Computer Graphics · Cluster
Ray Tracing
Intersections, acceleration structures, and sampling.
- 01 Ray-Triangle Intersection and the Watertight Edge Test How the ray-triangle test is derived from Cramer rule, why shared edges produce pinhole artifacts, and what a watertight edge function buys and costs.
- 02 Solving Quadratic Ray Intersections Without Losing the Far Root Why the textbook quadratic formula fails for distant spheres, how the stable form differs by an addition of magnitudes, and what the determinant sign means geometrically.
- 03 Ray Parameter Intervals and the Origin Offset Problem Why a secondary ray that starts exactly on a surface hits it again, what a scaled epsilon actually moves, and how an interval filter differs from a shadow-ray flag.
- 04 The Slab Test for Boxes and the Inverse-Direction Shortcut How the ray-box test becomes three interval intersections, why precomputed reciprocals turn axis-parallel rays into NaN, and what the IEEE comparison rules do with it.
- 05 Surface Area Heuristic and the Cost Model Behind BVH Splits Why the SAH estimates traversal work with surface area, how the sweep builds the candidate list in linear time, and when object splitting beats spatial splitting.
- 06 Ordered BVH Traversal and the Per-Ray Stack How front-to-back descent keeps the ray interval shrinking, why the stack depth is bounded by tree height rather than scene size, and what happens when it is not.
- 07 Stratified Pixel Sampling and the Aliasing of Regular Grids Why a fixed sample grid folds high-frequency geometry into moire patterns, how stratification bounds the per-stratum count, and what the resulting error actually scales as.
- 08 Two-Level Hierarchies for Instanced Scenes How a top-level structure over instances plus a shared bottom-level mesh keeps memory flat, what the transform costs per ray, and why overlapping instances defeat the pruning.
- 09 Low-Discrepancy Sequences and the Correlation They Leave Behind How the radical inverse builds a progressive sequence, what discrepancy measures, and why a sampled sequence strands its structure at correlated dimensions.
- 10 Compressed BVH Nodes and Quantized Bounds How bounds shrink to byte and short quanta, what the inverse mapping costs per test, and why the compressed tree changes traversal arithmetic and memory traffic.