Fragment Shader: Attribute Interpolation

Write a C program that simulates fragment shader attribute interpolation.

Requirements:

• Define three vertices with colors and w values: V0: position (0, 0), color red (1,0,0), w=1 V1: position (10, 0), color green (0,1,0), w=2 V2: position (5, 10), color blue (0,0,1), w=1
• For the fragment at screen position (5, 3):
  • Compute barycentric coordinates (u, v, w_bary) using the 2D screen positions
  • Compute linearly interpolated color: ured + vgreen + w_bary*blue
  • Compute perspective-correct interpolated color:
    • Interpolate red/w, green/w, blue/w using barycentric coords weighted by vertex w
    • Interpolate 1/w
    • Divide the result by interpolated 1/w
  • Print both interpolated colors
• Show the mathematical formulas used
• Compute and print the error (difference) between linear and perspective-correct results
• Explain why perspective correction matters for texture mapping
• Test at a second point (3, 2) to show the effect is consistent