Vaibhav Rathod's Notes

PathTracer Learning - Concept - Ray Definition

2 min read

  • Mathematical Definition

    • P(t) = origin + t * direction
    • origin — 3D point where the ray starts
    • direction — 3D unit vector (should be normalized)
    • t — parameter: distance along the ray
    • t > 0 → point is in front of origin
    • t < 0 → point is behind origin (usually invalid)

  • Ray Interval [t_min, t_max]

    • Not all values of t are valid
    • t_min > 0 — avoids self-intersection (shadow acne)
      • Typical value: 0.001 or 1e-4
      • Too small → shadow acne (ray hits its own surface)
      • Too large → misses nearby geometry (light leaking)
    • t_max — maximum ray distance
      • For primary rays: infinity (or very large number like 1e10)
      • For shadow rays: distance_to_light - epsilon
      • Prevents shadow rays from hitting geometry behind the light

  • Ray Types in a Path Tracer

    • Primary ray (camera ray)
      • Origin: camera position
      • Direction: through pixel (with optional jitter for anti-aliasing)
      • t_min = 0.001, t_max = infinity
    • Secondary ray (bounce ray)
      • Origin: hit point + offset along normal (to avoid self-intersection)
      • Direction: sampled from BRDF
      • t_min = 0.001, t_max = infinity
    • Shadow ray (visibility test)
      • Origin: hit point + offset
      • Direction: toward light sample
      • t_min = 0.001, t_max = distance_to_light * 0.999
      • Only need to know if occluded — use gl_RayFlagsTerminateOnFirstHitEXT

  • Self-Intersection Problem

    • When a ray bounces off a surface, the new ray origin is ON the surface
    • Floating point imprecision → ray may intersect the same surface again
    • Solutions
      • Offset origin along normal: origin = hit_point + N * 0.001
      • Use t_min = 0.001 (reject very close hits)
      • Offset in ray direction: origin = hit_point + ray_dir * 0.001 (for refraction)
    • For refraction (ray going INTO surface)
      • Offset in the OPPOSITE normal direction: origin = hit_point - N * 0.001

  • GLSL Representation

Graph View

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