|
|
import contour3; import animate; // settings.tex="pdflatex"; // settings.outformat="pdf"; size(10cm); currentprojection=orthographic(15,8,10); animation A; A.global=false; typedef real fct3(real,real,real); fct3 F(real t) { return new real(real x, real y, real z){return x^2+y^2-t*z^2+t-1;}; } int n=15; picture pic; real tmin=0.1, tmax=2; real step=(tmax-tmin)/n; draw(box((-5,-5,-5),(5,5,5))); for (int i=0; i < n; ++i) { save(); draw(contour3(F(tmin+i*step),(-5,-5,-5),(5,5,5),15),lightblue); pic.erase(); add(pic,bbox(5mm,FillDraw(lightyellow))); A.add(pic); restore(); } A.movie();
|
|
import geometry_dev; import animate; settings.tex="pdflatex"; animation A; size(12cm); for (int a=1; a < 20; ++a) { save(); point P=(-4.5,0); dot(P); inversion inv=inversion(1,P); line l1=line((0,0),(-0.35,1)), l2=line((0,0),(0.35,1)); path g1=inv*l1, g2=inv*l2; fill(g1^^g2,evenodd+lightgrey); draw(g1,linewidth(bp)); draw(g2,linewidth(bp)); for (int i:new int[]{-1,1}) { point P=(0,3i/a); triangle t=triangle(shift(P)*hline,l1,l2); int n=a; for (int j=0; j <= n; ++j) { circle C=excircle(t.AB); t=triangle(shift(angpoint(C,i*90))*hline,l1,l2); circle Cp=inv*C; path g=Cp; fill(g,0.95*yellow); draw(g,bp+red); draw(g,blue); } } picture pic; add(pic,bbox(5mm,Fill(rgb(0.95,0.95,0.8)))); A.add(pic); restore(); } A.pdf(keep=true);
|
|
import geometry_dev; import animate; animation A; size(15cm); int nAnim=75; int nCircle=6; real astep=360/nAnim; inversion inv=inversion((-1,-2),1); line L1=line(N,S); circle C=inv*L1; point center=C.C; for (int i=-nAnim; i < nAnim; ++i) { real r; r=0.001+4*(i/nAnim)^2; line L2=shift(2*r*E)*L1; transform T=shift(0,-2*r); transform R=rotate(astep*i,center); circle C0=circle(r*E+nCircle/2*sqrt(r)*N,r); circle[] Ci=sequence(new circle(int i){return T^i*C0;}, nCircle); fill(R*(path)C, 0.3*blue); circle Cl=R*(inv*L2); transform dsh=shift(Cl.r/3*unit(center-Cl.C)); radialshade((path)Cl,white,dsh*Cl.C,0,black,dsh*Cl.C,Cl.r); for (int i=0; i < Ci.length; ++i) { circle Ct=inv*Ci[i]; transform dsh=shift(Ct.r/3*unit(center-Ct.C)); radialshade(R*(path)Ct,red,dsh*R*Ct.C,0,black,dsh*R*Ct.C,Ct.r); } A.add(); erase(); } A.movie(BBox(2mm,Fill(black)));
|
|
import geometry_dev; import animate; settings.tex="pdflatex"; animation Anim; size(10cm,0); circle C=circle(origin,1); draw(C); point A=point(C,0), B, M; guide locus; for (real a=0.001; a < 360; a += 5) { save(); B=angpoint(C,a); triangle t=triangle(origin,A,B); draw(t); draw(incircle(t), bp+0.8*blue); triangle intouch=intouch(t); draw(intouch, dot); M=intouch(t.AC); label("$N$", Label("$M$", 0.8*red), "$P$", intouch); dot(M, 0.8*red); locus=locus..M; draw(locus, bp+0.8*red); Anim.add(); restore(); } Anim.pdf(keep=true);
|
|
/* Author: Nathan Carter. Explanation Here. */ include "./makecd.asy"; import animate; // settings.tex="pdflatex"; settings.keep=true; animation A; A.global=false; real length = 4; // seconds int fps = 50; real rad = 6; real ht = 2; real pixsz = 300; real ptsz = 1; int loops = 6; pen border = black; real frames = length*fps; picture tmp; size(pixsz); for (int i=100 ; i < 100+frames ; ++i) { save(); add(CayleyDiagram(nodeLocs, arrows, orders, arrowPens, cam = (rad*cos(2*i*pi/frames),rad*sin(2*i*pi/frames),ht), arrowThickness = 2, nodeSize = 0.02, arrowMargin = 1mm, depthCueing = true )); draw(box((-ptsz/2,-ptsz/2), (ptsz/2,ptsz/2)), border); A.add(); write( "Did " + (string)(i-99) + " out of " + (string)frames ); restore(); } write( "Merging..." ); A.movie(delay=(int)(100/fps)); write( "Done." );
|
|
//Author Jens Schwaiger. import polyhedron; import animate; settings.tex="pdflatex"; settings.outformat="pdf"; size(16cm); currentprojection=perspective(5,4,2); currentlight=(5,4,2); polyhedron Plane; Plane[0]=(-2,-2,-1.5)--(2.5,-2,-1.5)--(2.5,2.5,-1.5)--(-2,2.5,-1.5)--cycle; Plane[1]=(-2,-2,-1.5)--(-2,2.5,-1.5)--(-2,2.5,0)--(-2,-2,0)--cycle; int n=180; pen[] drawcol={black+1bp}; pen[] fcol1={0.8*red,0.8*blue,0.8*green,orange,heavycyan,gray}; animation anim; triple[] posofsolids; real angle; for(int janim=0; janim < n; ++janim){ for(int i=0; i < 5; ++i) { angle=2pi/5*i+2pi*janim/n; posofsolids[i]=(1.7*cos(angle)+1,1.7*sin(angle)+1,0); } transform3 T=rotate(-degrees(2*angle),Z); polyhedron[] parr={ shift(posofsolids[0])*T*icosahedron, shift(posofsolids[1])*T*dodecahedron, shift(posofsolids[2])*T*cube, shift(posofsolids[3])*T*rotate(45,Z)*octahedron, shift(posofsolids[4])*T*rotate(90,Z)*tetrahedron, Plane }; save(); filldraw(parr,fcol=fcol1,dcol=drawcol,op=0.9); anim.add(); restore(); } anim.movie(BBox(3mm,darkblue+3bp+miterjoin,FillDraw(paleblue)));
|
|
import polyhedron; import animation; settings.tex="pdflatex"; settings.outformat="pdf"; // for opacity animation A; size(8cm); // currentprojection=perspective(7,6,4); //if you want perspectivic look currentprojection=orthographic(1,0.5,1); //if you want othographic look currentlight=(1,1,2); // currentlight=nolight; int col=0; pen[] fcol={palegreen+paleblue+lightgrey}; fcol.cyclic(true); polyhedron[] parr; for (int i=0; i < 360; i += 2) { parr[0]=rotate(i,Z)*rhombicosDodec; save(); filldraw(parr,fcol,op=0.9); A.add(); restore(); } A.movie();
|
|
import graph3; import animation; import solids; animation A; A.global=false; int nbpts=500; real q=2/5; real pas=5*2*pi/nbpts; int angle=3; real R=3; unitsize(1cm); real x(real t){return R*cos(q*t)*cos(t);} real y(real t){return R*cos(q*t)*sin(t);} real z(real t){return R*sin(q*t);} triple[] P; real t=-pi; for (int i=0; i<nbpts; ++i) { t+=pas; P.push((x(t),y(t),z(t))); } currentprojection=orthographic((0,5,2)); currentlight=(3,3,5); pen p=rgb(0.1,0.1,0.58); transform3 t=rotate(angle,(0,0,0),(1,0.25,0.25)); filldraw(box((-R-0.5,-R-0.5),(R+0.5,R+0.5)), p, 3mm+black+miterjoin); revolution r=sphere(O,R); r.fill(p); for (int phi=0; phi<360; phi+=angle) { bool[] back,front; save(); for (int i=0; i<nbpts; ++i) { P[i]=t*P[i]; bool test=dot(P[i],currentprojection.camera) > 0; front.push(test); } draw(segment(P,front,operator ..),linewidth(1mm)); draw(segment(P,!front,operator ..),grey); A.add(); restore(); } A.movie(options="-density 200 -resample 96 -quality 75 -depth 8 -strip");
|
|
import animation; import graph; settings.tex="pdflatex"; settings.outformat="pdf"; unitsize(x=2cm,y=1.5cm); typedef real realfcn(real); real lambda=4; real T=2; real [] k=new real[3]; real [] w=new real[3]; k[0]=2pi/lambda; w[0]=2pi/T; real dk=-.5; k[1]=k[0]-dk; k[2]=k[0]+dk; real dw=1; w[1]=w[0]-dw; w[2]=w[0]+dw; real vp=w[1]/k[1]; real vg=dw/dk; realfcn F(real x) { return new real(real t) { return cos(k[1]*x-w[1]*t)+cos(k[2]*x-w[2]*t); }; }; realfcn G(real x) { return new real(real t) { return 2*cos(0.5*(k[2]-k[1])*x+0.5*(w[1]-w[2])*t); }; }; realfcn operator -(realfcn f) {return new real(real t) {return -f(t);};}; animation A; real tmax=abs(2pi/dk); real xmax=abs(2pi/dw); pen envelope=0.8*blue; pen fillpen=lightgrey; int n=50; real step=tmax/(n-1); for(int i=0; i < n; ++i) { save(); real t=i*step; real a=xmax*t/tmax-xmax/pi; real b=xmax*t/tmax; path f=graph(F(t),a,b); path g=graph(G(t),a,b); path h=graph(-G(t),a,b); fill(buildcycle(reverse(f),g),fillpen); draw(f); draw(g,envelope); draw(h,envelope); A.add(); restore(); } for(int i=0; i < n; ++i) { save(); real t=i*step; real a=-xmax/pi; real b=xmax; path f=graph(F(t),a,b); path g=graph(G(t),a,b); path h=graph(-G(t),a,b); path B=box((-xmax/pi,-2),(xmax,2)); fill(buildcycle(reverse(f),g,B),fillpen); fill(buildcycle(f,g,reverse(B)),fillpen); draw(f); draw(g,envelope); draw(h,envelope); A.add(); restore(); } A.movie();
|
|
import geometry_dev; import animate; // settings.tex="pdflatex"; // settings.outformat="pdf"; animation anim; size(12cm); ellipse ellipse(point F1, real a, real c, point tgt, vector dir) { line d=line(tgt,tgt+dir); line bis=perpendicular(tgt,d); line l=line(tgt,reflect(bis)*F1); point[] F=intersectionpoints(circle(F1,2*c),l); real a0=abs(F1-tgt)+abs(F[0]-tgt); real a1=F.length > 1 ? abs(F1-tgt)+abs(F[1]-tgt) : 0; return abs(a0/2-a) < 1e-5 ? ellipse(F1,F[0],a0/2) : ellipse(F1,F[1],a1/2); } point F1=(0,0), F2=(0,-3); dot("F",F1); ellipse el1=ellipse(F1,F2,2), el2; point Fp1=shift(0,2*el1.a)*F1; dot("F'",Fp1); line tgt, saxe=line(F1,false,-F2); for (int i=0; i < 360; i += 5) { save(); ellipse el=rotate(i,F1)*el1; point M=intersectionpoints(el,saxe)[0]; tgt=tangents(el,M)[0]; draw(tgt, 0.8*red); el2=ellipse(Fp1,el1.a,el1.c,M,tgt.u); draw(el2^^el, linewidth(bp)); anim.add(); restore(); } erase(); anim.movie();
|
|
import geometry_dev; import animate; settings.tex="pdflatex"; settings.outformat="pdf"; animation anim; size(12cm); ellipse ellipse(point F1, real a, real c, point tgt, vector dir) { line d=line(tgt,tgt+dir); line bis=perpendicular(tgt,d); line l=line(tgt,reflect(bis)*F1); point[] F=intersectionpoints(circle(F1,2*c),l); real a0=abs(F1-tgt)+abs(F[0]-tgt); real a1=F.length > 1 ? abs(F1-tgt)+abs(F[1]-tgt) : 0; return abs(a0/2-a) < 1e-5 ? ellipse(F1,F[0],a0/2) : ellipse(F1,F[1],a1/2); } point F1=(0,0), F2=(10,0); dot("F",F2); ellipse el1=ellipse(F1,F2,6), el2; draw(el1, linewidth(bp)); point Fp2=shift(2*el1.a,0)*F2; line tgt, saxe; pen[] p=new pen[]{0.8*green,0.8*blue,0.8*yellow,cyan}; path[] locus=sequence(new path(int i){return nullpath;},p.length); real t=1/(p.length-1); bool initlocus=true; for (int i=0; i < 360; i += 1) { save(); point Fm=rotate(i,F2)*Fp2; dot("F'",Fm); draw(Fm--F2, linewidth(2bp)); point M=intersectionpoints(el1, line(F2,false,Fm))[0]; tgt=tangents(el1,M)[0]; draw(tgt, 0.8*red); el2=ellipse(Fm, el1.a, el1.c, M, tgt.u); draw(el2.F1--el2.F2); for (int j=0; j < p.length; ++j) { point P=point(segment(el2.F2,Fm),0.5+j*t/2); locus[j]=initlocus ? P : locus[j]--P; dot(P, p[j]); draw(locus[j], bp+p[j]); } dot(el2.F2); draw(el2, linewidth(bp)); anim.add(); restore(); initlocus=false; } erase(); anim.movie();
|
|
// From an idea posted by Fabrice Couvreur import geometry_dev; import animate; settings.tex="pdflatex"; settings.outformat="pdf"; point A=(0,0), B=(8,0), C=(8,10); unitsize(5cm/B.x,5cm/C.y); animation Anim,Anim1; path locus; triangle t=triangle(A,B,C); transform proj=projection(t.BC); draw(t,linewidth(bp)); label(t); segment s=segment(t.AB); line l1 =line(t.BC); int n=50; // Points number of the locus real a=0, step=1/(n-1); for (int i=0; i < n; ++i) { save(); // Geometry part point M=point(s,a); line l2=parallel(M,l1); point Np=intersectionpoint(l2,t.AC); point P=proj*Np; dot("$M$",M,S,0.8*red); dot("$P$",P,E,0.8*red); dot("$N$",Np,W,0.8*red); fill(M--Np--P--B--cycle,0.8*red); perpendicularmark(t.BC,t.BA); Anim.add(); // Anim contain only the geometry part restore(); // Graph part picture gph; // picture of the graph unitsize(gph,5cm/B.x,4cm/C.y); // units for the graph show(gph,currentcoordsys); point Sp=(a*abs(B-A),abs(M-B)*abs(M-Np)); locus=locus..Sp; draw(gph,locus, bp+0.8*red); Anim1.add(gph); // Anim1 contain only the graph part a += step; } Anim1.export(); // make all Anim1 pictures to the same size. Anim1.purge(); for (int i=0; i < Anim.pictures.length; ++i) { // draw axis on all pictures of Anim1 draw(Anim1.pictures[i],Label("$x$",align=S,position=EndPoint),hline,Arrow); draw(Anim1.pictures[i],Label("$y$",align=W,position=EndPoint),vline,Arrow); // add each graph to the corresponding geometric picture add(Anim.pictures[i],Anim1.pictures[i].fit(),1.25*B); } Anim.movie();
|
|
/*Inspiration*/ import Lsystem; import animate; animation A; settings.tex="pdflatex"; settings.outformat="pdf"; size(10cm,0); string[][] rules={{"A","[+BFA][-BFA][^BFA][&BFA]"}, {"B", "'(0.7071)"}}; Lsystem3 plant=Lsystem3("A", rules, La=45); plant.iterate(5); tree3 g=plant.tree3(); for (int angle=0; angle < 360; angle += 5) { currentprojection=orthographic(rotate(angle,Z)*(10,10,6)); save(); for (int i : g.keys) draw((path3)g[i], linewidth(bp)+(g[i].depth > 3 ? brown : 0.8*green)); A.add(); restore(); } A.movie();
|
|
/*Inspiration*/ import Lsystem; import animate; settings.tex="pdflatex"; settings.outformat="pdf"; animation A; size(10cm,0); string[][] rules={{"X","^<XF^<XFX-F^>>XFX&F+>>XFX-F>X->"}}; Lsystem3 HilbertCurve3D=Lsystem3("X", rules, La=90, Lai=0); HilbertCurve3D.iterate(3); path3[] g=HilbertCurve3D.paths3(); triple M=(max(g)+min(g))/2; currentprojection=currentprojection=orthographic((10,10,6)); for (int angle=0; angle < 360; angle += 2) { save(); draw(rotate(angle,M,M+Z)*g[0], linewidth(bp)+0.9*yellow); A.add(); restore(); } A.movie(BBox(3mm, Fill(black)));
|
|
import graph_settings; import animate; size(10cm); settings.tex="pdflatex"; settings.outformat="pdf"; pair[] interp(pair[] a1, pair[] a2, real k) { if(a1.length != a2.length) abort("interp: arrays have differents length."); pair[] g; int l=a1.length; g=sequence(new pair(int j){ return interp(a1[j],a2[j],k); },l); return g; } path morphing(pair[] a1, pair[] a2, real k, interpolate join=operator --) { if(a1.length != a2.length) abort("morphing: arrays have differents length."); return join(...interp(a1, a2, k)); } pair[] nodes(path g, int n) { int np=round(n/length(g)); n=np == 0 ? n : np*length(g); return sequence(new pair(int i){return point(g, length(g)*i/n);}, n); } animation A; int nbpt=4; pair[] A1=nodes(unitsquare,nbpt); path g=(0,0)--(1,0)--(0,1)--(1,1)--cycle; pair[] A2=shift(2,1)*rotate(25)*nodes(g,nbpt); interpolate join=operator ..; // interpolate join=operator --; int n=40; real step=1/n; pen p1=0.8*red, p2=0.8*blue; filldraw(join(morphing(A1,A2,0,join),cycle), p1); filldraw(join(morphing(A1,A2,1,join),cycle), p2); for (int i=0; i <= n; ++i) { save(); filldraw(join(morphing(A1,A2,i*step,join),cycle),opacity(0.5)+interp(p1,p2,i*step)); A.add(); restore(); } A.movie();
|
|
import graph; import animate; size(15cm); settings.outformat="pdf"; pair[] interp(pair[] a1, pair[] a2, real k) { if(a1.length != a2.length) abort("interp: arrays have differents length."); pair[] g; int l=a1.length; g=sequence(new pair(int j){ return interp(a1[j],a2[j],k); },l); return g; } path morphing(pair[] a1, pair[] a2, real k, interpolate join=operator --) { if(a1.length != a2.length) abort("morphing: arrays have differents length."); return join(...interp(a1, a2, k)); } pair[] nodes(path g, int n) { int np=round(n/length(g)); n=np == 0 ? n : np*length(g); return sequence(new pair(int i){return point(g, length(g)*i/n);}, n); } animation A; real f(real t){ return exp(cos(t))-2*cos(4*t)+sin(t/12)^5;} path gf=polargraph(f,0,12*pi,1000); int nbpt=1000; pair[] A1=nodes(scale(5.5)*unitcircle,nbpt); pair[] A2=shift(0,0)*nodes(gf,nbpt); interpolate join=operator --; int n=50; real step=1/n; pen p1=0.8*red, p2=0.8*blue; for (int i=0; i <= n; ++i) { save(); filldraw(join(morphing(A1,A2,1,join),cycle), evenodd+p2); filldraw(join(morphing(A1,A2,i*step,join),cycle), evenodd+interp(p1,p2,i*step)); A.add(); restore(); } A.movie(BBox(3mm, 3bp+miterjoin+black, FillDraw(lightyellow)));
|
|
// pdf version of this animation: fig0160.pdf import labelpath; import animate; animation A; texpreamble("\usepackage[dvips,pdfpagemode=FullScreen]{hyperref}"); settings.outformat="pdf"; settings.tex="pdflatex"; defaultpen(fontsize(12pt)); size(16cm,0); usepackage("mathrsfs, amsfonts,amsmath,amssymb"); picture pic, pic1, pic2, pic3; real u=1, Y=2*pi+0.5; pair yM=(u,Y*u), ym=(u,-Y*u); path cle=scale(u)*unitcircle; path arcg=arc((0,0),1.5*u,115,155); void addtick(picture pic=currentpicture, Label L, pair z, pair dir=E, pen p=currentpen) { transform R=rotate(degrees(dir)); real width=1.5mm; Label L=L.copy(); L.position(z); L.align(NoAlign,E); L.align.dir=R*L.align.dir*1.3*width/mm; L.p(p); pic.add(new void(frame f, transform t) { path g=(-width,0)--(width,0); picture opic; draw(opic,shift(t*z)*R*g,p); add(f,opic.fit()); }); add(pic,L); } path roll(picture pic=currentpicture, real x, int nb=50) { real stp=x/(nb-1); return operator --(... sequence(new guide(int t){ real tt=t*stp; return shift(expi(tt))*((x-tt)*(-sin(tt),cos(tt))); },nb)); } pair EW(int sign){return sign > 0 ? E : W;} string pm(int sign){return sign > 0 ? "" : "-";} pen p(int sign){return sign > 0 ? red : blue;} pen pw(int sign){return p(sign)+(sign > 0 ? currentpen : white);} // Define common picture draw(scale(1.25)*"+", arcg, Arrow()); dot("$0$", point(cle,0)); draw((-u,0)--(u,0)^^(0,-u)--(0,u)); draw("$1$",(0,0)--point(cle,1.5),Arrows(FillDraw(white))); pic.add(currentpicture);// Save the common picture in 'pic'. // Starting picture 1 draw((u,0)--yM, linewidth(bp)+p(1), Arrow(TeXHead)); draw(ym--(u,0), linewidth(bp)+p(-1)); arrow("\underline{Axe des réels}",(u,-0.75*Y*u),W,1cm); real x=2.2, y=-x, maxe=2*pi+0.2; addtick(Label("$1$",align=E), (u,1), p(1)); addtick(Label("$\frac{\pi}{2}$",align=E), (u,pi/2), p(1)); addtick(Label("$\pi$",align=E), (u,pi), p(1)); addtick(Label("$\frac{3\pi}{2}$",align=E), (u,3pi/2), p(1)); addtick(Label("$2\pi$",align=E), (u,2pi), p(1)); addtick(Label("$-1$",align=W), (u,-1), p(-1)); addtick(Label("$-\frac{\pi}{2}$",align=W), (u,-pi/2), p(-1)); addtick(Label("$-\pi$",align=W), (u,-pi), p(-1)); addtick(Label("$-\frac{3\pi}{2}$",align=W), (u,-3pi/2), p(-1)); addtick(Label("$-2\pi$",align=W), (u,-2pi), p(-1)); draw(Label("$\mathscr{C}$",Relative(0.625)), cle,linewidth(bp)); A.add(); erase(); // Define the common picture for rolling part. picture picanim(int sign) { picture opic=pic.copy(); pen pmoins=sign > 0 ? p(-1) : p(-1)+white; draw(opic, (u,0)--yM, bp+white+p(1), Arrow(TeXHead)); draw(opic, ym--(u,0), linewidth(bp)+pmoins); arrow(opic,"\underline{Axe des réels}", (u,-0.75*Y*u), W, 1cm); addtick(opic, Label("$1$",align=E), (u,1), white+p(1)); addtick(opic, Label("$\frac{\pi}{2}$",align=E), (u,pi/2), white+p(1)); addtick(opic, Label("$\pi$",align=E), (u,pi), white+p(1)); addtick(opic, Label("$\frac{3\pi}{2}$",align=E), (u,3pi/2), white+p(1)); addtick(opic, Label("$2\pi$",align=E), (u,2*pi), white+p(1)); addtick(opic, Label("$-1$",align=W), (u,-1), pmoins); addtick(opic, Label("$-\frac{\pi}{2}$",align=W), (u,-pi/2), pmoins); addtick(opic, Label("$-\pi$",align=W), (u,-pi), pmoins); addtick(opic, Label("$-\frac{3\pi}{2}$",align=W), (u,-3pi/2), pmoins); addtick(opic, Label("$-2\pi$",align=W), (u,-2*pi), pmoins); return opic; } erase(); pic2=picanim(1); int nb=50; // Number of picture for rolling. real step=maxe/nb; for (int sign=1; sign > -2; sign -= 2) {// Rolling axis part (1 for positive values, -1 for ...); guide r1,rpis2, rpi, rpi32, rpi2; pair z; for (int i=0; i <= nb ; ++i) { real t=sign*i*step; // Where is the tangency. if(sign > 0) draw(Label("$\mathscr{C}$",Relative(0.625)), cle,linewidth(bp)); path tg=i == nb ? cle : arc((0,0),u,0,degrees(t)); // The rolled part. path g=u*expi(t)--shift(u*expi(t))*((Y-abs(t))*u*expi(sign*pi/2+t)); // The straight part. draw(g,linewidth(bp)+p(sign), sign > 0 ? Arrow(TeXHead) : None); if(t > 0) { if(abs(t) <= 1) { z=arcpoint(g, (1-abs(t))*u); addtick(Label(pm(sign)+"$1$",align=EW(sign)), z, expi(sign), p(sign)); r1=r1..z; } else addtick(Label(pm(sign)+"$1$",align=EW(sign), UnFill), u*(cos(sign),sin(sign)), dir(degrees(sign*1.0)), p(sign));} draw(r1, dashed+p(sign)); if(abs(t) <= pi/2) { z=arcpoint(g,(pi/2-abs(t))*u); addtick(Label("$"+pm(sign)+"\frac{\pi}{2}$",align=EW(sign)), z, expi(t), p(sign)); rpis2=rpis2..z; } else addtick(Label("$"+pm(sign)+"\frac{\pi}{2}$",align=EW(sign), UnFill), (0,sign*u), sign*N, p(sign)); draw(rpis2, dashed+p(sign)); if(abs(t) <= pi) { z=arcpoint(g,(pi-abs(t))*u); addtick(Label("$"+pm(sign)+"\pi$",align=EW(sign)), z, expi(t), p(sign)); rpi=rpi..z; } else addtick(Label("$"+pm(sign)+"\pi$",align=EW(sign), UnFill), (-u,0), W, p(sign)); draw(rpi,dashed); if(abs(t) <= 3*pi/2) { z=arcpoint(g,(3pi/2-abs(t))*u); addtick(Label("$"+pm(sign)+"\frac{3\pi}{2}$",align=EW(sign)), z, expi(t), p(sign)); rpi32=rpi32..z; } else addtick(Label("$"+pm(sign)+"\frac{3\pi}{2}$",align=EW(sign), UnFill), (0,-sign*u), sign*S, p(sign)); draw(rpi32, dashed+p(sign)); if(abs(t)-2*pi < -1e-5) { z=arcpoint(g,(2*pi-abs(t))*u); addtick(Label("$"+pm(sign)+"2\pi$",align=EW(sign)), z, expi(t), p(sign)); rpi2=rpi2..z; } else addtick(Label("$"+pm(sign)+"2\pi$",align=(sign > 0 ? 2 : 1)*EW(sign), UnFill), (u,0), E, p(sign)); draw(rpi2, dashed+p(sign)); if(i == nb && sign == 1) { draw(tg,linewidth(2*bp)+p(sign)); pic3.add(currentpicture); add(pic2); pic2=picanim(-1); pic2.add(pic3); } else add(pic2); // Add the common picture 'pic2'. draw(tg,linewidth(bp)+p(sign)); A.add(); if(sign > 0 || i != nb) erase(); } } for (int i=0; i < 10; ++i) A.add(); clip(scale(1.6)*cle); for (int i=0; i < 10; ++i) A.add(); eval(quote{ addtick(Label("$-\pi$",align=EW(-1), UnFill), (-u,0), W, p(-1)); addtick(Label("$-2\pi$",align=EW(-1), UnFill), (u,0), E, p(-1)); defaultfilename='temp_'; shipout(currentpicture.fit(scale(2cm)));},true); pair center=(min(currentpicture)+max(currentpicture))/2; int n=20; for (int i=0; i <= n; ++i) { erase(); label(scale(1+1.25*i/n)*graphic("temp_.pdf"),i/n*center); A.add(); } for (int i=0; i < 20; ++i) A.add(); for (int i=0; i < 10; ++i) A.add(A.pictures[0]); // Add the first picture in the animation. A.movie();
|
|
size(12cm,0); import hull_pi; import animation; animation A; settings.outformat="pdf"; pair[] cloud; int nbpt=200; // Generate random points. for (int i=0; i < nbpt; ++i) cloud.push((10*unitrand(),10*unitrand())); for (int i=1; i < 8; ++i) { // Control the depth for (int j=0; j < 30; ++j) { // Point of view = cloud[i] real depthMax=i/2; // Nodes of the hull pair[] hull=hull(cloud,depthMin=0,depthMax=depthMax,angleMin=10,angleMax=360,pivot=j); save();// Add new picture to the animation filldraw(polygon(hull),lightgrey); dot(cloud[j],3mm+green); dot(cloud,red); label("depthMax="+(string)depthMax); A.add(); restore(); } } A.movie();
|
|
/* One may want to play with an interactive Java applet */ import surface; import animation; animation A; size(15cm); currentprojection=orthographic(1,1,1.5); currentlight.source=(1,0,0.45); triple PXY=-X-Y; triple P00=PXY+0.5*Z, P03=-X+Y, P33=X+Y, P30=X-Y; triple[][] P0={ {PXY,PXY+(0,0.5,0),P03+(0,-0.5,0),P03}, {PXY+(0.5,0,0),(-0.5,-0.5,0),(-0.5,0.5,0),P03+(0.5,0,0)}, {P30+(-0.5,0,0),(0.5,-0.5,0),(0.5,0.5,0),P33+(-0.5,0,0)}, {P30,P30+(0,0.5,0),P33+(0,-0.5,0),P33} }; triple[][][] P1={ { {PXY,PXY+(0,0.5,0),P03+(0,-0.5,0),P03}, {PXY+(0.5,0,0),(-0.5,-0.5,-2),(-0.5,0.5,-2),P03+(0.5,0,0)}, {P30+(-0.5,0,0),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,0)}, {P30,P30+(0,0.5,0),P33+(0,-0.5,0),P33} }, { {P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03}, {P00+(0.5,-0.5,-1),(-0.5,-0.5,-2),(-0.5,0.5,-2),P03+(0.5,0,1)}, {P30+(-0.5,0,1),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,1)}, {P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33} }, { {P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03}, {P00+(0.5,-0.5,-1),(-0.5,-0.5,-2),(-0.5,0.5,2),P03+(0.5,0,1)}, {P30+(-0.5,0,1),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,1)}, {P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33} }, { {P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03}, {P00+(0.5,-0.5,-1),(-0.5,-0.5,-2),(-0.5,-0.5,2),P03+(0.5,0,1)}, {P30+(-0.5,0,1),(0.5,-0.5,-2),(0.5,0.5,-2),P33+(-0.5,0,1)}, {P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33} } }; triple[][] interp(triple[][] a, triple[][] b, real x) { triple[][] c; for (int i=0; i < a.length; ++i) { triple [] t; for (int j=0; j < a[i].length; ++j) { t.push(interp(a[i][j],b[i][j],x)); } c.push(t); } return c; } int n=20; real step=1/n; for (int i=0; i < P1.length; ++i) { for (int j=0; j <= n; ++j) { save(); triple[][] P=interp(P0,P1[i],j*step); surface s=P; draw(s,15,15,yellow,meshpen=grey); draw(s.external(), bp+red); dot("P[0][0]",P[0][0], align=N, black); dot("P[0][3]",P[0][3], black); dot("P[3][3]",P[3][3], align=S, black); dot("P[3][0]",P[3][0], align=W, black); draw(Label("P[0][1]",align=SW,EndPoint),P[0][0]--P[0][1], Arrow); draw(Label("P[1][0]",align=SE,EndPoint),P[0][0]--P[1][0], Arrow); draw(Label("P[0][2]",align=E,EndPoint),P[0][3]--P[0][2], Arrow); draw(Label("P[1][3]",align=W,EndPoint),P[0][3]--P[1][3], Arrow); draw(Label("P[2][3]",align=NE,EndPoint),P[3][3]--P[2][3], Arrow); draw(Label("P[3][2]",align=NW,EndPoint),P[3][3]--P[3][2], Arrow); draw(Label("P[3][1]",align=NE,EndPoint),P[3][0]--P[3][1], Arrow); draw(Label("P[2][0]", align=W,EndPoint),P[3][0]--P[2][0], Arrow); dot("P[1][1]",P[1][1], align=N); dot("P[1][2]",P[1][2], align=E); dot("P[2][2]",P[2][2], align=N); dot("P[2][1]",P[2][1], align=W); dot(s.internal()); A.add(); restore(); } P0=copy(P1[i]); } for (int i=A.pictures.length-1; i >= 0 ; --i) A.add(A.pictures[i]); A.movie(BBox(Fill(lightgrey)));
Dernière modification/Last modified: Wed Jun 25 16:31:56 CEST 2008
Philippe Ivaldi