Back-Face Culling with Cross Products

Write a C program that implements back-face culling for a set of triangles.

Requirements:

• Define a camera at position (0, 0, 5)
• Define these triangles with CCW winding (front facing when looking down -z): T1: A=(0,0,0), B=(1,0,0), C=(0,1,0) — facing camera, should survive T2: A=(0,0,0), B=(0,1,0), C=(1,0,0) — CW winding, should be culled T3: A=(-2,0,-3), B=(-1,0,-3), C=(-2,1,-3) — behind camera plane, facing away T4: A=(2,0,1), B=(3,0,1), C=(2,1,1) — in front, facing camera
• For each triangle:
  • Compute edge vectors: e1 = B - A, e2 = C - A
  • Compute normal: N = cross(e1, e2)
  • Compute view vector: V = camera - A
  • Compute dot product: N dot V
  • Print the normal, dot product, and whether the triangle is culled or kept
• Count and print the total number of triangles kept and culled
• Explain why winding order matters for culling
• Include a note about when culling should be disabled (transparency, two-sided materials)