PNTrangle implementation by OpenGL

A PN triangle is a cubic triangular Bezier patch. Control points are merely depending on the vertex positions and normals of a defining base triangle. Each PN triangle in a mesh is thus independent of neighboring triangles.

Normals of base triangle shall have different values. If not,normal variation cannot work.

Control point calcualation

The diagrams are extracted from paper. Read paper "Curved PN Triangles" for details.

GLSL TCS code

void evaluateControlPoints(in vec3 p1, in vec3 p2, in vec3 p3,in vec3 n1, in vec3 n2, in vec3 n3)
{
    //< Calculate Vertex control points
    b300 = p1;
    b030 = p2;
    b003 = p3;

    //< Weight
    float w12 = dot(p2 - p1, n1);
    float w21 = dot(p1 - p2, n2);
    float w23 = dot(p3 - p2, n2);
    float w32 = dot(p2 - p3, n3);
    float w31 = dot(p1 - p3, n3);
    float w13 = dot(p3 - p1, n1);

    //< Tangent control points
    b210 = (2.f * p1 + p2 - w12 * n1) / 3.f;
    b120 = (2.f * p2 + p1 - w21 * n2) / 3.f;
    b021 = (2.f * p2 + p3 - w23 * n2) / 3.f;
    b012 = (2.f * p3 + p2 - w32 * n3) / 3.f;
    b102 = (2.f * p3 + p1 - w31 * n3) / 3.f;
    b201 = (2.f * p1 + p3 - w13 * n1) / 3.f;

    //< Center Control point 
    vec3 ee = (b120 + b120 + b021 + b012 + b102 + b210) * 0.25f;
    vec3 vv = (p1 + p2 + p3) * 0.166666667f;
    b111 = ee - vv;
}


void evaluateNormalControlPoints(in vec3 p1, in vec3 p2, in vec3 p3,in vec3 n1, in vec3 n2, in vec3 n3)
{
    n200 = n1;
    n020 = n2;
    n002 = n3;

    float v12 = (2. * (dot(p2 - p1, n1 + n2) / dot(p2 - p1, p2 - p1)));
    float v23 = (2. * (dot(p3 - p2, n2 + n3) / dot(p3 - p2, p3 - p2)));
    float v31 = (2. * (dot(p1 - p3, n3 + n1) / dot(p1 - p3, p1 - p3)));

    n110 = normalize(n1 + n2 - v12 * (p2 - p1));
    n011 = normalize(n2 + n3 - v23 * (p3 - p2));
    n101 = normalize(n3 + n1 - v31 * (p1 - p3));
}

Questions

How to ensure no cracks after tessellation. I feel that it is hard to ensure that.

It is to mplement PN Triangle tessellation by OpenGL.

Features

• Implement PN Triangle Tessellation
• Camera supporting rotate, pan, zoom in / out.
• Capture Color Buffer & save to disk in tga format
• Rendering Image sequence
• snap & save to file
• Animation support

Plans

• [ ]

Control

• Key 'space' : animation loop rotate -> zoom in -> zoom out -> random
• Key 't': toggle tesselation
• Key 'w': toggle wireframe

Demo

Credits

• glew
• glfw
• glm
• stb image
• tiny obj loader