Finn Eggers Finn Eggers - 8 days ago 5
Java Question

Get position of any point in a triangle

My problem is following:
I've defined a triangle with 3 points.

The coordinate system is defined like this:


  • X-Axis heads to the right

  • Y-Axis heads upwards

  • Z-Axis heads out of my screen



This is the most common coordinate system used in OpenGL (i think).
Now I got my triangle. The X and Z values of every point are different.
I need to find the Y coordinate on my triangle by giving the X and Z coordinate.
Someone has written this method and called it barryCentric(Point a, Point b, Point c, Point pos) (I am pretty sure he meant "baryCentric" but fine.

public static float barryCentric(Vector3f p1, Vector3f p2, Vector3f p3, Vector3f pos) {
float det = (p2.z - p3.z) * (p1.x - p3.x) + (p3.x - p2.x) * (p1.z - p3.z);
float l1 = ((p2.z - p3.z) * (pos.x - p3.x) + (p3.x - p2.x) * (pos.y - p3.z)) / det;
float l2 = ((p3.z - p1.z) * (pos.x - p3.x) + (p1.x - p3.x) * (pos.y - p3.z)) / det;
float l3 = 1.0f - l1 - l2;
return l1 * p1.y + l2 * p2.y + l3 * p3.y;
}


I am not sure if that method makes any sense. He also uses the pos.y value so I guess this is not what I want. Does anyone know an algorithm that can help me with my problem ?

Greetings, Finn

MBo MBo
Answer

This method makes sense, it is implementation of barycentric interpolation - procedure finds barycentric coordinates of (x,z) point in triangle - l1,l2,l3 here, u,w,v in the linked page.

But implementation contains errors - you a right that one should not use unknown pos.y. Moreover, it is nonsense - subtraction z from y. So change pos.y to pos.z:

    float l1 = ((p2.z - p3.z) * (pos.x - p3.x) + (p3.x - p2.x) * (pos.z - p3.z)) / det;
    float l2 = ((p3.z - p1.z) * (pos.x - p3.x) + (p1.x - p3.x) * (pos.z - p3.z)) / det;
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