+s[1],n[2]+s[2]]);if(!this.offscreen([t,i,a,r])){let e,n,s,l;this.color?(e=this.data.Vertex(t,o,this.color[0]),n=this.data.Vertex(i,o,this.color[1]),s=this.data.Vertex(a,o,this.color[2]),l=this.data.Vertex(r,o,this.color[3])):(e=this.vertex(t,o),n=this.vertex(i,o),s=this.vertex(a,o),l=this.vertex(r,o)),this.data.indices.push(e),this.data.indices.push(n),this.data.indices.push(s),this.data.indices.push(e),this.data.indices.push(s),this.data.indices.push(l),this.append()}}process(e){if(this.transparent&&(materialIndex=this.color?-1-materialIndex:1+materialIndex),10==e.length)return this.process3(e);if(3==e.length)return this.processTriangle(e);if(4==e.length)return this.processQuad(e);let t=e[0],i=e[3],a=e[12],r=e[15],n=this.normal(i,e[2],e[1],t,e[4],e[8],a);iszero(n)&&iszero(n=this.normal(i,e[2],e[1],t,e[13],e[14],r))&&(n=this.normal(r,e[11],e[7],i,e[4],e[8],a));let s=this.normal(t,e[4],e[8],a,e[13],e[14],r);iszero(s)&&iszero(s=this.normal(t,e[4],e[8],a,e[11],e[7],i))&&(s=this.normal(i,e[2],e[1],t,e[13],e[14],r));let o=this.normal(a,e[13],e[14],r,e[11],e[7],i);iszero(o)&&iszero(o=this.normal(a,e[13],e[14],r,e[2],e[1],t))&&(o=this.normal(t,e[4],e[8],a,e[11],e[7],i));let l=this.normal(r,e[11],e[7],i,e[2],e[1],t);if(iszero(l)&&iszero(l=this.normal(r,e[11],e[7],i,e[4],e[8],a))&&(l=this.normal(a,e[13],e[14],r,e[2],e[1],t)),this.color){let h=this.color[0],c=this.color[1],d=this.color[2],m=this.color[3],f=this.data.Vertex(t,n,h),u=this.data.Vertex(a,s,c),v=this.data.Vertex(r,o,d),g=this.data.Vertex(i,l,m);this.Render(e,f,u,v,g,t,a,r,i,!1,!1,!1,!1,h,c,d,m)}else{let h=this.vertex(t,n),c=this.vertex(a,s),d=this.vertex(r,o),m=this.vertex(i,l);this.Render(e,h,c,d,m,t,a,r,i,!1,!1,!1,!1)}this.data.indices.length>0&&this.append()}append(){this.transparent?transparentData.append(this.data):this.color?colorData.append(this.data):materialData.append(this.data)}Render(e,t,i,a,r,n,s,o,l,h,c,d,m,f,u,v,g){if(this.Distance(e)<this.res2)this.offscreen([n,s,o])||(this.data.indices.push(t),this.data.indices.push(i),this.data.indices.push(a)),this.offscreen([n,o,l])||(this.data.indices.push(t),this.data.indices.push(a),this.data.indices.push(r));else{if(this.offscreen(e))return;let p=e[0],x=e[3],M=e[12],w=e[15],A=new Split3(p,e[1],e[2],x),b=new Split3(e[4],e[5],e[6],e[7]),S=new Split3(e[8],e[9],e[10],e[11]),R=new Split3(M,e[13],e[14],w),P=new Split3(p,e[4],e[8],M),D=new Split3(A.m0,b.m0,S.m0,R.m0),T=new Split3(A.m3,b.m3,S.m3,R.m3),y=new Split3(A.m5,b.m5,S.m5,R.m5),I=new Split3(A.m4,b.m4,S.m4,R.m4),z=new Split3(A.m2,b.m2,S.m2,R.m2),O=new Split3(x,e[7],e[11],w),E=[p,A.m0,A.m3,A.m5,P.m0,D.m0,T.m0,y.m0,P.m3,D.m3,T.m3,y.m3,P.m5,D.m5,T.m5,y.m5],_=[P.m5,D.m5,T.m5,y.m5,P.m4,D.m4,T.m4,y.m4,P.m2,D.m2,T.m2,y.m2,M,R.m0,R.m3,R.m5],L=[y.m5,I.m5,z.m5,O.m5,y.m4,I.m4,z.m4,O.m4,y.m2,I.m2,z.m2,O.m2,R.m5,R.m4,R.m2,w],N=[A.m5,A.m4,A.m2,x,y.m0,I.m0,z.m0,O.m0,y.m3,I.m3,z.m3,O.m3,y.m5,I.m5,z.m5,O.m5],C=E[15],B=this.normal(E[0],E[4],E[8],E[12],E[13],E[14],E[15]);iszero(B)&&iszero(B=this.normal(E[0],E[4],E[8],E[12],E[11],E[7],E[3]))&&(B=this.normal(E[3],E[2],E[1],E[0],E[13],E[14],E[15]));let F=this.normal(_[12],_[13],_[14],_[15],_[11],_[7],_[3]);iszero(F)&&iszero(F=this.normal(_[12],_[13],_[14],_[15],_[2],_[1],_[0]))&&(F=this.normal(_[0],_[4],_[8],_[12],_[11],_[7],_[3]));let V=this.normal(L[15],L[11],L[7],L[3],L[2],L[1],L[0]);iszero(V)&&iszero(V=this.normal(L[15],L[11],L[7],L[3],L[4],L[8],L[12]))&&(V=this.normal(L[12],L[13],L[14],L[15],L[2],L[1],L[0]));let H=this.normal(N[3],N[2],N[1],N[0],N[4],N[8],N[12]);iszero(H)&&iszero(H=this.normal(N[3],N[2],N[1],N[0],N[13],N[14],N[15]))&&(H=this.normal(N[15],N[11],N[7],N[3],N[4],N[8],N[12]));let G=this.normal(L[3],L[2],L[1],C,L[4],L[8],L[12]),U=this.Epsilon,W=[.5*(n[0]+s[0]),.5*(n[1]+s[1]),.5*(n[2]+s[2])];if(!h)if(h=Straightness(p,e[4],e[8],M)<this.res2){let e=unit(this.derivative(_[0],_[1],_[2],_[3]));W=[W[0]-U*e[0],W[1]-U*e[1],W[2]-U*e[2]]}else W=E[12];let Y=[.5*(s[0]+o[0]),.5*(s[1]+o[1]),.5*(s[2]+o[2])];if(!c)if(c=Straightness(M,e[13],e[14],w)<this.res2){let e=unit(this.derivative(L[12],L[8],L[4],L[0]));Y=[Y[0]-U*e[0],Y[1]-U*e[1],Y[2]-U*e[2]]}else Y=_[15];let j=[.5*(o[0]+l[0]),.5*(o[1]+l[1]),.5*(o[2]+l[2])];if(!d)if(d=Straightness(w,e[11],e[7],x)<this.res2){let e=unit(this.derivative(N[15],L[14],L[13],_[12]));j=[j[0]-U*e[0],j[1]-U*e[1],j[2]-U*e[2]]}else j=L[3];let k=[.5*(l[0]+n[0]),.5*(l[1]+n[1]),.5*(l[2]+n[2])];if(!m)if(m=Straightness(p,e[1],e[2],x)<this.res2){let e=unit(this.derivative(E[3],E[7],E[11],E[15]));k=[k[0]-U*e[0],k[1]-U*e[1],k[2]-U*e[2]]}else k=N[0];if(f){let e=Array(4),p=Array(4),x=Array(4),M=Array(4),w=Array(4);for(let t=0;t<4;++t)e[t]=.5*(f[t]+u[t]),p[t]=.5*(u[t]+v[t]),x[t]=.5*(v[t]+g[t]),M[t]=.5*(g[t]+f[t]),w[t]=.5*(e[t]+x[t]);let A=this.data.Vertex(W,B,e),b=this.data.Vertex(Y,F,p),S=this.data.Vertex(j,V,x),R=this.data.Vertex(k,H,M),P=this.data.Vertex(C,G,w);this.Render(E,t,A,P,R,n,W,C,k,h,!1,!1,m,f,e,w,M),this.Render(_,A,i,b,P,W,s,Y,C,h,c,!1,!1,e,u,p,w),this.Render(L,P,b,a,S,C,Y,o,j,!1,c,d,!1,w,p,v,x),this.Render(N,R,P,S,r,k,C,j,l,!1,!1,d,m,M,w,x,g)}else{let e=this.vertex(W,B),f=this.vertex(Y,F),u=this.vertex(j,V),v=this.vertex(k,H),g=this.vertex(C,G);this.Render(E,t,e,g,v,n,W,C,k,h,!1,!1,m),this.Render(_,e,i,f,g,W,s,Y,C,h,c,!1,!1),this.Render(L,g,f,a,u,C,Y,o,j,!1,c,d,!1),this.Render(N,v,g,u,r,k,C,j,l,!1,!1,d,m)}}}process3(e){this.Res2=BezierFactor*BezierFactor*this.res2;let t=e[0],i=e[6],a=e[9],r=this.normal(a,e[5],e[2],t,e[1],e[3],i),n=this.normal(t,e[1],e[3],i,e[7],e[8],a),s=this.normal(i,e[7],e[8],a,e[5],e[2],t);if(this.color){let o=this.color[0],l=this.color[1],h=this.color[2],c=this.data.Vertex(t,r,o),d=this.data.Vertex(i,n,l),m=this.data.Vertex(a,s,h);this.Render3(e,c,d,m,t,i,a,!1,!1,!1,o,l,h)}else{let o=this.vertex(t,r),l=this.vertex(i,n),h=this.vertex(a,s);this.Render3(e,o,l,h,t,i,a,!1,!1,!1)}this.data.indices.length>0&&this.append()}Render3(e,t,i,a,r,n,s,o,l,h,c,d,m){if(this.Distance3(e)<this.Res2)this.offscreen([r,n,s])||(this.data.indices.push(t),this.data.indices.push(i),this.data.indices.push(a));else{if(this.offscreen(e))return;let f=e[0],u=e[1],v=e[2],g=e[3],p=e[4],x=e[5],M=e[6],w=e[7],A=e[8],b=e[9],S=[.5*(b[0]+x[0]),.5*(b[1]+x[1]),.5*(b[2]+x[2])],R=[.5*(b[0]+A[0]),.5*(b[1]+A[1]),.5*(b[2]+A[2])],P=[.5*(x[0]+v[0]),.5*(x[1]+v[1]),.5*(x[2]+v[2])],D=[.5*(A[0]+p[0]),.5*(A[1]+p[1]),.5*(A[2]+p[2])],T=[.5*(A[0]+w[0]),.5*(A[1]+w[1]),.5*(A[2]+w[2])],y=[.5*(v[0]+p[0]),.5*(v[1]+p[1]),.5*(v[2]+p[2])],I=[.5*(v[0]+f[0]),.5*(v[1]+f[1]),.5*(v[2]+f[2])],z=[.5*(p[0]+g[0]),.5*(p[1]+g[1]),.5*(p[2]+g[2])],O=[.5*(w[0]+M[0]),.5*(w[1]+M[1]),.5*(w[2]+M[2])],E=[.5*(f[0]+u[0]),.5*(f[1]+u[1]),.5*(f[2]+u[2])],_=[.5*(u[0]+g[0]),.5*(u[1]+g[1]),.5*(u[2]+g[2])],L=[.5*(g[0]+M[0]),.5*(g[1]+M[1]),.5*(g[2]+M[2])],N=[.5*(S[0]+P[0]),.5*(S[1]+P[1]),.5*(S[2]+P[2])],C=[.5*(R[0]+T[0]),.5*(R[1]+T[1]),.5*(R[2]+T[2])],B=[.5*(P[0]+I[0]),.5*(P[1]+I[1]),.5*(P[2]+I[2])],F=[.5*D[0]+.25*(p[0]+u[0]),.5*D[1]+.25*(p[1]+u[1]),.5*D[2]+.25*(p[2]+u[2])],V=[.5*(T[0]+O[0]),.5*(T[1]+O[1]),.5*(T[2]+O[2])],H=[.5*y[0]+.25*(p[0]+w[0]),.5*y[1]+.25*(p[1]+w[1]),.5*y[2]+.25*(p[2]+w[2])],G=[.25*(x[0]+p[0])+.5*z[0],.25*(x[1]+p[1])+.5*z[1],.25*(x[2]+p[2])+.5*z[2]],U=[.5*(E[0]+_[0]),.5*(E[1]+_[1]),.5*(E[2]+_[2])],W=[.5*(_[0]+L[0]),.5*(_[1]+L[1]),.5*(_[2]+L[2])],Y=[.5*(H[0]+U[0]),.5*(H[1]+U[1]),.5*(H[2]+U[2])],j=[.5*(H[0]+W[0]),.5*(H[1]+W[1]),.5*(H[2]+W[2])],k=[.5*(U[0]+W[0]),.5*(U[1]+W[1]),.5*(U[2]+W[2])],X=[.5*(G[0]+V[0]),.5*(G[1]+V[1]),.5*(G[2]+V[2])],Z=[.5*(C[0]+G[0]),.5*(C[1]+G[1]),.5*(C[2]+G[2])],q=[.5*(C[0]+V[0]),.5*(C[1]+V[1]),.5*(C[2]+V[2])],K=[.5*(N[0]+F[0]),.5*(N[1]+F[1]),.5*(N[2]+F[2])],$=[.5*(B[0]+F[0]),.5*(B[1]+F[1]),.5*(B[2]+F[2])],Q=[.5*(N[0]+B[0]),.5*(N[1]+B[1]),.5*(N[2]+B[2])],J=[f,E,I,U,[.5*(y[0]+E[0]),.5*(y[1]+E[1]),.5*(y[2]+E[2])],B,k,Y,$,Q],ee=[k,W,j,L,[.5*(z[0]+O[0]),.5*(z[1]+O[1]),.5*(z[2]+O[2])],X,M,O,V,q],te=[Q,K,N,Z,[.5*(S[0]+D[0]),.5*(S[1]+D[1]),.5*(S[2]+D[2])],S,q,C,R,b],ie=[q,Z,X,K,[.25*(P[0]+T[0]+_[0]+p[0]),.25*(P[1]+T[1]+_[1]+p[1]),.25*(P[2]+T[2]+_[2]+p[2])],j,Q,$,Y,k],ae=this.normal(k,j,X,q,Z,K,Q),re=this.normal(q,Z,K,Q,$,Y,k),ne=this.normal(Q,$,Y,k,j,X,q),se=this.Epsilon,oe=[.5*(n[0]+s[0]),.5*(n[1]+s[1]),.5*(n[2]+s[2])];if(!o)if(o=Straightness(M,w,A,b)<this.res2){let e=unit(this.sumderivative(ie[0],ie[2],ie[5],ie[9],ie[1],ie[3],ie[6]));oe=[oe[0]-se*e[0],oe[1]-se*e[1],oe[2]-se*e[2]]}else oe=q;let le=[.5*(s[0]+r[0]),.5*(s[1]+r[1]),.5*(s[2]+r[2])];if(!l)if(l=Straightness(f,v,x,b)<this.res2){let e=unit(this.sumderivative(ie[6],ie[3],ie[1],ie[0],ie[7],ie[8],ie[9]));le=[le[0]-se*e[0],le[1]-se*e[1],le[2]-se*e[2]]}else le=Q;let he=[.5*(r[0]+n[0]),.5*(r[1]+n[1]),.5*(r[2]+n[2])];if(!h)if(h=Straightness(f,u,g,M)<this.res2){let e=unit(this.sumderivative(ie[9],ie[8],ie[7],ie[6],ie[5],ie[2],ie[0]));he=[he[0]-se*e[0],he[1]-se*e[1],he[2]-se*e[2]]}else he=k;if(c){let e=Array(4),f=Array(4),u=Array(4);for(let t=0;t<4;++t)e[t]=.5*(d[t]+m[t]),f[t]=.5*(m[t]+c[t]),u[t]=.5*(c[t]+d[t]);let v=this.data.Vertex(oe,ae,e),g=this.data.Vertex(le,re,f),p=this.data.Vertex(he,ne,u);this.Render3(J,t,p,g,r,he,le,!1,l,h,c,u,f),this.Render3(ee,p,i,v,he,n,oe,o,!1,h,u,d,e),this.Render3(te,g,v,a,le,oe,s,o,l,!1,f,e,m),this.Render3(ie,v,g,p,oe,le,he,!1,!1,!1,e,f,u)}else{let e=this.vertex(oe,ae),c=this.vertex(le,re),d=this.vertex(he,ne);this.Render3(J,t,d,c,r,he,le,!1,l,h),this.Render3(ee,d,i,e,he,n,oe,o,!1,h),this.Render3(te,c,e,a,le,oe,s,o,l,!1),this.Render3(ie,e,c,d,oe,le,he,!1,!1,!1)}}}Distance(e){let t=e[0],i=e[3],a=e[12],r=e[15],n=Distance2(r,t,this.normal(i,e[2],e[1],t,e[4],e[8],a));return n=Math.max(n,Straightness(t,e[1],e[2],i)),n=Math.max(n,Straightness(t,e[4],e[8],a)),n=Math.max(n,Straightness(i,e[7],e[11],r)),n=Math.max(n,Straightness(a,e[13],e[14],r)),n=Math.max(n,Straightness(e[4],e[5],e[6],e[7])),n=Math.max(n,Straightness(e[8],e[9],e[10],e[11])),n=Math.max(n,Straightness(e[1],e[5],e[9],e[13])),Math.max(n,Straightness(e[2],e[6],e[10],e[14]))}Distance3(e){let t=e[0],i=e[4],a=e[6],r=e[9],n=abs2([(t[0]+a[0]+r[0])*third-i[0],(t[1]+a[1]+r[1])*third-i[1],(t[2]+a[2]+r[2])*third-i[2]]);return n=Math.max(n,Straightness(t,e[1],e[3],a)),n=Math.max(n,Straightness(t,e[2],e[5],r)),Math.max(n,Straightness(a,e[7],e[8],r))}derivative(e,t,i,a){let r=[t[0]-e[0],t[1]-e[1],t[2]-e[2]];if(abs2(r)>this.epsilon)return r;let n=bezierPP(e,t,i);return abs2(n)>this.epsilon?n:bezierPPP(e,t,i,a)}sumderivative(e,t,i,a,r,n,s){let o=this.derivative(e,t,i,a),l=this.derivative(e,r,n,s);return[o[0]+l[0],o[1]+l[1],o[2]+l[2]]}normal(e,t,i,a,r,n,s){let o=r[0]-a[0],l=r[1]-a[1],h=r[2]-a[2],c=i[0]-a[0],d=i[1]-a[1],m=i[2]-a[2],f=[l*m-h*d,h*c-o*m,o*d-l*c];if(abs2(f)>this.epsilon)return unit(f);let u=[c,d,m],v=[o,l,h],g=bezierPP(a,i,t),p=bezierPP(a,r,n),x=cross(p,u),M=cross(v,g);if(abs2(f=[x[0]+M[0],x[1]+M[1],x[2]+M[2]])>this.epsilon)return unit(f);let w=bezierPPP(a,i,t,e),A=bezierPPP(a,r,n,s);x=cross(p,g),M=cross(v,w);let b=cross(A,u),S=cross(A,g),R=cross(p,w),P=cross(A,w);return unit([9*x[0]+3*(M[0]+b[0]+S[0]+R[0])+P[0],9*x[1]+3*(M[1]+b[1]+S[1]+R[1])+P[1],9*x[2]+3*(M[2]+b[2]+S[2]+R[2])+P[2]])}}class BezierCurve extends Geometry{constructor(e,t,i,a,r){super(),this.controlpoints=e,this.Min=a,this.Max=r,this.CenterIndex=t,this.MaterialIndex=i}setMaterialIndex(){this.setMaterial(material1Data,drawMaterial1)}processLine(e){let t=e[0],i=e[1];this.offscreen([t,i])||(this.data.indices.push(this.data.vertex1(t)),this.data.indices.push(this.data.vertex1(i)),this.append())}process(e){if(2==e.length)return this.processLine(e);let t=this.data.vertex1(e[0]),i=this.data.vertex1(e[3]);this.Render(e,t,i),this.data.indices.length>0&&this.append()}append(){material1Data.append(this.data)}Render(e,t,i){let a=e[0],r=e[1],n=e[2],s=e[3];if(Straightness(a,r,n,s)<this.res2)this.offscreen([a,s])||(this.data.indices.push(t),this.data.indices.push(i));else{if(this.offscreen(e))return;let o=[.5*(a[0]+r[0]),.5*(a[1]+r[1]),.5*(a[2]+r[2])],l=[.5*(r[0]+n[0]),.5*(r[1]+n[1]),.5*(r[2]+n[2])],h=[.5*(n[0]+s[0]),.5*(n[1]+s[1]),.5*(n[2]+s[2])],c=[.5*(o[0]+l[0]),.5*(o[1]+l[1]),.5*(o[2]+l[2])],d=[.5*(l[0]+h[0]),.5*(l[1]+h[1]),.5*(l[2]+h[2])],m=[.5*(c[0]+d[0]),.5*(c[1]+d[1]),.5*(c[2]+d[2])],f=[a,o,c,m],u=[m,d,h,s],v=this.data.vertex1(m);this.Render(f,t,v),this.Render(u,v,i)}}}class Pixel extends Geometry{constructor(e,t,i,a,r){super(),this.controlpoint=e,this.width=t,this.CenterIndex=0,this.MaterialIndex=i,this.Min=a,this.Max=r}setMaterialIndex(){this.setMaterial(material0Data,drawMaterial0)}process(e){this.data.indices.push(this.data.vertex0(this.controlpoint,this.width)),this.append()}append(){material0Data.append(this.data)}}class Triangles extends Geometry{constructor(e,t,i){super(),this.CenterIndex=0,this.MaterialIndex=e,this.Min=t,this.Max=i,this.Positions=Positions,this.Normals=Normals,this.Colors=Colors,this.Indices=Indices,Positions=[],Normals=[],Colors=[],Indices=[],this.transparent=Materials[e].diffuse[3]<1}setMaterialIndex(){this.transparent?this.setMaterial(transparentData,drawTransparent):this.setMaterial(triangleData,drawTriangle)}process(e){materialIndex=this.Colors.length>0?-1-materialIndex:1+materialIndex;for(let e=0,t=this.Indices.length;e<t;++e){let t=this.Indices[e],i=t[0],a=this.Positions[i[0]],r=this.Positions[i[1]],n=this.Positions[i[2]];if(!this.offscreen([a,r,n])){let e=t.length>1?t[1]:i;if(e&&0!=e.length||(e=i),this.Colors.length>0){let s=t.length>2?t[2]:i;s&&0!=s.length||(s=i);let o=this.Colors[s[0]],l=this.Colors[s[1]],h=this.Colors[s[2]];this.transparent|=o[3]+l[3]+h[3]<765,this.data.iVertex(i[0],a,this.Normals[e[0]],o),this.data.iVertex(i[1],r,this.Normals[e[1]],l),this.data.iVertex(i[2],n,this.Normals[e[2]],h)}else this.data.iVertex(i[0],a,this.Normals[e[0]]),this.data.iVertex(i[1],r,this.Normals[e[1]]),this.data.iVertex(i[2],n,this.Normals[e[2]])}}this.data.nvertices=this.Positions.length,this.data.indices.length>0&&this.append()}append(){this.transparent?transparentData.append(this.data):triangleData.append(this.data)}}function home(){mat4.identity(rotMat),initProjection(),setProjection(),remesh=!0,redraw=!0}function initShader(e=[]){let t=getShader(gl,vertex,gl.VERTEX_SHADER,e),i=getShader(gl,fragment,gl.FRAGMENT_SHADER,e),a=gl.createProgram();return gl.attachShader(a,t),gl.attachShader(a,i),gl.linkProgram(a),gl.getProgramParameter(a,gl.LINK_STATUS)||alert("Could not initialize shaders"),a}class Split3{constructor(e,t,i,a){this.m0=[.5*(e[0]+t[0]),.5*(e[1]+t[1]),.5*(e[2]+t[2])];let r=.5*(t[0]+i[0]),n=.5*(t[1]+i[1]),s=.5*(t[2]+i[2]);this.m2=[.5*(i[0]+a[0]),.5*(i[1]+a[1]),.5*(i[2]+a[2])],this.m3=[.5*(this.m0[0]+r),.5*(this.m0[1]+n),.5*(this.m0[2]+s)],this.m4=[.5*(r+this.m2[0]),.5*(n+this.m2[1]),.5*(s+this.m2[2])],this.m5=[.5*(this.m3[0]+this.m4[0]),.5*(this.m3[1]+this.m4[1]),.5*(this.m3[2]+this.m4[2])]}}function iszero(e){return 0==e[0]&&0==e[1]&&0==e[2]}function unit(e){let t=1/(Math.sqrt(e[0]*e[0]+e[1]*e[1]+e[2]*e[2])||1);return[e[0]*t,e[1]*t,e[2]*t]}function abs2(e){return e[0]*e[0]+e[1]*e[1]+e[2]*e[2]}function dot(e,t){return e[0]*t[0]+e[1]*t[1]+e[2]*t[2]}function cross(e,t){return[e[1]*t[2]-e[2]*t[1],e[2]*t[0]-e[0]*t[2],e[0]*t[1]-e[1]*t[0]]}function bezierPP(e,t,i){return[e[0]+i[0]-2*t[0],e[1]+i[1]-2*t[1],e[2]+i[2]-2*t[2]]}function bezierPPP(e,t,i,a){return[a[0]-e[0]+3*(t[0]-i[0]),a[1]-e[1]+3*(t[1]-i[1]),a[2]-e[2]+3*(t[2]-i[2])]}function Straightness(e,t,i,a){let r=[third*(a[0]-e[0]),third*(a[1]-e[1]),third*(a[2]-e[2])];return Math.max(abs2([t[0]-r[0]-e[0],t[1]-r[1]-e[1],t[2]-r[2]-e[2]]),abs2([a[0]-r[0]-i[0],a[1]-r[1]-i[1],a[2]-r[2]-i[2]]))}function Distance2(e,t,i){let a=dot([e[0]-t[0],e[1]-t[1],e[2]-t[2]],i);return a*a}function corners(e,t){return[e,[e[0],e[1],t[2]],[e[0],t[1],e[2]],[e[0],t[1],t[2]],[t[0],e[1],e[2]],[t[0],e[1],t[2]],[t[0],t[1],e[2]],t]}function COBTarget(e,t){mat4.fromTranslation(translMat,[center.x,center.y,center.z]),mat4.invert(cjMatInv,translMat),mat4.multiply(e,t,cjMatInv),mat4.multiply(e,translMat,e)}function setUniforms(e,t){let i=t==pixelShader;gl.useProgram(t),t.vertexPositionAttribute=gl.getAttribLocation(t,"position"),gl.enableVertexAttribArray(t.vertexPositionAttribute),i&&(t.vertexWidthAttribute=gl.getAttribLocation(t,"width"),gl.enableVertexAttribArray(t.vertexWidthAttribute));let a=t!=noNormalShader&&!i&&Lights.length>0;if(a&&(t.vertexNormalAttribute=gl.getAttribLocation(t,"normal"),gl.enableVertexAttribArray(t.vertexNormalAttribute)),t.vertexMaterialAttribute=gl.getAttribLocation(t,"materialIndex"),-1!=t.vertexMaterialAttribute&&gl.enableVertexAttribArray(t.vertexMaterialAttribute),t.projViewMatUniform=gl.getUniformLocation(t,"projViewMat"),t.viewMatUniform=gl.getUniformLocation(t,"viewMat"),t.normMatUniform=gl.getUniformLocation(t,"normMat"),t!=colorShader&&t!=transparentShader||(t.vertexColorAttribute=gl.getAttribLocation(t,"color"),gl.enableVertexAttribArray(t.vertexColorAttribute)),a)for(let e=0;e<Lights.length;++e)Lights[e].setUniform(t,e);if(-1!=t.vertexMaterialAttribute)for(let i=0;i<e.materials.length;++i)e.materials[i].setUniform(t,i);gl.uniformMatrix4fv(t.projViewMatUniform,!1,projViewMat),gl.uniformMatrix4fv(t.viewMatUniform,!1,viewMat),gl.uniformMatrix3fv(t.normMatUniform,!1,normMat)}function handleMouseDown(e){mouseDownOrTouchActive=!0,lastMouseX=e.clientX,lastMouseY=e.clientY}let pinchStart,touchStartTime,pinch=!1;function pinchDistance(e){return Math.hypot(e[0].pageX-e[1].pageX,e[0].pageY-e[1].pageY)}function handleTouchStart(e){e.preventDefault();let t=e.targetTouches;swipe=rotate=pinch=!1,zooming||(1!=t.length||mouseDownOrTouchActive||(touchStartTime=(new Date).getTime(),touchId=t[0].identifier,lastMouseX=t[0].pageX,lastMouseY=t[0].pageY),2!=t.length||mouseDownOrTouchActive||(touchId=t[0].identifier,pinchStart=pinchDistance(t),pinch=!0))}function handleMouseUpOrTouchEnd(e){mouseDownOrTouchActive=!1}function rotateScene(e,t,i,a,r){if(e==i&&t==a)return;let[n,s]=arcball([e,-t],[i,-a]);mat4.fromRotation(rotMats,2*r*ArcballFactor*n/lastzoom,s),mat4.multiply(rotMat,rotMats,rotMat)}function shiftScene(e,t,i,a){let r=1/lastzoom;shift.x+=(i-e)*r*halfCanvasWidth,shift.y-=(a-t)*r*halfCanvasHeight}function panScene(e,t,i,a){orthographic?shiftScene(e,t,i,a):(center.x+=(i-e)*(viewParam.xmax-viewParam.xmin),center.y-=(a-t)*(viewParam.ymax-viewParam.ymin))}function updateViewMatrix(){COBTarget(viewMat,rotMat),mat4.translate(viewMat,viewMat,[center.x,center.y,0]),mat3.fromMat4(viewMat3,viewMat),mat3.invert(normMat,viewMat3),mat4.multiply(projViewMat,projMat,viewMat)}function capzoom(){let e=Math.sqrt(Number.MAX_VALUE),t=1/e;Zoom<=t&&(Zoom=t),Zoom>=e&&(Zoom=e),Zoom!=lastzoom&&(remesh=!0),lastzoom=Zoom}function zoomImage(e){let t=zoomStep*halfCanvasHeight*e;const i=Math.log(.1*Number.MAX_VALUE)/Math.log(zoomFactor);Math.abs(t)<i&&(Zoom*=zoomFactor**t,capzoom())}function normMouse(e){let t=e[0],i=e[1],a=Math.hypot(t,i);return a>1&&(denom=1/a,t*=denom,i*=denom),[t,i,Math.sqrt(Math.max(1-i*i-t*t,0))]}function arcball(e,t){let i=normMouse(e),a=normMouse(t),r=dot(i,a);return r>1?r=1:r<-1&&(r=-1),[Math.acos(r),unit(cross(i,a))]}function zoomScene(e,t,i,a){zoomImage(t-a)}const 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t;processDrag(e.clientX,e.clientY,t=e.getModifierState("Control")?DRAGMODE_SHIFT:e.getModifierState("Shift")?DRAGMODE_ZOOM:e.getModifierState("Alt")?DRAGMODE_PAN:DRAGMODE_ROTATE)}let zooming=!1,swipe=!1,rotate=!1;function handleTouchMove(e){if(e.preventDefault(),zooming)return;let t=e.targetTouches;if(!pinch&&1==t.length&&touchId==t[0].identifier){let e=t[0].pageX,i=t[0].pageY,a=e-lastMouseX,r=i-lastMouseY,n=a*a+r*r<=shiftHoldDistance*shiftHoldDistance;if(n&&!swipe&&!rotate&&(new Date).getTime()-touchStartTime>shiftWaitTime&&(navigator.vibrate&&window.navigator.vibrate(vibrateTime),swipe=!0),swipe)processDrag(e,i,DRAGMODE_SHIFT);else if(!n){rotate=!0,processDrag(t[0].pageX,t[0].pageY,DRAGMODE_ROTATE,.5)}}if(pinch&&!swipe&&2==t.length&&touchId==t[0].identifier){let e=pinchDistance(t),i=e-pinchStart;zooming=!0,(i*=zoomPinchFactor)>zoomPinchCap&&(i=zoomPinchCap),i<-zoomPinchCap&&(i=-zoomPinchCap),zoomImage(i/size2),pinchStart=e,swipe=rotate=zooming=!1,setProjection(),redraw=!0}}let pixelShader,noNormalShader,materialShader,colorShader,transparentShader,zbuffer=[];function transformVertices(e){let t=viewMat[2],i=viewMat[6],a=viewMat[10];zbuffer.length=e.length;for(let r=0;r<e.length;++r){let n=6*r;zbuffer[r]=t*e[n]+i*e[n+1]+a*e[n+2]}}function drawMaterial0(){drawBuffer(material0Data,pixelShader),material0Data.clear()}function drawMaterial1(){drawBuffer(material1Data,noNormalShader),material1Data.clear()}function drawMaterial(){drawBuffer(materialData,materialShader),materialData.clear()}function drawColor(){drawBuffer(colorData,colorShader),colorData.clear()}function drawTriangle(){drawBuffer(triangleData,transparentShader),triangleData.clear()}function drawTransparent(){let e=transparentData.indices;if(e.length>0){transformVertices(transparentData.vertices);let t=e.length/3,i=Array(t).fill().map((e,t)=>t);i.sort(function(t,i){let a=3*t;Ia=e[a],Ib=e[a+1],Ic=e[a+2];let r=3*i;return 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e=.5*t*r*n,i=2*e*s,a=t*n*o;viewParam.xmin=-e-i,viewParam.xmax=e-i,viewParam.ymin=b[1]*n-a,viewParam.ymax=B[1]*n-a}else{let t=.5*e/(r*Zoom),i=e*n*s,a=2*t*o;viewParam.xmin=b[0]*n-i,viewParam.xmax=B[0]*n-i,viewParam.ymin=-t-a,viewParam.ymax=t-a}}else{let e=H*n,t=e*r,i=2*t*s,a=2*e*o;viewParam.xmin=-t-i,viewParam.xmax=t-i,viewParam.ymin=-e-a,viewParam.ymax=e-a}}function setProjection(){setDimensions(canvasWidth,canvasHeight,shift.x,shift.y),(orthographic?mat4.ortho:mat4.frustum)(projMat,viewParam.xmin,viewParam.xmax,viewParam.ymin,viewParam.ymax,-viewParam.zmax,-viewParam.zmin),updateViewMatrix()}function initProjection(){H=-Math.tan(.5*angle)*B[2],center.x=center.y=0,center.z=.5*(b[2]+B[2]),lastzoom=Zoom=Zoom0,viewParam.zmin=b[2],viewParam.zmax=B[2],shift.x=shift.y=0}function setViewport(){gl.viewportWidth=canvasWidth,gl.viewportHeight=canvasHeight,gl.viewport(0,0,gl.viewportWidth,gl.viewportHeight),gl.scissor(0,0,gl.viewportWidth,gl.viewportHeight)}function setCanvas(){canvas.width=canvasWidth,canvas.height=canvasHeight,embedded&&(offscreen.width=canvasWidth,offscreen.height=canvasHeight),size2=Math.hypot(canvasWidth,canvasHeight),halfCanvasWidth=.5*canvasWidth,halfCanvasHeight=.5*canvasHeight}function setsize(e,t){e>maxViewportWidth&&(e=maxViewportWidth),t>maxViewportHeight&&(t=maxViewportHeight),shift.x*=e/canvasWidth,shift.y*=t/canvasHeight,canvasWidth=e,canvasHeight=t,setCanvas(),setViewport(),home()}function expand(){setsize(canvasWidth*resizeStep+.5,canvasHeight*resizeStep+.5)}function shrink(){setsize(Math.max(canvasWidth/resizeStep+.5,1),Math.max(canvasHeight/resizeStep+.5,1))}function webGLStart(){if(canvas=document.getElementById("Asymptote"),embedded=window.parent.document!=document,initGL(),absolute&&!embedded)canvasWidth*=window.devicePixelRatio,canvasHeight*=window.devicePixelRatio;else{0==canvas.width&&(canvas.width=Math.max(window.innerWidth-windowTrim,windowTrim)),0==canvas.height&&(canvas.height=Math.max(window.innerHeight-windowTrim,windowTrim));let e=canvasWidth/canvasHeight;canvas.width>canvas.height*e?canvas.width=Math.min(canvas.height*e,canvas.width):canvas.height=Math.min(canvas.width/e,canvas.height),canvas.width>0&&(canvasWidth=canvas.width),canvas.height>0&&(canvasHeight=canvas.height)}setCanvas(),ArcballFactor=1+8*Math.hypot(viewportmargin[0],viewportmargin[1])/size2,viewportshift[0]/=Zoom0,viewportshift[1]/=Zoom0,gl.enable(gl.BLEND),gl.blendFunc(gl.SRC_ALPHA,gl.ONE_MINUS_SRC_ALPHA),gl.enable(gl.DEPTH_TEST),gl.enable(gl.SCISSOR_TEST),setViewport(),home(),canvas.onmousedown=handleMouseDown,document.onmouseup=handleMouseUpOrTouchEnd,document.onmousemove=handleMouseMove,canvas.onkeydown=handleKey,canvas.addEventListener("wheel",handleMouseWheel,!1),canvas.addEventListener("touchstart",handleTouchStart,!1),canvas.addEventListener("touchend",handleMouseUpOrTouchEnd,!1),canvas.addEventListener("touchcancel",handleMouseUpOrTouchEnd,!1),canvas.addEventListener("touchleave",handleMouseUpOrTouchEnd,!1),canvas.addEventListener("touchmove",handleTouchMove,!1),document.addEventListener("keydown",handleKey,!1),tick()}
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e[0]=1,e[1]=0,e[2]=0,e[3]=0,e[4]=0,e[5]=1,e[6]=0,e[7]=0,e[8]=0,e[9]=0,e[10]=1,e[11]=0,e[12]=t[0],e[13]=t[1],e[14]=t[2],e[15]=1,e},t.fromRotation=function(e,t,i){var r=i[0],n=i[1],s=i[2],o=Math.sqrt(r*r+n*n+s*s),l=void 0,h=void 0,c=void 0;if(Math.abs(o)<a.EPSILON)return null;return r*=o=1/o,n*=o,s*=o,l=Math.sin(t),h=Math.cos(t),c=1-h,e[0]=r*r*c+h,e[1]=n*r*c+s*l,e[2]=s*r*c-n*l,e[3]=0,e[4]=r*n*c-s*l,e[5]=n*n*c+h,e[6]=s*n*c+r*l,e[7]=0,e[8]=r*s*c+n*l,e[9]=n*s*c-r*l,e[10]=s*s*c+h,e[11]=0,e[12]=0,e[13]=0,e[14]=0,e[15]=1,e},t.frustum=function(e,t,i,a,r,n,s){var o=1/(i-t),l=1/(r-a),h=1/(n-s);return e[0]=2*n*o,e[1]=0,e[2]=0,e[3]=0,e[4]=0,e[5]=2*n*l,e[6]=0,e[7]=0,e[8]=(i+t)*o,e[9]=(r+a)*l,e[10]=(s+n)*h,e[11]=-1,e[12]=0,e[13]=0,e[14]=s*n*2*h,e[15]=0,e},t.ortho=function(e,t,i,a,r,n,s){var o=1/(t-i),l=1/(a-r),h=1/(n-s);return e[0]=-2*o,e[1]=0,e[2]=0,e[3]=0,e[4]=0,e[5]=-2*l,e[6]=0,e[7]=0,e[8]=0,e[9]=0,e[10]=2*h,e[11]=0,e[12]=(t+i)*o,e[13]=(r+a)*l,e[14]=(s+n)*h,e[15]=1,e};var a=function(e){if(e&&e.__esModule)return e;var t={};if(null!=e)for(var i in e)Object.prototype.hasOwnProperty.call(e,i)&&(t[i]=e[i]);return t.default=e,t}(i(0));function r(e,t,i){var a=t[0],r=t[1],n=t[2],s=t[3],o=t[4],l=t[5],h=t[6],c=t[7],d=t[8],m=t[9],f=t[10],u=t[11],v=t[12],g=t[13],p=t[14],x=t[15],M=i[0],w=i[1],A=i[2],b=i[3];return e[0]=M*a+w*o+A*d+b*v,e[1]=M*r+w*l+A*m+b*g,e[2]=M*n+w*h+A*f+b*p,e[3]=M*s+w*c+A*u+b*x,M=i[4],w=i[5],A=i[6],b=i[7],e[4]=M*a+w*o+A*d+b*v,e[5]=M*r+w*l+A*m+b*g,e[6]=M*n+w*h+A*f+b*p,e[7]=M*s+w*c+A*u+b*x,M=i[8],w=i[9],A=i[10],b=i[11],e[8]=M*a+w*o+A*d+b*v,e[9]=M*r+w*l+A*m+b*g,e[10]=M*n+w*h+A*f+b*p,e[11]=M*s+w*c+A*u+b*x,M=i[12],w=i[13],A=i[14],b=i[15],e[12]=M*a+w*o+A*d+b*v,e[13]=M*r+w*l+A*m+b*g,e[14]=M*n+w*h+A*f+b*p,e[15]=M*s+w*c+A*u+b*x,e}}])});let canvasWidth,canvasHeight,b,B,angle,Zoom0,viewportmargin,zoomFactor,zoomPinchFactor,zoomPinchCap,zoomStep,shiftHoldDistance,shiftWaitTime,vibrateTime,embedded,canvas,gl,alpha,offscreen,context,maxMaterials,halfCanvasWidth,halfCanvasHeight,Zoom,P=[],Materials=[],Lights=[],Centers=[],Background=[1,1,1,1],absolute=!1,viewportshift=[0,0],nlights=0,Nmaterials=1,materials=[],pixel=.75,BezierFactor=.4,FillFactor=.1,maxViewportWidth=window.innerWidth,maxViewportHeight=window.innerHeight;const windowTrim=10;let lastzoom,H,zmin,zmax,size2,ArcballFactor,positionBuffer,materialBuffer,colorBuffer,indexBuffer,resizeStep=1.2,Fuzz2=1e3*Number.EPSILON,Fuzz4=Fuzz2*Fuzz2,third=1/3,rotMat=mat4.create(),projMat=mat4.create(),viewMat=mat4.create(),projViewMat=mat4.create(),normMat=mat3.create(),viewMat3=mat3.create(),rotMats=mat4.create(),cjMatInv=mat4.create(),translMat=mat4.create(),center={x:0,y:0,z:0},shift={x:0,y:0},viewParam={xmin:0,xmax:0,ymin:0,ymax:0,zmin:0,zmax:0},redraw=!0,remesh=!0,mouseDownOrTouchActive=!1,lastMouseX=null,lastMouseY=null,touchID=null,Positions=[],Normals=[],Colors=[],Indices=[];class Material{constructor(e,t,i,a,r,n){this.diffuse=e,this.emissive=t,this.specular=i,this.shininess=a,this.metallic=r,this.fresnel0=n}setUniform(e,t){let i=i=>gl.getUniformLocation(e,"Materials["+t+"]."+i);gl.uniform4fv(i("diffuse"),new Float32Array(this.diffuse)),gl.uniform4fv(i("emissive"),new Float32Array(this.emissive)),gl.uniform4fv(i("specular"),new Float32Array(this.specular)),gl.uniform4f(i("parameters"),this.shininess,this.metallic,this.fresnel0,0)}}let indexExt,enumPointLight=1,enumDirectionalLight=2;class Light{constructor(e,t){this.direction=e,this.color=t}setUniform(e,t){let i=i=>gl.getUniformLocation(e,"Lights["+t+"]."+i);gl.uniform3fv(i("direction"),new Float32Array(this.direction)),gl.uniform3fv(i("color"),new Float32Array(this.color))}}function initShaders(){let e=gl.getParameter(gl.MAX_VERTEX_UNIFORM_VECTORS);maxMaterials=Math.floor((e-14)/4),Nmaterials=Math.min(Math.max(Nmaterials,Materials.length),maxMaterials),noNormalShader=initShader(),pixelShader=initShader(["WIDTH"]),materialShader=initShader(["NORMAL"]),colorShader=initShader(["NORMAL","COLOR"]),transparentShader=initShader(["NORMAL","COLOR","TRANSPARENT"])}function setBuffers(){positionBuffer=gl.createBuffer(),materialBuffer=gl.createBuffer(),colorBuffer=gl.createBuffer(),indexBuffer=gl.createBuffer()}function noGL(){gl||alert("Could not initialize WebGL")}function saveAttributes(){let e=window.parent.document.asygl[alpha];e.gl=gl,e.nlights=Lights.length,e.Nmaterials=Nmaterials,e.maxMaterials=maxMaterials,e.noNormalShader=noNormalShader,e.pixelShader=pixelShader,e.materialShader=materialShader,e.colorShader=colorShader,e.transparentShader=transparentShader}function restoreAttributes(){let e=window.parent.document.asygl[alpha];gl=e.gl,nlights=e.nlights,Nmaterials=e.Nmaterials,maxMaterials=e.maxMaterials,noNormalShader=e.noNormalShader,pixelShader=e.pixelShader,materialShader=e.materialShader,colorShader=e.colorShader,transparentShader=e.transparentShader}function initGL(){if(alpha=Background[3]<1,embedded){let e=window.parent.document;null==e.asygl&&(e.asygl=Array(2)),context=canvas.getContext("2d"),(offscreen=e.offscreen)||(offscreen=e.createElement("canvas"),e.offscreen=offscreen),e.asygl[alpha]&&e.asygl[alpha].gl?(restoreAttributes(),(Lights.length!=nlights||Math.min(Materials.length,maxMaterials)>Nmaterials)&&(initShaders(),saveAttributes())):((gl=offscreen.getContext("webgl",{alpha:alpha}))||noGL(),initShaders(),e.asygl[alpha]={},saveAttributes())}else(gl=canvas.getContext("webgl",{alpha:alpha}))||noGL(),initShaders();setBuffers(),indexExt=gl.getExtension("OES_element_index_uint")}function getShader(e,t,i,a=[]){let r=`#version 100\n#ifdef GL_FRAGMENT_PRECISION_HIGH\n precision highp float;\n#else\n precision mediump float;\n#endif\n #define nlights ${Lights.length}\n\n const int Nlights=${Math.max(Lights.length,1)};\n\n #define Nmaterials ${Nmaterials}\n`;orthographic&&(r+="#define ORTHOGRAPHIC\n"),a.forEach(e=>r+="#define "+e+"\n");let n=e.createShader(i);return e.shaderSource(n,r+t),e.compileShader(n),e.getShaderParameter(n,e.COMPILE_STATUS)?n:(alert(e.getShaderInfoLog(n)),null)}function drawBuffer(e,t,i=e.indices){if(0==e.indices.length)return;let a=t==pixelShader,r=t!=noNormalShader&&!a;setUniforms(e,t),gl.bindBuffer(gl.ARRAY_BUFFER,positionBuffer),gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(e.vertices),gl.STATIC_DRAW),gl.vertexAttribPointer(t.vertexPositionAttribute,3,gl.FLOAT,!1,r?24:a?16:12,0),r&&Lights.length>0?gl.vertexAttribPointer(t.vertexNormalAttribute,3,gl.FLOAT,!1,24,12):a&&gl.vertexAttribPointer(t.vertexWidthAttribute,1,gl.FLOAT,!1,16,12),-1!=t.vertexMaterialAttribute&&(gl.bindBuffer(gl.ARRAY_BUFFER,materialBuffer),gl.bufferData(gl.ARRAY_BUFFER,new Int16Array(e.materialIndices),gl.STATIC_DRAW),gl.vertexAttribPointer(t.vertexMaterialAttribute,1,gl.SHORT,!1,2,0)),t!=colorShader&&t!=transparentShader||(gl.bindBuffer(gl.ARRAY_BUFFER,colorBuffer),gl.bufferData(gl.ARRAY_BUFFER,new Uint8Array(e.colors),gl.STATIC_DRAW),gl.vertexAttribPointer(t.vertexColorAttribute,4,gl.UNSIGNED_BYTE,!0,0,0)),gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER,indexBuffer),gl.bufferData(gl.ELEMENT_ARRAY_BUFFER,indexExt?new Uint32Array(i):new Uint16Array(i),gl.STATIC_DRAW),gl.drawElements(r?gl.TRIANGLES:a?gl.POINTS:gl.LINES,i.length,indexExt?gl.UNSIGNED_INT:gl.UNSIGNED_SHORT,0)}class vertexBuffer{constructor(){this.clear()}clear(){this.vertices=[],this.materialIndices=[],this.colors=[],this.indices=[],this.nvertices=0,this.materials=[],this.materialTable=[]}vertex(e,t){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.vertices.push(t[0]),this.vertices.push(t[1]),this.vertices.push(t[2]),this.materialIndices.push(materialIndex),this.nvertices++}Vertex(e,t,i=[0,0,0,0]){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.vertices.push(t[0]),this.vertices.push(t[1]),this.vertices.push(t[2]),this.materialIndices.push(materialIndex),this.colors.push(i[0]),this.colors.push(i[1]),this.colors.push(i[2]),this.colors.push(i[3]),this.nvertices++}vertex1(e){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.materialIndices.push(materialIndex),this.nvertices++}vertex0(e,t){return this.vertices.push(e[0]),this.vertices.push(e[1]),this.vertices.push(e[2]),this.vertices.push(t),this.materialIndices.push(materialIndex),this.nvertices++}iVertex(e,t,i,a=[0,0,0,0]){let r=6*e;this.vertices[r]=t[0],this.vertices[r+1]=t[1],this.vertices[r+2]=t[2],this.vertices[r+3]=i[0],this.vertices[r+4]=i[1],this.vertices[r+5]=i[2],this.materialIndices[e]=materialIndex;let n=4*e;this.colors[n]=a[0],this.colors[n+1]=a[1],this.colors[n+2]=a[2],this.colors[n+3]=a[3],this.indices.push(e)}append(e){append(this.vertices,e.vertices),append(this.materialIndices,e.materialIndices),append(this.colors,e.colors),appendOffset(this.indices,e.indices,this.nvertices),this.nvertices+=e.nvertices}}let materialIndex,material0Data=new vertexBuffer,material1Data=new vertexBuffer,materialData=new vertexBuffer,colorData=new vertexBuffer,transparentData=new vertexBuffer,triangleData=new vertexBuffer;function append(e,t){let i=e.length,a=t.length;e.length+=a;for(let r=0;r<a;++r)e[i+r]=t[r]}function appendOffset(e,t,i){let a=e.length,r=t.length;e.length+=t.length;for(let n=0;n<r;++n)e[a+n]=t[n]+i}class Geometry{constructor(){this.data=new vertexBuffer,this.Onscreen=!1,this.m=[]}offscreen(e){let t=projViewMat,i=e[0],a=i[0],r=i[1],n=i[2],s=1/(t[3]*a+t[7]*r+t[11]*n+t[15]);this.x=this.X=(t[0]*a+t[4]*r+t[8]*n+t[12])*s,this.y=this.Y=(t[1]*a+t[5]*r+t[9]*n+t[13])*s;for(let i=1,a=e.length;i<a;++i){let a=e[i],r=a[0],n=a[1],s=a[2],o=1/(t[3]*r+t[7]*n+t[11]*s+t[15]),l=(t[0]*r+t[4]*n+t[8]*s+t[12])*o,h=(t[1]*r+t[5]*n+t[9]*s+t[13])*o;l<this.x?this.x=l:l>this.X&&(this.X=l),h<this.y?this.y=h:h>this.Y&&(this.Y=h)}return(this.X<-1.01||this.x>1.01||this.Y<-1.01||this.y>1.01)&&(this.Onscreen=!1,!0)}T(e){let t=this.c[0],i=this.c[1],a=this.c[2],r=e[0]-t,n=e[1]-i,s=e[2]-a;return[r*normMat[0]+n*normMat[3]+s*normMat[6]+t,r*normMat[1]+n*normMat[4]+s*normMat[7]+i,r*normMat[2]+n*normMat[5]+s*normMat[8]+a]}Tcorners(e,t){return[this.T(e),this.T([e[0],e[1],t[2]]),this.T([e[0],t[1],e[2]]),this.T([e[0],t[1],t[2]]),this.T([t[0],e[1],e[2]]),this.T([t[0],e[1],t[2]]),this.T([t[0],t[1],e[2]]),this.T(t)]}setMaterial(e,t){null==e.materialTable[this.MaterialIndex]&&(e.materials.length>=Nmaterials&&t(),e.materialTable[this.MaterialIndex]=e.materials.length,e.materials.push(Materials[this.MaterialIndex])),materialIndex=e.materialTable[this.MaterialIndex]}render(){let e;if(this.setMaterialIndex(),0==this.CenterIndex?e=corners(this.Min,this.Max):(this.c=Centers[this.CenterIndex-1],e=this.Tcorners(this.Min,this.Max)),this.offscreen(e))return void this.data.clear();let t,i=this.controlpoints;if(0==this.CenterIndex){if(!remesh&&this.Onscreen)return void this.append();t=i}else{let e=i.length;t=Array(e);for(let a=0;a<e;++a)t[a]=this.T(i[a])}let a=orthographic?1:this.Min[2]/B[2],r=pixel*Math.hypot(a*(viewParam.xmax-viewParam.xmin),a*(viewParam.ymax-viewParam.ymin))/size2;this.res2=r*r,this.Epsilon=FillFactor*r,this.data.clear(),this.Onscreen=!0,this.process(t)}}class BezierPatch extends Geometry{constructor(e,t,i,a,r,n){super(),this.controlpoints=e,this.Min=a,this.Max=r,this.color=n,this.CenterIndex=t;let s=e.length;if(n){let e=n[0][3]+n[1][3]+n[2][3];this.transparent=16==s||4==s?e+n[3][3]<1020:e<765}else this.transparent=Materials[i].diffuse[3]<1;this.MaterialIndex=i,this.vertex=this.transparent?this.data.Vertex.bind(this.data):this.data.vertex.bind(this.data),this.L2norm(this.controlpoints)}setMaterialIndex(){this.transparent?this.setMaterial(transparentData,drawTransparent):this.color?this.setMaterial(colorData,drawColor):this.setMaterial(materialData,drawMaterial)}L2norm(e){let t=e[0];this.epsilon=0;let i=e.length;for(let a=1;a<i;++a)this.epsilon=Math.max(this.epsilon,abs2([e[a][0]-t[0],e[a][1]-t[1],e[a][2]-t[2]]));this.epsilon*=Fuzz4}processTriangle(e){let t=e[0],i=e[1],a=e[2],r=unit(cross([i[0]-t[0],i[1]-t[1],i[2]-t[2]],[a[0]-t[0],a[1]-t[1],a[2]-t[2]]));this.offscreen([t,i,a])||(this.color?(this.data.indices.push(this.data.Vertex(t,r,this.color[0])),this.data.indices.push(this.data.Vertex(i,r,this.color[1])),this.data.indices.push(this.data.Vertex(a,r,this.color[2]))):(this.data.indices.push(this.vertex(t,r)),this.data.indices.push(this.vertex(i,r)),this.data.indices.push(this.vertex(a,r))),this.append())}processQuad(e){let t=e[0],i=e[1],a=e[2],r=e[3],n=cross([i[0]-t[0],i[1]-t[1],i[2]-t[2]],[a[0]-i[0],a[1]-i[1],a[2]-i[2]]),s=cross([a[0]-r[0],a[1]-r[1],a[2]-r[2]],[r[0]-t[0],r[1]-t[1],r[2]-t[2]]),o=unit([n[0]+s[0],n[1]+s[1],n[2]+s[2]]);if(!this.offscreen([t,i,a,r])){let e,n,s,l;this.color?(e=this.data.Vertex(t,o,this.color[0]),n=this.data.Vertex(i,o,this.color[1]),s=this.data.Vertex(a,o,this.color[2]),l=this.data.Vertex(r,o,this.color[3])):(e=this.vertex(t,o),n=this.vertex(i,o),s=this.vertex(a,o),l=this.vertex(r,o)),this.data.indices.push(e),this.data.indices.push(n),this.data.indices.push(s),this.data.indices.push(e),this.data.indices.push(s),this.data.indices.push(l),this.append()}}process(e){if(this.transparent&&(materialIndex=this.color?-1-materialIndex:1+materialIndex),10==e.length)return this.process3(e);if(3==e.length)return this.processTriangle(e);if(4==e.length)return this.processQuad(e);let t=e[0],i=e[3],a=e[12],r=e[15],n=this.normal(i,e[2],e[1],t,e[4],e[8],a);iszero(n)&&iszero(n=this.normal(i,e[2],e[1],t,e[13],e[14],r))&&(n=this.normal(r,e[11],e[7],i,e[4],e[8],a));let s=this.normal(t,e[4],e[8],a,e[13],e[14],r);iszero(s)&&iszero(s=this.normal(t,e[4],e[8],a,e[11],e[7],i))&&(s=this.normal(i,e[2],e[1],t,e[13],e[14],r));let o=this.normal(a,e[13],e[14],r,e[11],e[7],i);iszero(o)&&iszero(o=this.normal(a,e[13],e[14],r,e[2],e[1],t))&&(o=this.normal(t,e[4],e[8],a,e[11],e[7],i));let l=this.normal(r,e[11],e[7],i,e[2],e[1],t);if(iszero(l)&&iszero(l=this.normal(r,e[11],e[7],i,e[4],e[8],a))&&(l=this.normal(a,e[13],e[14],r,e[2],e[1],t)),this.color){let h=this.color[0],c=this.color[1],d=this.color[2],m=this.color[3],f=this.data.Vertex(t,n,h),u=this.data.Vertex(a,s,c),v=this.data.Vertex(r,o,d),g=this.data.Vertex(i,l,m);this.Render(e,f,u,v,g,t,a,r,i,!1,!1,!1,!1,h,c,d,m)}else{let h=this.vertex(t,n),c=this.vertex(a,s),d=this.vertex(r,o),m=this.vertex(i,l);this.Render(e,h,c,d,m,t,a,r,i,!1,!1,!1,!1)}this.data.indices.length>0&&this.append()}append(){this.transparent?transparentData.append(this.data):this.color?colorData.append(this.data):materialData.append(this.data)}Render(e,t,i,a,r,n,s,o,l,h,c,d,m,f,u,v,g){if(this.Distance(e)<this.res2)this.offscreen([n,s,o])||(this.data.indices.push(t),this.data.indices.push(i),this.data.indices.push(a)),this.offscreen([n,o,l])||(this.data.indices.push(t),this.data.indices.push(a),this.data.indices.push(r));else{if(this.offscreen(e))return;let p=e[0],x=e[3],M=e[12],w=e[15],A=new Split3(p,e[1],e[2],x),b=new Split3(e[4],e[5],e[6],e[7]),S=new Split3(e[8],e[9],e[10],e[11]),R=new Split3(M,e[13],e[14],w),P=new Split3(p,e[4],e[8],M),D=new Split3(A.m0,b.m0,S.m0,R.m0),T=new Split3(A.m3,b.m3,S.m3,R.m3),y=new Split3(A.m5,b.m5,S.m5,R.m5),I=new Split3(A.m4,b.m4,S.m4,R.m4),z=new Split3(A.m2,b.m2,S.m2,R.m2),O=new Split3(x,e[7],e[11],w),E=[p,A.m0,A.m3,A.m5,P.m0,D.m0,T.m0,y.m0,P.m3,D.m3,T.m3,y.m3,P.m5,D.m5,T.m5,y.m5],_=[P.m5,D.m5,T.m5,y.m5,P.m4,D.m4,T.m4,y.m4,P.m2,D.m2,T.m2,y.m2,M,R.m0,R.m3,R.m5],L=[y.m5,I.m5,z.m5,O.m5,y.m4,I.m4,z.m4,O.m4,y.m2,I.m2,z.m2,O.m2,R.m5,R.m4,R.m2,w],N=[A.m5,A.m4,A.m2,x,y.m0,I.m0,z.m0,O.m0,y.m3,I.m3,z.m3,O.m3,y.m5,I.m5,z.m5,O.m5],C=E[15],B=this.normal(E[0],E[4],E[8],E[12],E[13],E[14],E[15]);iszero(B)&&iszero(B=this.normal(E[0],E[4],E[8],E[12],E[11],E[7],E[3]))&&(B=this.normal(E[3],E[2],E[1],E[0],E[13],E[14],E[15]));let F=this.normal(_[12],_[13],_[14],_[15],_[11],_[7],_[3]);iszero(F)&&iszero(F=this.normal(_[12],_[13],_[14],_[15],_[2],_[1],_[0]))&&(F=this.normal(_[0],_[4],_[8],_[12],_[11],_[7],_[3]));let V=this.normal(L[15],L[11],L[7],L[3],L[2],L[1],L[0]);iszero(V)&&iszero(V=this.normal(L[15],L[11],L[7],L[3],L[4],L[8],L[12]))&&(V=this.normal(L[12],L[13],L[14],L[15],L[2],L[1],L[0]));let H=this.normal(N[3],N[2],N[1],N[0],N[4],N[8],N[12]);iszero(H)&&iszero(H=this.normal(N[3],N[2],N[1],N[0],N[13],N[14],N[15]))&&(H=this.normal(N[15],N[11],N[7],N[3],N[4],N[8],N[12]));let G=this.normal(L[3],L[2],L[1],C,L[4],L[8],L[12]),U=this.Epsilon,W=[.5*(n[0]+s[0]),.5*(n[1]+s[1]),.5*(n[2]+s[2])];if(!h)if(h=Straightness(p,e[4],e[8],M)<this.res2){let e=unit(this.derivative(_[0],_[1],_[2],_[3]));W=[W[0]-U*e[0],W[1]-U*e[1],W[2]-U*e[2]]}else W=E[12];let Y=[.5*(s[0]+o[0]),.5*(s[1]+o[1]),.5*(s[2]+o[2])];if(!c)if(c=Straightness(M,e[13],e[14],w)<this.res2){let e=unit(this.derivative(L[12],L[8],L[4],L[0]));Y=[Y[0]-U*e[0],Y[1]-U*e[1],Y[2]-U*e[2]]}else Y=_[15];let j=[.5*(o[0]+l[0]),.5*(o[1]+l[1]),.5*(o[2]+l[2])];if(!d)if(d=Straightness(w,e[11],e[7],x)<this.res2){let e=unit(this.derivative(N[15],L[14],L[13],_[12]));j=[j[0]-U*e[0],j[1]-U*e[1],j[2]-U*e[2]]}else j=L[3];let k=[.5*(l[0]+n[0]),.5*(l[1]+n[1]),.5*(l[2]+n[2])];if(!m)if(m=Straightness(p,e[1],e[2],x)<this.res2){let e=unit(this.derivative(E[3],E[7],E[11],E[15]));k=[k[0]-U*e[0],k[1]-U*e[1],k[2]-U*e[2]]}else k=N[0];if(f){let e=Array(4),p=Array(4),x=Array(4),M=Array(4),w=Array(4);for(let t=0;t<4;++t)e[t]=.5*(f[t]+u[t]),p[t]=.5*(u[t]+v[t]),x[t]=.5*(v[t]+g[t]),M[t]=.5*(g[t]+f[t]),w[t]=.5*(e[t]+x[t]);let A=this.data.Vertex(W,B,e),b=this.data.Vertex(Y,F,p),S=this.data.Vertex(j,V,x),R=this.data.Vertex(k,H,M),P=this.data.Vertex(C,G,w);this.Render(E,t,A,P,R,n,W,C,k,h,!1,!1,m,f,e,w,M),this.Render(_,A,i,b,P,W,s,Y,C,h,c,!1,!1,e,u,p,w),this.Render(L,P,b,a,S,C,Y,o,j,!1,c,d,!1,w,p,v,x),this.Render(N,R,P,S,r,k,C,j,l,!1,!1,d,m,M,w,x,g)}else{let e=this.vertex(W,B),f=this.vertex(Y,F),u=this.vertex(j,V),v=this.vertex(k,H),g=this.vertex(C,G);this.Render(E,t,e,g,v,n,W,C,k,h,!1,!1,m),this.Render(_,e,i,f,g,W,s,Y,C,h,c,!1,!1),this.Render(L,g,f,a,u,C,Y,o,j,!1,c,d,!1),this.Render(N,v,g,u,r,k,C,j,l,!1,!1,d,m)}}}process3(e){this.Res2=BezierFactor*BezierFactor*this.res2;let t=e[0],i=e[6],a=e[9],r=this.normal(a,e[5],e[2],t,e[1],e[3],i),n=this.normal(t,e[1],e[3],i,e[7],e[8],a),s=this.normal(i,e[7],e[8],a,e[5],e[2],t);if(this.color){let o=this.color[0],l=this.color[1],h=this.color[2],c=this.data.Vertex(t,r,o),d=this.data.Vertex(i,n,l),m=this.data.Vertex(a,s,h);this.Render3(e,c,d,m,t,i,a,!1,!1,!1,o,l,h)}else{let o=this.vertex(t,r),l=this.vertex(i,n),h=this.vertex(a,s);this.Render3(e,o,l,h,t,i,a,!1,!1,!1)}this.data.indices.length>0&&this.append()}Render3(e,t,i,a,r,n,s,o,l,h,c,d,m){if(this.Distance3(e)<this.Res2)this.offscreen([r,n,s])||(this.data.indices.push(t),this.data.indices.push(i),this.data.indices.push(a));else{if(this.offscreen(e))return;let f=e[0],u=e[1],v=e[2],g=e[3],p=e[4],x=e[5],M=e[6],w=e[7],A=e[8],b=e[9],S=[.5*(b[0]+x[0]),.5*(b[1]+x[1]),.5*(b[2]+x[2])],R=[.5*(b[0]+A[0]),.5*(b[1]+A[1]),.5*(b[2]+A[2])],P=[.5*(x[0]+v[0]),.5*(x[1]+v[1]),.5*(x[2]+v[2])],D=[.5*(A[0]+p[0]),.5*(A[1]+p[1]),.5*(A[2]+p[2])],T=[.5*(A[0]+w[0]),.5*(A[1]+w[1]),.5*(A[2]+w[2])],y=[.5*(v[0]+p[0]),.5*(v[1]+p[1]),.5*(v[2]+p[2])],I=[.5*(v[0]+f[0]),.5*(v[1]+f[1]),.5*(v[2]+f[2])],z=[.5*(p[0]+g[0]),.5*(p[1]+g[1]),.5*(p[2]+g[2])],O=[.5*(w[0]+M[0]),.5*(w[1]+M[1]),.5*(w[2]+M[2])],E=[.5*(f[0]+u[0]),.5*(f[1]+u[1]),.5*(f[2]+u[2])],_=[.5*(u[0]+g[0]),.5*(u[1]+g[1]),.5*(u[2]+g[2])],L=[.5*(g[0]+M[0]),.5*(g[1]+M[1]),.5*(g[2]+M[2])],N=[.5*(S[0]+P[0]),.5*(S[1]+P[1]),.5*(S[2]+P[2])],C=[.5*(R[0]+T[0]),.5*(R[1]+T[1]),.5*(R[2]+T[2])],B=[.5*(P[0]+I[0]),.5*(P[1]+I[1]),.5*(P[2]+I[2])],F=[.5*D[0]+.25*(p[0]+u[0]),.5*D[1]+.25*(p[1]+u[1]),.5*D[2]+.25*(p[2]+u[2])],V=[.5*(T[0]+O[0]),.5*(T[1]+O[1]),.5*(T[2]+O[2])],H=[.5*y[0]+.25*(p[0]+w[0]),.5*y[1]+.25*(p[1]+w[1]),.5*y[2]+.25*(p[2]+w[2])],G=[.25*(x[0]+p[0])+.5*z[0],.25*(x[1]+p[1])+.5*z[1],.25*(x[2]+p[2])+.5*z[2]],U=[.5*(E[0]+_[0]),.5*(E[1]+_[1]),.5*(E[2]+_[2])],W=[.5*(_[0]+L[0]),.5*(_[1]+L[1]),.5*(_[2]+L[2])],Y=[.5*(H[0]+U[0]),.5*(H[1]+U[1]),.5*(H[2]+U[2])],j=[.5*(H[0]+W[0]),.5*(H[1]+W[1]),.5*(H[2]+W[2])],k=[.5*(U[0]+W[0]),.5*(U[1]+W[1]),.5*(U[2]+W[2])],X=[.5*(G[0]+V[0]),.5*(G[1]+V[1]),.5*(G[2]+V[2])],Z=[.5*(C[0]+G[0]),.5*(C[1]+G[1]),.5*(C[2]+G[2])],q=[.5*(C[0]+V[0]),.5*(C[1]+V[1]),.5*(C[2]+V[2])],K=[.5*(N[0]+F[0]),.5*(N[1]+F[1]),.5*(N[2]+F[2])],$=[.5*(B[0]+F[0]),.5*(B[1]+F[1]),.5*(B[2]+F[2])],Q=[.5*(N[0]+B[0]),.5*(N[1]+B[1]),.5*(N[2]+B[2])],J=[f,E,I,U,[.5*(y[0]+E[0]),.5*(y[1]+E[1]),.5*(y[2]+E[2])],B,k,Y,$,Q],ee=[k,W,j,L,[.5*(z[0]+O[0]),.5*(z[1]+O[1]),.5*(z[2]+O[2])],X,M,O,V,q],te=[Q,K,N,Z,[.5*(S[0]+D[0]),.5*(S[1]+D[1]),.5*(S[2]+D[2])],S,q,C,R,b],ie=[q,Z,X,K,[.25*(P[0]+T[0]+_[0]+p[0]),.25*(P[1]+T[1]+_[1]+p[1]),.25*(P[2]+T[2]+_[2]+p[2])],j,Q,$,Y,k],ae=this.normal(k,j,X,q,Z,K,Q),re=this.normal(q,Z,K,Q,$,Y,k),ne=this.normal(Q,$,Y,k,j,X,q),se=this.Epsilon,oe=[.5*(n[0]+s[0]),.5*(n[1]+s[1]),.5*(n[2]+s[2])];if(!o)if(o=Straightness(M,w,A,b)<this.res2){let e=unit(this.sumderivative(ie[0],ie[2],ie[5],ie[9],ie[1],ie[3],ie[6]));oe=[oe[0]-se*e[0],oe[1]-se*e[1],oe[2]-se*e[2]]}else oe=q;let le=[.5*(s[0]+r[0]),.5*(s[1]+r[1]),.5*(s[2]+r[2])];if(!l)if(l=Straightness(f,v,x,b)<this.res2){let e=unit(this.sumderivative(ie[6],ie[3],ie[1],ie[0],ie[7],ie[8],ie[9]));le=[le[0]-se*e[0],le[1]-se*e[1],le[2]-se*e[2]]}else le=Q;let he=[.5*(r[0]+n[0]),.5*(r[1]+n[1]),.5*(r[2]+n[2])];if(!h)if(h=Straightness(f,u,g,M)<this.res2){let e=unit(this.sumderivative(ie[9],ie[8],ie[7],ie[6],ie[5],ie[2],ie[0]));he=[he[0]-se*e[0],he[1]-se*e[1],he[2]-se*e[2]]}else he=k;if(c){let e=Array(4),f=Array(4),u=Array(4);for(let t=0;t<4;++t)e[t]=.5*(d[t]+m[t]),f[t]=.5*(m[t]+c[t]),u[t]=.5*(c[t]+d[t]);let v=this.data.Vertex(oe,ae,e),g=this.data.Vertex(le,re,f),p=this.data.Vertex(he,ne,u);this.Render3(J,t,p,g,r,he,le,!1,l,h,c,u,f),this.Render3(ee,p,i,v,he,n,oe,o,!1,h,u,d,e),this.Render3(te,g,v,a,le,oe,s,o,l,!1,f,e,m),this.Render3(ie,v,g,p,oe,le,he,!1,!1,!1,e,f,u)}else{let e=this.vertex(oe,ae),c=this.vertex(le,re),d=this.vertex(he,ne);this.Render3(J,t,d,c,r,he,le,!1,l,h),this.Render3(ee,d,i,e,he,n,oe,o,!1,h),this.Render3(te,c,e,a,le,oe,s,o,l,!1),this.Render3(ie,e,c,d,oe,le,he,!1,!1,!1)}}}Distance(e){let t=e[0],i=e[3],a=e[12],r=e[15],n=Distance2(r,t,this.normal(i,e[2],e[1],t,e[4],e[8],a));return n=Math.max(n,Straightness(t,e[1],e[2],i)),n=Math.max(n,Straightness(t,e[4],e[8],a)),n=Math.max(n,Straightness(i,e[7],e[11],r)),n=Math.max(n,Straightness(a,e[13],e[14],r)),n=Math.max(n,Straightness(e[4],e[5],e[6],e[7])),n=Math.max(n,Straightness(e[8],e[9],e[10],e[11])),n=Math.max(n,Straightness(e[1],e[5],e[9],e[13])),Math.max(n,Straightness(e[2],e[6],e[10],e[14]))}Distance3(e){let t=e[0],i=e[4],a=e[6],r=e[9],n=abs2([(t[0]+a[0]+r[0])*third-i[0],(t[1]+a[1]+r[1])*third-i[1],(t[2]+a[2]+r[2])*third-i[2]]);return n=Math.max(n,Straightness(t,e[1],e[3],a)),n=Math.max(n,Straightness(t,e[2],e[5],r)),Math.max(n,Straightness(a,e[7],e[8],r))}derivative(e,t,i,a){let r=[t[0]-e[0],t[1]-e[1],t[2]-e[2]];if(abs2(r)>this.epsilon)return r;let n=bezierPP(e,t,i);return abs2(n)>this.epsilon?n:bezierPPP(e,t,i,a)}sumderivative(e,t,i,a,r,n,s){let o=this.derivative(e,t,i,a),l=this.derivative(e,r,n,s);return[o[0]+l[0],o[1]+l[1],o[2]+l[2]]}normal(e,t,i,a,r,n,s){let o=r[0]-a[0],l=r[1]-a[1],h=r[2]-a[2],c=i[0]-a[0],d=i[1]-a[1],m=i[2]-a[2],f=[l*m-h*d,h*c-o*m,o*d-l*c];if(abs2(f)>this.epsilon)return unit(f);let u=[c,d,m],v=[o,l,h],g=bezierPP(a,i,t),p=bezierPP(a,r,n),x=cross(p,u),M=cross(v,g);if(abs2(f=[x[0]+M[0],x[1]+M[1],x[2]+M[2]])>this.epsilon)return unit(f);let w=bezierPPP(a,i,t,e),A=bezierPPP(a,r,n,s);x=cross(p,g),M=cross(v,w);let b=cross(A,u),S=cross(A,g),R=cross(p,w),P=cross(A,w);return unit([9*x[0]+3*(M[0]+b[0]+S[0]+R[0])+P[0],9*x[1]+3*(M[1]+b[1]+S[1]+R[1])+P[1],9*x[2]+3*(M[2]+b[2]+S[2]+R[2])+P[2]])}}class BezierCurve extends Geometry{constructor(e,t,i,a,r){super(),this.controlpoints=e,this.Min=a,this.Max=r,this.CenterIndex=t,this.MaterialIndex=i}setMaterialIndex(){this.setMaterial(material1Data,drawMaterial1)}processLine(e){let t=e[0],i=e[1];this.offscreen([t,i])||(this.data.indices.push(this.data.vertex1(t)),this.data.indices.push(this.data.vertex1(i)),this.append())}process(e){if(2==e.length)return this.processLine(e);let t=this.data.vertex1(e[0]),i=this.data.vertex1(e[3]);this.Render(e,t,i),this.data.indices.length>0&&this.append()}append(){material1Data.append(this.data)}Render(e,t,i){let a=e[0],r=e[1],n=e[2],s=e[3];if(Straightness(a,r,n,s)<this.res2)this.offscreen([a,s])||(this.data.indices.push(t),this.data.indices.push(i));else{if(this.offscreen(e))return;let o=[.5*(a[0]+r[0]),.5*(a[1]+r[1]),.5*(a[2]+r[2])],l=[.5*(r[0]+n[0]),.5*(r[1]+n[1]),.5*(r[2]+n[2])],h=[.5*(n[0]+s[0]),.5*(n[1]+s[1]),.5*(n[2]+s[2])],c=[.5*(o[0]+l[0]),.5*(o[1]+l[1]),.5*(o[2]+l[2])],d=[.5*(l[0]+h[0]),.5*(l[1]+h[1]),.5*(l[2]+h[2])],m=[.5*(c[0]+d[0]),.5*(c[1]+d[1]),.5*(c[2]+d[2])],f=[a,o,c,m],u=[m,d,h,s],v=this.data.vertex1(m);this.Render(f,t,v),this.Render(u,v,i)}}}class Pixel extends Geometry{constructor(e,t,i,a,r){super(),this.controlpoint=e,this.width=t,this.CenterIndex=0,this.MaterialIndex=i,this.Min=a,this.Max=r}setMaterialIndex(){this.setMaterial(material0Data,drawMaterial0)}process(e){this.data.indices.push(this.data.vertex0(this.controlpoint,this.width)),this.append()}append(){material0Data.append(this.data)}}class Triangles extends Geometry{constructor(e,t,i){super(),this.CenterIndex=0,this.MaterialIndex=e,this.Min=t,this.Max=i,this.Positions=Positions,this.Normals=Normals,this.Colors=Colors,this.Indices=Indices,Positions=[],Normals=[],Colors=[],Indices=[],this.transparent=Materials[e].diffuse[3]<1}setMaterialIndex(){this.transparent?this.setMaterial(transparentData,drawTransparent):this.setMaterial(triangleData,drawTriangle)}process(e){materialIndex=this.Colors.length>0?-1-materialIndex:1+materialIndex;for(let e=0,t=this.Indices.length;e<t;++e){let t=this.Indices[e],i=t[0],a=this.Positions[i[0]],r=this.Positions[i[1]],n=this.Positions[i[2]];if(!this.offscreen([a,r,n])){let e=t.length>1?t[1]:i;if(e&&0!=e.length||(e=i),this.Colors.length>0){let s=t.length>2?t[2]:i;s&&0!=s.length||(s=i);let o=this.Colors[s[0]],l=this.Colors[s[1]],h=this.Colors[s[2]];this.transparent|=o[3]+l[3]+h[3]<765,this.data.iVertex(i[0],a,this.Normals[e[0]],o),this.data.iVertex(i[1],r,this.Normals[e[1]],l),this.data.iVertex(i[2],n,this.Normals[e[2]],h)}else this.data.iVertex(i[0],a,this.Normals[e[0]]),this.data.iVertex(i[1],r,this.Normals[e[1]]),this.data.iVertex(i[2],n,this.Normals[e[2]])}}this.data.nvertices=this.Positions.length,this.data.indices.length>0&&this.append()}append(){this.transparent?transparentData.append(this.data):triangleData.append(this.data)}}function home(){mat4.identity(rotMat),initProjection(),setProjection(),remesh=!0,redraw=!0}function initShader(e=[]){let t=getShader(gl,vertex,gl.VERTEX_SHADER,e),i=getShader(gl,fragment,gl.FRAGMENT_SHADER,e),a=gl.createProgram();return gl.attachShader(a,t),gl.attachShader(a,i),gl.linkProgram(a),gl.getProgramParameter(a,gl.LINK_STATUS)||alert("Could not initialize shaders"),a}class Split3{constructor(e,t,i,a){this.m0=[.5*(e[0]+t[0]),.5*(e[1]+t[1]),.5*(e[2]+t[2])];let r=.5*(t[0]+i[0]),n=.5*(t[1]+i[1]),s=.5*(t[2]+i[2]);this.m2=[.5*(i[0]+a[0]),.5*(i[1]+a[1]),.5*(i[2]+a[2])],this.m3=[.5*(this.m0[0]+r),.5*(this.m0[1]+n),.5*(this.m0[2]+s)],this.m4=[.5*(r+this.m2[0]),.5*(n+this.m2[1]),.5*(s+this.m2[2])],this.m5=[.5*(this.m3[0]+this.m4[0]),.5*(this.m3[1]+this.m4[1]),.5*(this.m3[2]+this.m4[2])]}}function iszero(e){return 0==e[0]&&0==e[1]&&0==e[2]}function unit(e){let t=1/(Math.sqrt(e[0]*e[0]+e[1]*e[1]+e[2]*e[2])||1);return[e[0]*t,e[1]*t,e[2]*t]}function abs2(e){return e[0]*e[0]+e[1]*e[1]+e[2]*e[2]}function dot(e,t){return e[0]*t[0]+e[1]*t[1]+e[2]*t[2]}function cross(e,t){return[e[1]*t[2]-e[2]*t[1],e[2]*t[0]-e[0]*t[2],e[0]*t[1]-e[1]*t[0]]}function bezierPP(e,t,i){return[e[0]+i[0]-2*t[0],e[1]+i[1]-2*t[1],e[2]+i[2]-2*t[2]]}function bezierPPP(e,t,i,a){return[a[0]-e[0]+3*(t[0]-i[0]),a[1]-e[1]+3*(t[1]-i[1]),a[2]-e[2]+3*(t[2]-i[2])]}function Straightness(e,t,i,a){let r=[third*(a[0]-e[0]),third*(a[1]-e[1]),third*(a[2]-e[2])];return Math.max(abs2([t[0]-r[0]-e[0],t[1]-r[1]-e[1],t[2]-r[2]-e[2]]),abs2([a[0]-r[0]-i[0],a[1]-r[1]-i[1],a[2]-r[2]-i[2]]))}function Distance2(e,t,i){let a=dot([e[0]-t[0],e[1]-t[1],e[2]-t[2]],i);return a*a}function corners(e,t){return[e,[e[0],e[1],t[2]],[e[0],t[1],e[2]],[e[0],t[1],t[2]],[t[0],e[1],e[2]],[t[0],e[1],t[2]],[t[0],t[1],e[2]],t]}function COBTarget(e,t){mat4.fromTranslation(translMat,[center.x,center.y,center.z]),mat4.invert(cjMatInv,translMat),mat4.multiply(e,t,cjMatInv),mat4.multiply(e,translMat,e)}function setUniforms(e,t){let i=t==pixelShader;gl.useProgram(t),t.vertexPositionAttribute=gl.getAttribLocation(t,"position"),gl.enableVertexAttribArray(t.vertexPositionAttribute),i&&(t.vertexWidthAttribute=gl.getAttribLocation(t,"width"),gl.enableVertexAttribArray(t.vertexWidthAttribute));let a=t!=noNormalShader&&!i&&Lights.length>0;if(a&&(t.vertexNormalAttribute=gl.getAttribLocation(t,"normal"),gl.enableVertexAttribArray(t.vertexNormalAttribute)),t.vertexMaterialAttribute=gl.getAttribLocation(t,"materialIndex"),-1!=t.vertexMaterialAttribute&&gl.enableVertexAttribArray(t.vertexMaterialAttribute),t.projViewMatUniform=gl.getUniformLocation(t,"projViewMat"),t.viewMatUniform=gl.getUniformLocation(t,"viewMat"),t.normMatUniform=gl.getUniformLocation(t,"normMat"),t!=colorShader&&t!=transparentShader||(t.vertexColorAttribute=gl.getAttribLocation(t,"color"),gl.enableVertexAttribArray(t.vertexColorAttribute)),a)for(let e=0;e<Lights.length;++e)Lights[e].setUniform(t,e);if(-1!=t.vertexMaterialAttribute)for(let i=0;i<e.materials.length;++i)e.materials[i].setUniform(t,i);gl.uniformMatrix4fv(t.projViewMatUniform,!1,projViewMat),gl.uniformMatrix4fv(t.viewMatUniform,!1,viewMat),gl.uniformMatrix3fv(t.normMatUniform,!1,normMat)}function handleMouseDown(e){mouseDownOrTouchActive=!0,lastMouseX=e.clientX,lastMouseY=e.clientY}let pinchStart,touchStartTime,pinch=!1;function pinchDistance(e){return Math.hypot(e[0].pageX-e[1].pageX,e[0].pageY-e[1].pageY)}function handleTouchStart(e){e.preventDefault();let t=e.targetTouches;swipe=rotate=pinch=!1,zooming||(1!=t.length||mouseDownOrTouchActive||(touchStartTime=(new Date).getTime(),touchId=t[0].identifier,lastMouseX=t[0].pageX,lastMouseY=t[0].pageY),2!=t.length||mouseDownOrTouchActive||(touchId=t[0].identifier,pinchStart=pinchDistance(t),pinch=!0))}function handleMouseUpOrTouchEnd(e){mouseDownOrTouchActive=!1}function rotateScene(e,t,i,a,r){if(e==i&&t==a)return;let[n,s]=arcball([e,-t],[i,-a]);mat4.fromRotation(rotMats,2*r*ArcballFactor*n/lastzoom,s),mat4.multiply(rotMat,rotMats,rotMat)}function shiftScene(e,t,i,a){let r=1/lastzoom;shift.x+=(i-e)*r*halfCanvasWidth,shift.y-=(a-t)*r*halfCanvasHeight}function panScene(e,t,i,a){orthographic?shiftScene(e,t,i,a):(center.x+=(i-e)*(viewParam.xmax-viewParam.xmin),center.y-=(a-t)*(viewParam.ymax-viewParam.ymin))}function updateViewMatrix(){COBTarget(viewMat,rotMat),mat4.translate(viewMat,viewMat,[center.x,center.y,0]),mat3.fromMat4(viewMat3,viewMat),mat3.invert(normMat,viewMat3),mat4.multiply(projViewMat,projMat,viewMat)}function capzoom(){let e=Math.sqrt(Number.MAX_VALUE),t=1/e;Zoom<=t&&(Zoom=t),Zoom>=e&&(Zoom=e),Zoom!=lastzoom&&(remesh=!0),lastzoom=Zoom}function zoomImage(e){let t=zoomStep*halfCanvasHeight*e;const i=Math.log(.1*Number.MAX_VALUE)/Math.log(zoomFactor);Math.abs(t)<i&&(Zoom*=zoomFactor**t,capzoom())}function normMouse(e){let t=e[0],i=e[1],a=Math.hypot(t,i);return a>1&&(denom=1/a,t*=denom,i*=denom),[t,i,Math.sqrt(Math.max(1-i*i-t*t,0))]}function arcball(e,t){let i=normMouse(e),a=normMouse(t),r=dot(i,a);return r>1?r=1:r<-1&&(r=-1),[Math.acos(r),unit(cross(i,a))]}function zoomScene(e,t,i,a){zoomImage(t-a)}const DRAGMODE_ROTATE=1,DRAGMODE_SHIFT=2,DRAGMODE_ZOOM=3,DRAGMODE_PAN=4;function processDrag(e,t,i,a=1){let r;switch(i){case DRAGMODE_ROTATE:r=rotateScene;break;case DRAGMODE_SHIFT:r=shiftScene;break;case DRAGMODE_ZOOM:r=zoomScene;break;case DRAGMODE_PAN:r=panScene;break;default:r=((e,t,i,a)=>{})}r((lastMouseX-halfCanvasWidth)/halfCanvasWidth,(lastMouseY-halfCanvasHeight)/halfCanvasHeight,(e-halfCanvasWidth)/halfCanvasWidth,(t-halfCanvasHeight)/halfCanvasHeight,a),lastMouseX=e,lastMouseY=t,setProjection(),redraw=!0}function handleKey(e){let t=[];switch(e.key){case"x":t=[1,0,0];break;case"y":t=[0,1,0];break;case"z":t=[0,0,1];break;case"h":home();break;case"+":case"=":case">":expand();break;case"-":case"_":case"<":shrink()}t.length>0&&(mat4.rotate(rotMat,rotMat,.1,t),updateViewMatrix(),redraw=!0)}function handleMouseWheel(e){e.preventDefault(),e.deltaY<0?Zoom*=zoomFactor:Zoom/=zoomFactor,capzoom(),setProjection(),redraw=!0}function handleMouseMove(e){if(!mouseDownOrTouchActive)return;let t;processDrag(e.clientX,e.clientY,t=e.getModifierState("Control")?DRAGMODE_SHIFT:e.getModifierState("Shift")?DRAGMODE_ZOOM:e.getModifierState("Alt")?DRAGMODE_PAN:DRAGMODE_ROTATE)}let zooming=!1,swipe=!1,rotate=!1;function handleTouchMove(e){if(e.preventDefault(),zooming)return;let t=e.targetTouches;if(!pinch&&1==t.length&&touchId==t[0].identifier){let e=t[0].pageX,i=t[0].pageY,a=e-lastMouseX,r=i-lastMouseY,n=a*a+r*r<=shiftHoldDistance*shiftHoldDistance;if(n&&!swipe&&!rotate&&(new Date).getTime()-touchStartTime>shiftWaitTime&&(navigator.vibrate&&window.navigator.vibrate(vibrateTime),swipe=!0),swipe)processDrag(e,i,DRAGMODE_SHIFT);else if(!n){rotate=!0,processDrag(t[0].pageX,t[0].pageY,DRAGMODE_ROTATE,.5)}}if(pinch&&!swipe&&2==t.length&&touchId==t[0].identifier){let e=pinchDistance(t),i=e-pinchStart;zooming=!0,(i*=zoomPinchFactor)>zoomPinchCap&&(i=zoomPinchCap),i<-zoomPinchCap&&(i=-zoomPinchCap),zoomImage(i/size2),pinchStart=e,swipe=rotate=zooming=!1,setProjection(),redraw=!0}}let pixelShader,noNormalShader,materialShader,colorShader,transparentShader,zbuffer=[];function transformVertices(e){let t=viewMat[2],i=viewMat[6],a=viewMat[10];zbuffer.length=e.length;for(let r=0;r<e.length;++r){let n=6*r;zbuffer[r]=t*e[n]+i*e[n+1]+a*e[n+2]}}function drawMaterial0(){drawBuffer(material0Data,pixelShader),material0Data.clear()}function drawMaterial1(){drawBuffer(material1Data,noNormalShader),material1Data.clear()}function drawMaterial(){drawBuffer(materialData,materialShader),materialData.clear()}function drawColor(){drawBuffer(colorData,colorShader),colorData.clear()}function drawTriangle(){drawBuffer(triangleData,transparentShader),triangleData.clear()}function drawTransparent(){let e=transparentData.indices;if(e.length>0){transformVertices(transparentData.vertices);let t=e.length/3,i=Array(t).fill().map((e,t)=>t);i.sort(function(t,i){let a=3*t;Ia=e[a],Ib=e[a+1],Ic=e[a+2];let r=3*i;return IA=e[r],IB=e[r+1],IC=e[r+2],zbuffer[Ia]+zbuffer[Ib]+zbuffer[Ic]<zbuffer[IA]+zbuffer[IB]+zbuffer[IC]?-1:1});let a=Array(e.length);for(let r=0;r<t;++r){let t=3*i[r];a[3*r]=e[t],a[3*r+1]=e[t+1],a[3*r+2]=e[t+2]}gl.depthMask(!1),drawBuffer(transparentData,transparentShader,a),gl.depthMask(!0)}transparentData.clear()}function drawBuffers(){drawMaterial0(),drawMaterial1(),drawMaterial(),drawColor(),drawTriangle(),drawTransparent()}function draw(){embedded&&(offscreen.width=canvas.width,offscreen.height=canvas.height,setViewport()),gl.clearColor(Background[0],Background[1],Background[2],Background[3]),gl.clear(gl.COLOR_BUFFER_BIT|gl.DEPTH_BUFFER_BIT);for(let e=0;e<P.length;++e)P[e].render();drawBuffers(),embedded&&(context.clearRect(0,0,canvas.width,canvas.height),context.drawImage(offscreen,0,0)),remesh=!1}function tick(){requestAnimationFrame(tick),redraw&&(draw(),redraw=!1)}function setDimensions(e,t,i,a){let r=e/t,n=1/lastzoom,s=(i/e+viewportshift[0])*lastzoom,o=(a/t+viewportshift[1])*lastzoom;if(orthographic){let e=B[0]-b[0],t=B[1]-b[1];if(e<t*r){let e=.5*t*r*n,i=2*e*s,a=t*n*o;viewParam.xmin=-e-i,viewParam.xmax=e-i,viewParam.ymin=b[1]*n-a,viewParam.ymax=B[1]*n-a}else{let t=.5*e/(r*Zoom),i=e*n*s,a=2*t*o;viewParam.xmin=b[0]*n-i,viewParam.xmax=B[0]*n-i,viewParam.ymin=-t-a,viewParam.ymax=t-a}}else{let e=H*n,t=e*r,i=2*t*s,a=2*e*o;viewParam.xmin=-t-i,viewParam.xmax=t-i,viewParam.ymin=-e-a,viewParam.ymax=e-a}}function setProjection(){setDimensions(canvasWidth,canvasHeight,shift.x,shift.y),(orthographic?mat4.ortho:mat4.frustum)(projMat,viewParam.xmin,viewParam.xmax,viewParam.ymin,viewParam.ymax,-viewParam.zmax,-viewParam.zmin),updateViewMatrix()}function initProjection(){H=-Math.tan(.5*angle)*B[2],center.x=center.y=0,center.z=.5*(b[2]+B[2]),lastzoom=Zoom=Zoom0,viewParam.zmin=b[2],viewParam.zmax=B[2],shift.x=shift.y=0}function setViewport(){gl.viewportWidth=canvasWidth,gl.viewportHeight=canvasHeight,gl.viewport(0,0,gl.viewportWidth,gl.viewportHeight),gl.scissor(0,0,gl.viewportWidth,gl.viewportHeight)}function setCanvas(){canvas.width=canvasWidth,canvas.height=canvasHeight,embedded&&(offscreen.width=canvasWidth,offscreen.height=canvasHeight),size2=Math.hypot(canvasWidth,canvasHeight),halfCanvasWidth=.5*canvasWidth,halfCanvasHeight=.5*canvasHeight}function setsize(e,t){e>maxViewportWidth&&(e=maxViewportWidth),t>maxViewportHeight&&(t=maxViewportHeight),shift.x*=e/canvasWidth,shift.y*=t/canvasHeight,canvasWidth=e,canvasHeight=t,setCanvas(),setViewport(),home()}function expand(){setsize(canvasWidth*resizeStep+.5,canvasHeight*resizeStep+.5)}function shrink(){setsize(Math.max(canvasWidth/resizeStep+.5,1),Math.max(canvasHeight/resizeStep+.5,1))}function webGLStart(){if(canvas=document.getElementById("Asymptote"),embedded=window.parent.document!=document,initGL(),absolute&&!embedded)canvasWidth*=window.devicePixelRatio,canvasHeight*=window.devicePixelRatio;else{0==canvas.width&&(canvas.width=Math.max(window.innerWidth-windowTrim,windowTrim)),0==canvas.height&&(canvas.height=Math.max(window.innerHeight-windowTrim,windowTrim));let e=canvasWidth/canvasHeight;canvas.width>canvas.height*e?canvas.width=Math.min(canvas.height*e,canvas.width):canvas.height=Math.min(canvas.width/e,canvas.height),canvas.width>0&&(canvasWidth=canvas.width),canvas.height>0&&(canvasHeight=canvas.height)}setCanvas(),ArcballFactor=1+8*Math.hypot(viewportmargin[0],viewportmargin[1])/size2,viewportshift[0]/=Zoom0,viewportshift[1]/=Zoom0,gl.enable(gl.BLEND),gl.blendFunc(gl.SRC_ALPHA,gl.ONE_MINUS_SRC_ALPHA),gl.enable(gl.DEPTH_TEST),gl.enable(gl.SCISSOR_TEST),setViewport(),home(),canvas.onmousedown=handleMouseDown,document.onmouseup=handleMouseUpOrTouchEnd,document.onmousemove=handleMouseMove,canvas.onkeydown=handleKey,canvas.addEventListener("wheel",handleMouseWheel,!1),canvas.addEventListener("touchstart",handleTouchStart,!1),canvas.addEventListener("touchend",handleMouseUpOrTouchEnd,!1),canvas.addEventListener("touchcancel",handleMouseUpOrTouchEnd,!1),canvas.addEventListener("touchleave",handleMouseUpOrTouchEnd,!1),canvas.addEventListener("touchmove",handleTouchMove,!1),document.addEventListener("keydown",handleKey,!1),tick()}