I have some troubles coding a sketch (using processing 2 with the Pshape library). Basically, what I want to do is a code that generate a visual pattern, something that looks a lot like the logo for the  creative applications logo: I want the shape of an ellipse to be filled with triangles, each of them with a different color, maybe even with radiants (one color per vertex).

The method I choose for this is to calculate the area of the ellipse, then try to calculate the area of every triangle I create, add them all until it sums up to the area of the ellipse.

So, here's my code:

2. int num = 200; //just used to set up the arrays
3. PShape s[] = new PShape[num]; //the triangle
4. float x[] = new float[num];
5. float y[] = new float[num]; //its coordinates
6. float v_x[][] = new float[num][num]; 
7. float v_y[][] = new float[num][num]; //the coordinates of every vertex that has been created this far
8. 
   
9. float ray; //the radius of the circle
10. float aire_cercle; //the area of the circle
11. float aire_tri_totale; //the addition of each and every triangle's area
12. float aire_tri; //the being-created triangle's area
13. int t;
14. int n_vertex;
15. int i;
16. 
    
17. void setup() {
18.   size(800, 600, P2D);
19.   frameRate(8); //I like things to go slow at first, so I can understand what's happening
20.   fill(80, 124, 132, 90);
21.   stroke(255);
22.   ray = 0.5*(height/1.2);
23.   background(0);
24.   //basic setup, nothing interesting here, I just set the radius of my circle
25. }
26. 
    
27. void draw() {
28. 
    
29.   translate(width/2, height/2); // I want things to start from the center of the screen
30. 
    
31.   aire_cercle = (ray*ray)*PI; //That's the area of my ellipse
32.   println(aire_cercle);
33. 
    
34.   //I want triangles to be created as long as their area do not match the ellipse's area
35.   while (aire_tri_totale < aire_cercle) { 
36. 
    
37.     s[t] = createShape(); //we create a new shape
38. 
    
39.       beginShape();
40. 
    
41.     for (i = 0; i < 3; i++) { //i is the number of the vertex being created
42.       if (t == 0) { //if this is the first shape, she can start wherever she wants
43.         x[i] = random(-ray, ray);
44.         y[i] = random(-ray, ray);
45.       }
46. 
    
47.       else { //else, it will have to merge two of its three vertices to the previous shape
48.         if (i == 0) {
49.           x[i] = v_x[t-1][ceil(random(0, 1))]; //let's choose a vertex
50.           y[i] = v_y[t-1][ceil(random(0, 1))];
51.         }
52.         else if (i ==1) {
53.           x[i] = v_x[t-1][ceil(random(1, 2))]; //and another one
54.           y[i] = v_y[t-1][ceil(random(1, 2))];
55.         }
56.         else {
57.           //and finally, the third one is random within a certain range 
58.           //(so that there ain't one big shape taking all of the place)
59.           x[i] = random(x[i-1]-ray/8, x[i-1]+ray/8); 
60.           y[i] = random(y[i-1]-ray/8, y[i-1]+ray/8);
61.         }
62.       }
63. 
    
64.       v_x[t][i] = x[i];
65.       v_y[t][i] = y[i];
66.       //every vertice's coordinates gets to be stocked
67. 
    
68.       vertex(x[i], y[i]); //and is created
69.     }
70.     endShape(CLOSE);
71.     for (i = 2; i > 0; i--) {
72.       aire_tri += abs(((x[i]*y[i-1]) - (x[i-1]*y[i]))/2);
73.       /*
74.       I found this formula on a forum to calculate the area of a polygon. I can't really understand what
75.       it's doing though, moreover seeing if something wrong...
76.       As I recall, it is suppose to "go back" to each vertex, multiplying one of its coordinates with
77.       the other of the previous one, divising it all by 2...
78.       Nah, I can't even understand what I'm saying...
79.       */
80.     }
81. 
    
82.     aire_tri_totale += aire_tri;
83.     t++;
84.     println(aire_tri_totale);
85.   }
86. 
    
87.   noLoop();
88. }

And as you can see... It's not working...

I have absolutely no idea what's going wrong, since the problem, I guess, lies in the part where the area is being calculated and that I can barely look without crying blood. Have I mentioned that I am a total failure when it comes to maths?

It even seems like the triangles a getting bigger every time one is created, which is totally unwanted, of course...

That's why I'm turning it to you, asking for help. As I am in a bit of a hurry, I would love to have someone giving me an hand on this.

Sorry if my english is a bit approximative, frenchman here, speaking.

Au revoir et merci d'avance!

Edit: I almost forgot, another issue, I would like vertices not to be created within a pre-existing triangle. Something like a hit-test system should do the trick, however I find myself incapable of creating, or at least, incorporate a thing like  that