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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /graphics/asymptote/examples/soccerball.asy
Initial commit
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diff --git a/graphics/asymptote/examples/soccerball.asy b/graphics/asymptote/examples/soccerball.asy
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+import graph3;
+size(400);
+currentlight.background=palegreen;
+
+defaultrender=render(compression=Zero,merge=true);
+
+real c=(1+sqrt(5))/2;
+
+triple[] z={(c,1,0),(-c,1,0),(-c,-1,0),(c,-1,0)};
+triple[] x={(0,c,1),(0,-c,1),(0,-c,-1),(0,c,-1)};
+triple[] y={(1,0,c),(1,0,-c),(-1,0,-c),(-1,0,c)};
+
+triple[][] Q={
+ {z[0],y[1],x[3],x[0],y[0],z[3]},
+ {z[1],x[0],x[3],y[2],z[2],y[3]},
+ {z[2],z[1],y[2],x[2],x[1],y[3]},
+ {z[3],z[0],y[0],x[1],x[2],y[1]},
+ {x[0],x[3],z[1],y[3],y[0],z[0]},
+ {x[1],x[2],z[2],y[3],y[0],z[3]},
+ {x[2],x[1],z[3],y[1],y[2],z[2]},
+ {x[3],x[0],z[0],y[1],y[2],z[1]},
+ {y[0],y[3],x[1],z[3],z[0],x[0]},
+ {y[1],y[2],x[2],z[3],z[0],x[3]},
+ {y[2],y[1],x[3],z[1],z[2],x[2]},
+ {y[3],y[0],x[0],z[1],z[2],x[1]}
+};
+
+int nArc=4;
+
+path3 p=Arc(O,Q[0][0],Q[0][1],nArc);
+real R=abs(point(p,reltime(p,1/3)));
+
+triple[][] P;
+for(int i=0;i < Q.length;++i){
+ P[i]=new triple[] ;
+ for(int j=0;j < Q[i].length;++j){
+ P[i][j]=Q[i][j]/R;
+ }
+}
+
+// FIXME: Use a baryicentric coordinate mesh
+surface sphericaltriangle(triple center, triple A, triple B, triple C,
+ int nu=3, int nv=nu) {
+ path3 tri1=Arc(center,A,B,nArc);
+ path3 tri2=Arc(center,A,C,nArc);
+ path3 tri3=Arc(center,B,C,nArc);
+ triple tri(pair p) {
+ path3 cr=Arc(O,relpoint(tri2,p.x),relpoint(tri3,p.x),nArc);
+ return relpoint(cr,p.y);
+ };
+
+ return surface(tri,(0,0),(1-sqrtEpsilon,1),nu,nv,Spline);
+}
+
+for(int i=0;i < P.length;++i){
+ triple[] pentagon=sequence(new triple(int k) {
+ path3 p=Arc(O,P[i][0],P[i][k+1],nArc);
+ return point(p,reltime(p,1/3));
+ },5);
+ pentagon.cyclic=true;
+ draw(sequence(new path3(int k) {
+ return Arc(O,pentagon[k],pentagon[k+1],nArc);},5),linewidth(2pt));
+ triple M=unit(sum(pentagon)/5);
+ for(int i=0;i < 5;++i){
+ surface sf=sphericaltriangle(O,pentagon[i],M,pentagon[i+1]);
+ draw(sf,black);
+ }
+}
+
+for(int i=0;i < P.length;++i) {
+ for(int j=1;j <= 5;++j) {
+ triple K=P[i][0];
+ triple A=P[i][j];
+ triple B=P[i][(j % 5)+1];
+ path3[] p={Arc(O,K,A,nArc),Arc(O,A,B,nArc),Arc(O,B,K,nArc)};
+ draw(subpath(p[0],reltime(p[0],1/3),reltime(p[0],2/3)),linewidth(4pt));
+ triple[] hexagon={point(p[0],reltime(p[0],1/3)),
+ point(p[0],reltime(p[0],2/3)),
+ point(p[1],reltime(p[1],1/3)),
+ point(p[1],reltime(p[1],2/3)),
+ point(p[2],reltime(p[2],1/3)),
+ point(p[2],reltime(p[2],2/3))};
+ hexagon.cyclic=true;
+ triple M=unit(sum(hexagon)/6);
+ for(int i=0;i < 6;++i) {
+ surface sf=sphericaltriangle(O,hexagon[i],M,hexagon[i+1]);
+ draw(sf,white);
+ }
+ }
+}