Vertex Shader: Model-View-Projection Transform

Write a C program that implements a vertex shader transformation pipeline.

Requirements:

• Define a 4x4 matrix struct and a vec4 struct
• Implement matrix-vector multiplication for a 4x4 matrix and a 4D vector
• Define a vertex in model space: (1, 0, 0, 1)
• Define matrices:
  • Model: translation by (5, 0, 0) — moves the vertex to world space
  • View: translation by (0, 0, -10) — camera at (0,0,10) looking at origin
  • Projection: simple orthographic matrix that maps x,y to [-1,1] for a 10-unit range
• Compute and print the vertex at each stage:
  • Model space
  • After model matrix (world space)
  • After view matrix (view space)
  • After projection matrix (clip space)
• Multiply the matrices together (P * V * M) and apply the combined matrix to the original vertex
• Verify that the combined matrix gives the same result as applying each matrix in sequence
• Print all matrices and intermediate results with 2 decimal places
• Explain why the w component starts at 1 and why perspective division is needed