TriangleUVW.pde

Triangle fromT;
Triangle toT;

void setup(){
  fullScreen();
  strokeWeight(20);
  ArrayList<PVector> vertices = polygon(-width/4, 0, 3, 1000);
  fromT = new Triangle(vertices.get(0), vertices.get(1), vertices.get(2));
  toT = new Triangle(new PVector(width/4, -height/4), new PVector(width/2, height/4), new PVector(width/4, height/4));
}

void draw(){
  background(255);
  translate(width/2, height/2);
  fromT.P = new PVector(mouseX-width/2, mouseY-height/2);
  fromT.show();
  PVector uvw = fromT.getUVW();
  toT.setUVW(uvw);
  toT.show();
}

class Triangle{
  PVector A, B, C;
  PVector P = new PVector();;
  Triangle(PVector A, PVector B, PVector C){
    this.A = A;
    this.B = B;
    this.C = C;
  }
  
  PVector getUVW(){
    float ABCArea = getArea();
    float APBArea = new Triangle(A, P, B).getArea();
    float BPCArea = new Triangle(B, P, C).getArea();
    float CPAArea = new Triangle(C, P, A).getArea();
    float u = CPAArea/ABCArea;
    float v = APBArea/ABCArea;
    float w = BPCArea/ABCArea;
    return new PVector(u, v, w);
  }
  
  void setUVW(PVector uvw){//xyz >= uvw
    P = PVector.add(PVector.mult(A, uvw.z), PVector.mult(B, uvw.x)).add(PVector.mult(C, uvw.y));
  }
  
  float getArea(){//with Heon's formula
    float a = PVector.dist(B, C);
    float b = PVector.dist(C, A);
    float c = PVector.dist(A, B);
    float s = (a+b+c)/2;
    return sqrt(s*(s-a)*(s-b)*(s-c));
  }
  
  void show(){
    triangle(A, B, C);
    circle(P, 100);
  }
}

void triangle(PVector A, PVector B, PVector C){
  triangle(A.x, A.y, B.x, B.y, C.x, C.y);
}

void circle(PVector P, float r){
  ellipse(P.x, P.y, r, r);
}

ArrayList<PVector> polygon(float x, float y, int n, float r) {
  ArrayList<PVector> result = new ArrayList<PVector>();
  for (float i = 0; i < n; i++) {
    result.add(new PVector(x+sin(i/n*TWO_PI)*r, y-cos(i/n*TWO_PI)*r));
  }
  return result;
}