A New Approach to Line-Sphere and Line-Quadrics Intersection Detection and Computation

TL;DR

This paper introduces a novel method for detecting and computing intersections between lines and quadric surfaces, optimizing performance for ray tracing in computer graphics through pre-computation and hardware acceleration.

Contribution

It presents a new formulation that separates geometric properties, enabling pre-computation and efficient implementation on SSE instructions and GPUs.

Findings

Enhanced intersection detection efficiency

Suitable for GPU acceleration

Applicable to complex geometric rendering

Abstract

Line intersection with convex and un-convex polygons or polyhedron algorithms are well known as line clipping algorithms and very often used in computer graphics. Rendering of geometrical problems often leads to ray tracing techniques, when an intersection of many lines with spheres or quadrics is a critical issue due to ray-tracing algorithm complexity. A new formulation of detection and computation of the intersection of line (ray) with a quadric surface is presented, which separates geometric properties of the line and quadrics that enables pre-computation. The presented approach is especially convenient for implementation with SSE instructions or on GPU