Mathematics: Intersection 3D

The following table shows what queries are implemented and gives you an easy lookup for the source code. The acronyms are point (PNT), line (LIN), ray (RAY), segment (SEG), plane (PLN), triangle (TRI), rectangle (RCT), circle (CIR), ellipse (ELL), aligned box (ABX), oriented box (OBX), orthogonal frustum (FRU), tetrahedron (TET), polyhedron (PHD), halfspace (HSP), sphere (SPH), ellipsoid (EPD), capsule (CAP), cone (CON), cylinder (CYL), and torus (TOR). Selecting a table entry will load the source code in a separate browser tab. If you are looking for a query that is not in this table, send us a request and we will try to schedule time to implement it.

  LIN RAY SEG PLN TRI RCT CIR ELL ABX OBX FRU TET PHD HSP SPH EPD CAP CON CYL TOR
LIN - - - - - - - - - - -
RAY - - - - - - - - - - -
SEG - - - - - - - - - -
PLN - - - - - - - - -
TRI - - - - - - - - - - - - -
RCT - - - - - - - - - - - - - - - - - - - -
CIR - - - - - - - - - - - - - - - - - - -
ELL - - - - - - - - - - - - - - - - - - -
ABX - - - - - - - - - - - -
OBX - - - - - - - -
FRU - - - - - - - - - - - - - - - - - -
TET - - - - - - - - - - - - - - - - - - - -
PHD - - - - - - - - - - - - - - - - - - - -
HSP - - - - - - - - - - - - -
SPH - - - - - - - - -
EPD - - - - - - - - - - - - - -
CAP - - - - - - - - - - - - - -
CON - - - - - - - - - - - - - -
CYL - - - - - - - - - - - - -
TOR - - - - - - - - - - - - - - - - - - - -



A great portal for various 3D intersection algorithms is Eric Haine's web page that is associated with the Real-Time Rendering book.
Template definition for test-intersection queries (TIQuery) and find-intersection queries (FIQuery). Intersection queries for two intervals (1-dimensional query).
Linear-planar intersection queries: line, ray, or segment versus plane or triangle
Linear-volumetric intersection queries: line, ray, or segment versus alignedbox, orientedbox, sphere, ellipsoid, cylinder, cone, or capsule; segment-halfspace
Planar-planar intersection queries: plane-plane, plane-triangle, plane-circle or triangle, convexpolygon-plane (partition into positive, negative, and coincident parts)
Planar-volumetric intersection queries: plane versus orientedbox, sphere, ellipsoid, cylinder, capsule; triangle-halfspace, triangle-orientedbox
Volumetric-volumetric intersection queries.