HMath.Geometry.Collision¶

Description

Bounded two-dimensional convex collision reference algorithms. Inputs are finite point sets whose convex hulls are the shapes. GJK uses support mapping and simplex reduction; EPA expands a support polytope for penetration; SAT tests every polygon edge normal. Touching counts as collision. Caller iteration budgets prevent unbounded work; EPA reports an estimated support-gap error, not a formal floating-point error bound. Curved 3D primitives have separate exact signed-distance APIs.

On this page¶

API	Purpose
gjk	Convex intersection by Gilbert-Johnson-Keerthi support/simplex iterations.
Penetration	Normal moves the second shape away from the first by penetrationDepth.
Penetration	Declaration and type contract below.
penetrationDepth	Estimated overlap depth along penetrationNormal, in coordinate units.
penetrationNormal	Separating direction of the returned EPA penetration estimate.
penetrationError	Remaining absolute support gap at the stopping iteration.
penetrationIterations	Completed expanding-polytope iterations.
epa	Expanding polytope penetration estimate.
separatingAxis	Separating-axis collision and minimum overlap for convex polygons.

Documentation

gjk

gjk :: Int -> [Point2] -> [Point2] -> Either MathError Bool Source #

Convex intersection by Gilbert-Johnson-Keerthi support/simplex iterations.

Penetration

data Penetration Source #

Normal moves the second shape away from the first by penetrationDepth. A zero-depth touch may have the deterministic normal (1,0).

Constructors

Penetration
Fields penetrationDepth :: Double Estimated overlap depth along penetrationNormal, in coordinate units. penetrationNormal :: Point2 Separating direction of the returned EPA penetration estimate. penetrationError :: Double Remaining absolute support gap at the stopping iteration. penetrationIterations :: Int Completed expanding-polytope iterations.

Instances

Instances details

Show Penetration Source #
Instance details Defined in HMath.Geometry.Collision Methods showsPrec :: Int -> Penetration -> ShowS # show :: Penetration -> String # showList :: [Penetration] -> ShowS #
Eq Penetration Source #
Instance details Defined in HMath.Geometry.Collision Methods (==) :: Penetration -> Penetration -> Bool # (/=) :: Penetration -> Penetration -> Bool #

epa

epa :: Int -> Double -> [Point2] -> [Point2] -> Either MathError (Maybe Penetration) Source #

Expanding polytope penetration estimate. The tolerance is an absolute support-gap stopping threshold, positive finite and <=1e50.

separatingAxis

separatingAxis :: [Point2] -> [Point2] -> Either MathError (Maybe Penetration) Source #

Separating-axis collision and minimum overlap for convex polygons. Shapes must have nonzero area; containment depth uses the distance to the nearer separating interval endpoint, rather than only the interval intersection.