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-rw-r--r--Master/texmf/asymptote/graph3.asy208
1 files changed, 30 insertions, 178 deletions
diff --git a/Master/texmf/asymptote/graph3.asy b/Master/texmf/asymptote/graph3.asy
index 8fe6c9ed5c6..c2630e10f11 100644
--- a/Master/texmf/asymptote/graph3.asy
+++ b/Master/texmf/asymptote/graph3.asy
@@ -1509,6 +1509,27 @@ path3[] segment(triple[] v, bool[] cond, interpolate3 join=operator --)
segment.length);
}
+bool uperiodic(triple[][] a) {
+ int n=a.length;
+ if(n == 0) return false;
+ int m=a[0].length;
+ triple[] a0=a[0];
+ triple[] a1=a[n-1];
+ real epsilon=sqrtEpsilon*norm(a);
+ for(int j=0; j < m; ++j)
+ if(abs(a0[j]-a1[j]) > epsilon) return false;
+ return true;
+}
+bool vperiodic(triple[][] a) {
+ int n=a.length;
+ if(n == 0) return false;
+ int m=a[0].length-1;
+ real epsilon=sqrtEpsilon*norm(a);
+ for(int i=0; i < n; ++i)
+ if(abs(a[i][0]-a[i][m]) > epsilon) return false;
+ return true;
+}
+
// return the surface described by a matrix f
surface surface(triple[][] f, bool[][] cond={})
{
@@ -1533,6 +1554,7 @@ surface surface(triple[][] f, bool[][] cond={})
}
surface s=surface(count);
+ s.index=new int[nx][ny];
int k=-1;
for(int i=0; i < nx; ++i) {
bool[] condi,condp;
@@ -1542,122 +1564,18 @@ surface surface(triple[][] f, bool[][] cond={})
}
triple[] fi=f[i];
triple[] fp=f[i+1];
+ int[] indexi=s.index[i];
for(int j=0; j < ny; ++j) {
if(all || (condi[j] && condi[j+1] && condp[j] && condp[j+1]))
s.s[++k]=patch(new triple[] {fi[j],fp[j],fp[j+1],fi[j+1]});
- }
- }
- return s;
-}
-
-private surface bispline(real[][] z, real[][] p, real[][] q, real[][] r,
- real[] x, real[] y, bool[][] cond={})
-{ // z[i][j] is the value at (x[i],y[j])
- // p and q are the first derivatives with respect to x and y, respectively
- // r is the second derivative ddu/dxdy
- int n=x.length-1;
- int m=y.length-1;
-
- bool all=cond.length == 0;
-
- int count;
- if(all)
- count=n*m;
- else {
- count=0;
- for(int i=0; i < n; ++i) {
- bool[] condi=cond[i];
- for(int j=0; j < m; ++j)
- if(condi[j]) ++count;
- }
- }
-
- surface g=surface(count);
- int k=-1;
- for(int i=0; i < n; ++i) {
- bool[] condi=all ? null : cond[i];
- real xi=x[i];
- real[] zi=z[i];
- real[] zp=z[i+1];
- real[] ri=r[i];
- real[] rp=r[i+1];
- real[] pi=p[i];
- real[] pp=p[i+1];
- real[] qi=q[i];
- real[] qp=q[i+1];
- real xp=x[i+1];
- real hx=(xp-xi)/3;
- for(int j=0; j < m; ++j) {
- real yj=y[j];
- real yp=y[j+1];
- if(all || condi[j]) {
- triple[][] P=array(4,array(4,O));
- real hy=(yp-yj)/3;
- real hxy=hx*hy;
- // first x and y directions
- for(int k=0; k < 4; ++k) {
- P[k][0] += xi*X;
- P[0][k] += yj*Y;
- P[k][1] += (xp+2*xi)/3*X;
- P[1][k] += (yp+2*yj)/3*Y;
- P[k][2] += (2*xp+xi)/3*X;
- P[2][k] += (2*yp+yj)/3*Y;
- P[k][3] += xp*X;
- P[3][k] += yp*Y;
- }
- // now z, first the value
- P[0][0] += zi[j]*Z;
- P[0][3] += zp[j]*Z;
- P[3][0] += zi[j+1]*Z;
- P[3][3] += zp[j+1]*Z;
- // 2nd, first derivative
- P[0][1] += (P[0][0].z+hx*pi[j])*Z;
- P[3][1] += (P[3][0].z+hx*pi[j+1])*Z;
- P[0][2] += (P[0][3].z-hx*pp[j])*Z;
- P[3][2] += (P[3][3].z-hx*pp[j+1])*Z;
- P[1][0] += (P[0][0].z+hy*qi[j])*Z;
- P[1][3] += (P[0][3].z+hy*qp[j])*Z;
- P[2][0] += (P[3][0].z-hy*qi[j+1])*Z;
- P[2][3] += (P[3][3].z-hy*qp[j+1])*Z;
- // 3nd, second derivative
- P[1][1] += (P[1][0].z+P[0][1].z-P[0][0].z+hxy*ri[j])*Z;
- P[2][1] += (P[2][0].z+P[3][1].z-P[3][0].z-hxy*ri[j+1])*Z;
- P[1][2] += (P[0][2].z+P[1][3].z-P[0][3].z-hxy*rp[j])*Z;
- P[2][2] += (P[3][2].z+P[2][3].z-P[3][3].z+hxy*rp[j+1])*Z;
- g.s[++k]=patch(P);
+ indexi[j]=k;
}
- }
}
- return g;
-}
-// return the surface described by a real matrix f, interpolated with
-// xsplinetype and ysplinetype.
-surface surface(real[][] f, real[] x, real[] y,
- splinetype xsplinetype=null, splinetype ysplinetype=xsplinetype,
- bool[][] cond={})
-{
- real epsilon=sqrtEpsilon*max(abs(y));
- if(xsplinetype == null)
- xsplinetype=(abs(x[0]-x[x.length-1]) <= epsilon) ? periodic : notaknot;
- if(ysplinetype == null)
- ysplinetype=(abs(y[0]-y[y.length-1]) <= epsilon) ? periodic : notaknot;
- int n=x.length; int m=y.length;
- real[][] ft=transpose(f);
- real[][] tp=new real[m][];
- for(int j=0; j < m; ++j)
- tp[j]=xsplinetype(x,ft[j]);
- real[][] q=new real[n][];
- for(int i=0; i < n; ++i)
- q[i]=ysplinetype(y,f[i]);
- real[][] qt=transpose(q);
- real[] d1=xsplinetype(x,qt[0]);
- real[] d2=xsplinetype(x,qt[m-1]);
- real[][] r=new real[n][];
- real[][] p=transpose(tp);
- for(int i=0; i < n; ++i)
- r[i]=clamped(d1[i],d2[i])(y,p[i]);
- return bispline(f,p,q,r,x,y,cond);
+ if(uperiodic(f)) s.ucyclic(true);
+ if(vperiodic(f)) s.vcyclic(true);
+
+ return s;
}
// return the surface described by a real matrix f, interpolated with
@@ -1738,74 +1656,8 @@ surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu,
splinetype[] usplinetype, splinetype[] vsplinetype=Spline,
bool cond(pair z)=null)
{
- real[] upt=uniform(a.x,b.x,nu);
- real[] vpt=uniform(a.y,b.y,nv);
- real[] ipt=sequence(nu+1);
- real[] jpt=sequence(nv+1);
- real[][] fx=new real[nu+1][nv+1];
- real[][] fy=new real[nu+1][nv+1];
- real[][] fz=new real[nu+1][nv+1];
-
- bool[][] active;
- bool all=cond == null;
- if(!all) active=new bool[nu+1][nv+1];
-
- real norm;
- for(int i=0; i <= nu; ++i) {
- real upti=upt[i];
- real[] fxi=fx[i];
- real[] fyi=fy[i];
- real[] fzi=fz[i];
- bool[] activei=all ? null : active[i];
- for(int j=0; j <= nv; ++j) {
- pair z=(upti,vpt[j]);
- triple f=(all || (activei[j]=cond(z))) ? f(z) : O;
- norm=max(norm,abs(f));
- fxi[j]=f.x;
- fyi[j]=f.y;
- fzi[j]=f.z;
- }
- }
-
- real epsilon=sqrtEpsilon*norm;
-
- if(usplinetype.length == 0) {
- bool uperiodic(real[][] a) {
- for(int j=0; j < nv; ++j)
- if(abs(a[0][j]-a[nu][j]) > epsilon) return false;
- return true;
- }
- usplinetype=new splinetype[] {uperiodic(fx) ? periodic : notaknot,
- uperiodic(fy) ? periodic : notaknot,
- uperiodic(fz) ? periodic : notaknot};
- } else if(usplinetype.length != 3) abort("usplinetype must have length 3");
-
- if(vsplinetype.length == 0) {
- bool vperiodic(real[][] a) {
- for(int i=0; i < nu; ++i)
- if(abs(a[i][0]-a[i][nv]) > epsilon) return false;
- return true;
- }
- vsplinetype=new splinetype[] {vperiodic(fx) ? periodic : notaknot,
- vperiodic(fy) ? periodic : notaknot,
- vperiodic(fz) ? periodic : notaknot};
- } else if(vsplinetype.length != 3) abort("vsplinetype must have length 3");
-
- surface sx=surface(fx,ipt,jpt,usplinetype[0],vsplinetype[0],active);
- surface sy=surface(fy,ipt,jpt,usplinetype[1],vsplinetype[1],active);
- surface sz=surface(fz,ipt,jpt,usplinetype[2],vsplinetype[2],active);
-
- surface s=surface(sx.s.length);
- for(int k=0; k < sx.s.length; ++k) {
- triple[][] Q=new triple[4][4];
- for(int i=0; i < 4 ; ++i) {
- for(int j=0; j < 4 ; ++j) {
- Q[i][j]=(sx.s[k].P[i][j].z,sy.s[k].P[i][j].z,sz.s[k].P[i][j].z);
- }
- s.s[k]=patch(Q);
- }
- }
- return s;
+ return surface(f,uniform(a.x,b.x,nu),uniform(a.y,b.y,nv),
+ usplinetype,vsplinetype,cond);
}
// return the surface described by a real function f over box(a,b),
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-17 09:39:58 +0000