Week2 of the project

Everything works fine

Author: Marc Bickel

Week2_Sketch/Week2_Sketch.pde

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+void settings() {
+  size (1000, 1000, P2D);
+}
+void setup() {
+}
+void draw() {
+  background(255, 255, 255);
+My3DPoint eye = new My3DPoint(0, 0, -5000);
+My3DPoint origin = new My3DPoint(0, 0, 0);
+My3DBox input3DBox = new My3DBox(origin, 100, 150, 300);
+//rotated around x
+float[][] transform1 = rotateXMatrix(PI/8);
+input3DBox = transformBox(input3DBox, transform1);
+projectBox(eye, input3DBox).render();
+//rotated and translated
+float[][] transform2 = translationMatrix(200, 200, 0);
+input3DBox = transformBox(input3DBox, transform2);
+projectBox(eye, input3DBox).render();
+//rotated, translated, and scaled
+float[][] transform3 = scaleMatrix(2, 2, 2);
+input3DBox = transformBox(input3DBox, transform3);
+projectBox(eye, input3DBox).render();
+}
+
+class My2DPoint {
+  float x;
+  float y;
+  My2DPoint(float x, float y) {
+    this.x = x;
+  this.y = y;
+  }
+}
+
+class My3DPoint {
+  float x;
+  float y;
+  float z;
+  My3DPoint(float x, float y, float z) {
+    this.x = x;
+    this.y = y;
+    this.z = z;
+  }
+}
+
+My2DPoint projectPoint(My3DPoint eye, My3DPoint p) {
+  float c = eye.z / (eye.z - p.z);
+  return new My2DPoint(c * (p.x - eye.x), c * (p.y - eye.y));
+}
+
+class My2DBox {
+  My2DPoint[] s;
+  My2DBox(My2DPoint[] s) {
+    this.s = s;
+  }
+  void render(){
+    line(s[0].x, s[0].y, s[1].x, s[1].y);
+    line(s[0].x, s[0].y, s[4].x, s[4].y);
+    line(s[0].x, s[0].y, s[3].x, s[3].y);
+    line(s[1].x, s[1].y, s[2].x, s[2].y);
+    line(s[1].x, s[1].y, s[5].x, s[5].y);
+    line(s[4].x, s[4].y, s[5].x, s[5].y);
+    line(s[4].x, s[4].y, s[7].x, s[7].y);
+    line(s[5].x, s[5].y, s[6].x, s[6].y);
+    line(s[3].x, s[3].y, s[7].x, s[7].y);
+    line(s[3].x, s[3].y, s[2].x, s[2].y);
+    line(s[7].x, s[7].y, s[6].x, s[6].y);
+    line(s[6].x, s[6].y, s[2].x, s[2].y);
+  }
+}
+
+class My3DBox {
+  My3DPoint[] p;
+  My3DBox(My3DPoint origin, float dimX, float dimY, float dimZ){
+    float x = origin.x;
+    float y = origin.y;
+    float z = origin.z;
+    this.p = new My3DPoint[]{new My3DPoint(x,y+dimY,z+dimZ),
+      new My3DPoint(x,y,z+dimZ),
+      new My3DPoint(x+dimX,y,z+dimZ),
+      new My3DPoint(x+dimX,y+dimY,z+dimZ),
+      new My3DPoint(x,y+dimY,z),
+      origin,
+      new My3DPoint(x+dimX,y,z),
+      new My3DPoint(x+dimX,y+dimY,z)
+    };
+  }
+  My3DBox(My3DPoint[] p) {
+    this.p = p;
+  }
+}
+
+My2DBox projectBox (My3DPoint eye, My3DBox box) {
+  My2DPoint[] tabel = new My2DPoint[8];
+  for (int i = 0; i < box.p.length; ++i) {
+    tabel[i] = projectPoint(eye, box.p[i]);
+  }
+  return new My2DBox(tabel);
+}
+
+float[] homogeneous3DPoint (My3DPoint p) {
+  float[] result = {p.x, p.y, p.z , 1};
+  return result;
+}
+
+float[][] rotateXMatrix(float angle) {
+  return(new float[][] {{1, 0 , 0 , 0},
+                        {0, cos(angle), sin(angle) , 0},
+                        {0, -sin(angle) , cos(angle) , 0},
+                        {0, 0 , 0 , 1}});
+}
+float[][] rotateYMatrix(float angle) {
+  return(new float[][] {{cos(angle), 0 , sin(angle), 0},
+                        {0, 1, 0 , 0},
+                        { -sin(angle), 0, cos(angle) , 0},
+                        {0, 0 , 0 , 1}});
+}
+float[][] rotateZMatrix(float angle) {
+  return(new float[][] {{cos(angle), -sin(angle), 0, 0},
+                        {sin(angle), cos(angle), 0 , 0},
+                        {0, 0, 1, 0},
+                        {0, 0 , 0 , 1}});
+}
+float[][] scaleMatrix(float x, float y, float z) {
+  return(new float[][] {{x, 0, 0, 0},
+                        {0, y, 0 , 0},
+                        {0, 0, z, 0},
+                        {0, 0 , 0 , 1}});
+}
+float[][] translationMatrix(float x, float y, float z) {
+  return(new float[][] {{1, 0, 0, x},
+                        {0, 1, 0 , y},
+                        {0, 0, 1, z},
+                        {0, 0 , 0 , 1}});
+}
+
+float[] matrixProduct(float[][] a, float[] b) {
+  float[] result = new float[4];
+  float sum = 0;
+  for (int i = 0; i < 4; ++i) {
+    sum = 0;
+    for (int j = 0; j < 4; ++j) {
+      sum += a[i][j] * b[j];
+    }
+    result[i] = sum;
+  }
+  return result;
+}
+
+My3DBox transformBox(My3DBox box, float[][] transformMatrix) {
+  My3DPoint[] result = new My3DPoint[8];
+  for (int i = 0; i < box.p.length; ++i) {
+    result[i] = euclidian3DPoint(matrixProduct(transformMatrix, homogeneous3DPoint(box.p[i])));
+  }
+  return new My3DBox(result);
+  
+}
+
+My3DPoint euclidian3DPoint (float[] a) {
+  My3DPoint result = new My3DPoint(a[0]/a[3], a[1]/a[3], a[2]/a[3]);
+  return result;
+}