Vaibhav Rathod's Notes

PathTracer Learning - Project - Math Library

1 min read

  • 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

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