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private import math;
import three;
real epsilon=10*realEpsilon;
// Routines for hidden surface removal (via binary space partition):
// Structure face is derived from picture.
struct face {
picture pic;
transform t;
frame fit;
triple normal,point;
triple min,max;
void operator init(path3 p) {
this.normal=normal(p);
if(this.normal == O) abort("path is linear");
this.point=point(p,0);
min=min(p);
max=max(p);
}
face copy() {
face f=new face;
f.pic=pic.copy();
f.t=t;
f.normal=normal;
f.point=point;
f.min=min;
f.max=max;
add(f.fit,fit);
return f;
}
}
picture operator cast(face f) {return f.pic;}
face operator cast(path3 p) {return face(p);}
struct line {
triple point;
triple dir;
}
private line intersection(face a, face b)
{
line L;
L.point=intersectionpoint(a.normal,a.point,b.normal,b.point);
L.dir=unit(cross(a.normal,b.normal));
return L;
}
struct half {
pair[] left,right;
// Sort the points in the pair array z according to whether they lie on the
// left or right side of the line L in the direction dir passing through P.
// Points exactly on L are considered to be on the right side.
// Also push any points of intersection of L with the path operator --(... z)
// onto each of the arrays left and right.
void operator init(pair dir, pair P ... pair[] z) {
pair lastz;
pair invdir=dir != 0 ? 1/dir : 0;
bool left,last;
for(int i=0; i < z.length; ++i) {
left=(invdir*z[i]).y > (invdir*P).y;
if(i > 0 && last != left) {
pair w=extension(P,P+dir,lastz,z[i]);
this.left.push(w);
this.right.push(w);
}
if(left) this.left.push(z[i]);
else this.right.push(z[i]);
last=left;
lastz=z[i];
}
}
}
struct splitface {
face back,front;
}
// Return the pieces obtained by splitting face a by face cut.
splitface split(face a, face cut, projection P)
{
splitface S;
void nointersection() {
if(abs(dot(a.point-P.camera,a.normal)) >=
abs(dot(cut.point-P.camera,cut.normal))) {
S.back=a;
S.front=null;
} else {
S.back=null;
S.front=a;
}
}
if(P.infinity) {
P=P.copy();
static real factor=1/sqrtEpsilon;
P.camera *= factor*max(abs(a.min),abs(a.max),
abs(cut.min),abs(cut.max));
}
if((abs(a.normal-cut.normal) < epsilon ||
abs(a.normal+cut.normal) < epsilon)) {
nointersection();
return S;
}
line L=intersection(a,cut);
if(dot(P.camera-L.point,P.camera-P.target) < 0) {
nointersection();
return S;
}
pair point=a.t*project(L.point,P);
pair dir=a.t*project(L.point+L.dir,P)-point;
pair invdir=dir != 0 ? 1/dir : 0;
triple apoint=L.point+cross(L.dir,a.normal);
bool left=(invdir*(a.t*project(apoint,P))).y >= (invdir*point).y;
real t=intersect(apoint,P.camera,cut.normal,cut.point);
bool rightfront=left ^ (t <= 0 || t >= 1);
face back=a, front=a.copy();
pair max=max(a.fit);
pair min=min(a.fit);
half h=half(dir,point,max,(min.x,max.y),min,(max.x,min.y),max);
if(h.right.length == 0) {
if(rightfront) front=null;
else back=null;
} else if(h.left.length == 0) {
if(rightfront) back=null;
else front=null;
}
if(front != null)
clip(front.fit,operator --(... rightfront ? h.right : h.left)--cycle,
zerowinding);
if(back != null)
clip(back.fit,operator --(... rightfront ? h.left : h.right)--cycle,
zerowinding);
S.back=back;
S.front=front;
return S;
}
// A binary space partition
struct bsp
{
bsp back;
bsp front;
face node;
// Construct the bsp.
void operator init(face[] faces, projection P) {
if(faces.length != 0) {
this.node=faces.pop();
face[] front,back;
for(int i=0; i < faces.length; ++i) {
splitface split=split(faces[i],this.node,P);
if(split.front != null) front.push(split.front);
if(split.back != null) back.push(split.back);
}
this.front=bsp(front,P);
this.back=bsp(back,P);
}
}
// Draw from back to front.
void add(frame f) {
if(back != null) back.add(f);
add(f,node.fit,group=true);
if(labels(node.fit)) layer(f); // Draw over any existing TeX layers.
if(front != null) front.add(f);
}
}
void add(picture pic=currentpicture, face[] faces,
projection P=currentprojection)
{
int n=faces.length;
face[] Faces=new face[n];
for(int i=0; i < n; ++i)
Faces[i]=faces[i].copy();
pic.add(new void (frame f, transform t, transform T,
pair m, pair M) {
// Fit all of the pictures so we know their exact sizes.
face[] faces=new face[n];
for(int i=0; i < n; ++i) {
faces[i]=Faces[i].copy();
face F=faces[i];
F.t=t*T*F.pic.T;
F.fit=F.pic.fit(t,T*F.pic.T,m,M);
}
bsp bsp=bsp(faces,P);
if(bsp != null) bsp.add(f);
});
for(int i=0; i < n; ++i) {
picture F=Faces[i].pic;
pic.userBox3(F.userMin3(), F.userMax3());
pic.bounds.append(F.T, F.bounds);
// The above 2 lines should be replaced with a routine in picture which
// copies only sizing data from another picture.
}
}
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