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Projection.pde
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Wed, Jun 26, 21:05

Projection.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();
}
float[] matrixProduct(float[][] a, float[] b) {
float[] r=new float[b.length];
for (int i=0; i<a.length; ++i) {
float sum=0;
for (int j=0; j<a[0].length; ++j) {
sum+=a[i][j]*b[j];
}
r[i]=sum;
}
return r;
}
My3DBox transformBox(My3DBox box, float[][] transformMatrix) {
My3DPoint[] newP=new My3DPoint[box.p.length];
for (int i=0; i<newP.length; ++i) {
newP[i]=euclidian3DPoint(matrixProduct(transformMatrix, homogeneous3DPoint(box.p[i])));
}
return new My3DBox(newP);
}
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}});
}
My3DPoint euclidian3DPoint (float[] a) {
My3DPoint result = new My3DPoint(a[0]/a[3], a[1]/a[3], a[2]/a[3]);
return result;
}
float[] homogeneous3DPoint (My3DPoint p) {
float[] result = {p.x, p.y, p.z, 1};
return result;
}
My2DBox projectBox (My3DPoint eye, My3DBox box) {
My3DPoint[] threeDP=box.p;
My2DPoint[] twoDP=new My2DPoint[threeDP.length];
for (int i=0; i<threeDP.length; ++i) {
twoDP[i]=projectPoint(eye, threeDP[i]);
}
return new My2DBox(twoDP);
}
class My2DBox {
My2DPoint[] s;
My2DBox(My2DPoint[] s) {
this.s = s;
}
void render() {
for (int i=0; i<4; i++) {
line(s[i].x, s[i].y, s[(i+1)%4].x, s[(i+1)%4].y);
line(s[i].x, s[i].y, s[i+4].x, s[i+4].y);
line(s[i+4].x, s[i+4].y, s[((i+5)%4)+4].x, s[((i+5)%4)+4].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;
}
}
My2DPoint projectPoint(My3DPoint e, My3DPoint p) {
return new My2DPoint((p.x-e.x)/(1-p.z/e.z), (p.y-e.y)/(1-p.z/e.z));
}
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;
}
}

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