sierpinski carpet.
exercise in recursion. iterations projected forward through scaling, showing the cantor sets in the carpet.
click to start over if it stops.
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/*Triangle2D rectTriangleCW (Point2D C, Point2D D, float angle){ // clockwise recangle triangle with A, B in it. angle is the angle EDC in (0,PI) Point2D E; E = new Point2D( D.x + ( cos(angle) * C.x ), D.y + ( cos(angle) * C.y ) ); return(new Triangle2D(C,D,E)); } Polygon2D squareCW (Point2D A, Point2D B){ // clockwise square with A, B in it Point2D C; Point2D D; Point2D[] SQ; D = new Point2D(10,10); C = new Point2D(10,10); SQ = new Point2D[4]; SQ[0] = A; SQ[1] = B; SQ[2] = C; SQ[3] = D; return(new Polygon2D( 4, SQ)); class Point2D { float x; float y; Point2D (float X,float Y){ x = X; y = Y; } void display(){ ellipseMode(CENTER_RADIUS); ellipse(x, y, 2, 2); } } class Triangle2D { Point2D A, B, C; Triangle2D (Point2D A, Point2D B, Point2D C){ // constructor this.A = A; this.B = B; this.C = C; } // closes method Triangle2D (float x1, float y1, float x2, float y2, float x3, float y3){ // constructor this.A = new Point2D(x1,y1); this.B = new Point2D(x2,y2); this.C = new Point2D(x3,y3); } // closes method void display(){ line(A.x, A.y, B.x, B.y); line(B.x, B.y, C.x, C.y); line(C.x, C.y, A.x, A.y); A.display(); B.display(); C.display(); } void displayLines(){ line(A.x, A.y, B.x, B.y); line(B.x, B.y, C.x, C.y); line(C.x, C.y, A.x, A.y); } void displayPoints(){ A.display(); B.display(); C.display(); } void displayFill(){ triangle(A.x, A.y, B.x, B.y, C.x, C.y); } } class Square2D { Point2D A, B, C, D; Square2D (Point2D A, Point2D B, Point2D C, Point2D D){ // constructor this.A = A; this.B = B; this.C = C; this.D = D; } // closes method Square2D (float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4){ // constructor this.A = new Point2D(x1,y1); this.B = new Point2D(x2,y2); this.C = new Point2D(x3,y3); this.D = new Point2D(x4,y4); } // closes method void display(){ line(A.x, A.y, B.x, B.y); line(B.x, B.y, C.x, C.y); line(C.x, C.y, D.x, D.y); line(D.x, D.y, A.x, A.y); A.display(); B.display(); C.display(); D.display(); } void displayLines(){ line(A.x, A.y, B.x, B.y); line(B.x, B.y, C.x, C.y); line(C.x, C.y, D.x, D.y); line(D.x, D.y, A.x, A.y); } void displayPoints(){ A.display(); B.display(); C.display(); D.display(); } void displayFill(){ triangle(A.x, A.y, B.x, B.y, C.x, C.y); triangle(A.x, A.y, C.x, C.y, D.x, D.y); } } class Vector2D { Point2D A; float angle, magnitude; Vector2D (Point2D A, float angle, float magnitude){ // constructor this.A = A; this.angle = angle; this.magnitude = magnitude; } // closes method Vector2D (float x,float y, float angle, float magnitude){ // constructor this.A = new Point2D(x,y); this.angle = angle; this.magnitude = magnitude; } // closes method void display(){ line(A.x, A.y, A.x + ( magnitude * sin(angle) ), A.y + ( magnitude * cos(angle) ) ); A.display(); } void displayEnd(){ Point2D B; B = new Point2D(A.x + ( magnitude * sin(angle) ), A.y + ( magnitude * cos(angle) ) ); B.display(); } Point2D startPoint(){ return (A); } Point2D endPoint(){ Point2D B; B = new Point2D(A.x + ( magnitude * sin(angle) ), A.y + ( magnitude * cos(angle) ) ); return (B); } } class Polygon2D { int vertices; Point2D[] A; Polygon2D (int vertices, Point2D[ ]A ){ // constructor this.vertices = vertices; this.A = new Point2D[vertices]; for (int i = 0; i < vertices; i++){ this.A[i] = A[i]; } } // closes method void display(){ for (int i = 0; i < vertices; i++){ int k = (i + 1) % (vertices); line(A[i].x, A[i].y, A[k].x , A[k].y ); A[i].display(); } } void displayFill(){ // work it out this one } } Point2D midPoint(Point2D X,Point2D Y){ Point2D mid; mid = new Point2D( X.x +( (Y.x-X.x)/2 ), X.y +( (Y.y-X.y)/2 ) ); // fun to change any of this 2 for a 3 return (mid); } Point2D randomChoice(Point2D X, Point2D Y, Point2D Z){ float r = random(0,3); Point2D rand; if (r < 1f) rand = new Point2D( Y.x, Y.y ); else{ if(r < 2f) rand = new Point2D( X.x, X.y ); else rand = new Point2D( Z.x, Z.y ); } return (rand); } Point2D randomPoint(){ float rx = random(0,1); float ry = random(0,1); Point2D rand; rand = new Point2D( width * rx, height * ry ); return (rand); } float area2(Point2D A, Point2D B, Point2D C) { return (A.x - C.x) * (B.y - C.y) - (A.y - C.y) * (B.x - C.x); } boolean insideTriangle(Point2D A, Point2D B, Point2D C, Point2D P){ // ABC is assumed to be c ounterclockwise return area2(A, B ,P ) >= 0 && area2(B, C, P) >= 0 && area2(C, A, P) >= 0; } void triangulate (Point2D[] P,Triangle2D[] tr) { // P contains all n polygon vertices in ccw order // the resulting triangles will be stored in array tr // this array tr must have lenght n-2 int n = P.length, j = n - 1, iA = 0, iB, iC; int[] next = new int[n]; for (int i= 0; i < n; i++) { next[j] = i; j = i; } for (int k = 0; k < n-2; k++) { // find a suitable triangle consisting of // two edges and an internal diagonal Point2D A, B, C; boolean triaFound = false; int count = 0; while (!triaFound && ++count < n) { iB = next[iA]; iC = next[iB]; A = P[iA]; B = P[iB]; C = P[iC]; if(area2(A, B, C) >= 0) { // edges AB and BC, diagonal AC // test to see if no other polygon vertex // lies within triangle ABC: j = next[iC]; while( j != iA && !insideTriangle(A, B, C, P[j])) j = next[j]; if ( j == iA) { // then triangle ABC contains no other vertex: tr[k] = new Triangle2D(A, B, C); next[iA] = iC; triaFound = true; } } iA = next[iA]; } if (count == n) { println("not a simple polygon" + " or vertex sequence not counterclockwise"); } } } float distance2(Point2D P, Point2D Q) { float dx = P.x = Q.x, dy = P.y = Q.y; return dx * dx + dy * dy; }

Source code: sierpinskiSquare_0

Built with Processing