Project: Math Library

• Parent: PathTracer Learning
• Phase: PathTracer Learning - Phase 1 - Math for Graphics

Goal

• Build a minimal math library for the CPU path tracer
• Understand the math by implementing it, not just using GLM

Components to Implement

• Vec3
  • +, -, *, / operators (component-wise and scalar)
  • dot(a, b) — dot product
  • cross(a, b) — cross product
  • length(v) — Euclidean length
  • normalize(v) — unit vector
  • reflect(v, n) — reflection
  • refract(v, n, eta) — refraction (Snell’s law)
  • lerp(a, b, t) — linear interpolation
• Ray
  • origin, direction fields
  • at(t) — point along ray
• Transform (4×4 matrix)
  • translate, rotate, scale constructors
  • Matrix multiply
  • transform_point(p) — apply to point (w=1)
  • transform_direction(d) — apply to direction (w=0)
  • inverse() — for normal transform

Test Cases

• dot(vec3(1,0,0), vec3(0,1,0)) == 0 (perpendicular)
• dot(vec3(1,0,0), vec3(1,0,0)) == 1 (parallel unit vectors)
• length(normalize(v)) == 1 for any non-zero v
• cross(vec3(1,0,0), vec3(0,1,0)) == vec3(0,0,1) (right-hand rule)
• reflect(vec3(1,-1,0), vec3(0,1,0)) == vec3(1,1,0) (mirror in XZ plane)

Notes

• Use float not double — GPU uses float, keep consistent
• SIMD optimization later — get correctness first
• Consider using GLM for the actual path tracer once concepts are understood