Perspective-Correct Interpolation

Write a C program that compares linear and perspective-correct interpolation of a color attribute across a triangle.

Requirements:

• Define a triangle in 3D: A=(-1, -1, 2, w=2), B=(1, -1, 3, w=3), C=(0, 1, 4, w=4)
• The color attribute at each vertex: A=red(1,0,0), B=green(0,1,0), C=blue(0,0,1)
• For a test point P in screen space at barycentric coordinates (u=0.33, v=0.33, w=0.34):
  • Compute the linearly interpolated color: uA_color + vB_color + w*C_color
  • Compute the perspective-correct interpolated color using 1/w weights
  • Print both results side by side
• Also test at the edge midpoint between A and B (u=0.5, v=0.5, w=0)
• Show the formula used for both methods
• Calculate the error (difference) between linear and perspective-correct results
• Print a summary explaining why linear interpolation fails under perspective projection
• Use 2 decimal places for all float output