HMath.Geometry.Primitives¶

Description

Checked distances, containment, intersections and primitive signed distance functions. Boundaries are included, rays return their nonnegative parameter (direction need not be normalized), and coincident/overlapping intersections are explicit. Metrics accept dimensions 1..16; discrete Jaccard uses sets.

On this page¶

API	Purpose
Metric	Minkowski p must be finite and at least one.
Euclidean	Declaration and type contract below.
Manhattan	Declaration and type contract below.
Chebyshev	Declaration and type contract below.
Minkowski	Declaration and type contract below.
distance	Euclidean, L1, Linfinity, or scaled Lp distance.
cosineDistance	One minus cosine similarity; zero vectors are undefined.
hammingDistance	Number of unequal positions (not normalized).
jaccardDistance	Set Jaccard distance; two empty sets have distance zero.
hausdorffDistance	Symmetric Hausdorff distance on two nonempty finite clouds, at most 1024 each.
mahalanobisDistance	Mahalanobis distance using a checked symmetric positive-definite covariance.
pointLineDistance	Distance to an infinite line; a zero direction is an error.
pointSegmentDistance	Distance to a closed segment, including a zero-length segment.
pointPlaneDistance	Unsigned perpendicular plane distance.
orientation	Exact orientation of the represented finite Double coordinates.
incircle	Exact in-circle sign, orientation-independent: positive means inside.
polygonLocation	Simple polygon position, with boundary separate from interior.
triangleLocation	Triangle position using exact orientation signs.
sphereContains	Closed sphere containment.
boxContains	Closed axis-aligned box containment.
ellipseContains	Closed ellipse containment after rotation to its principal axes.
triangleBarycentric	Weights (a,b,c) summing to one; valid outside the triangle as well.
circumcenter	Circumcenter, obtained from exact rational perpendicular-bisector equations.
incenter	Incenter weighted by opposite side lengths.
Intersection2	Two-dimensional intersection, with a coincident line or overlapping segment explicit.
NoIntersection	Declaration and type contract below.
IntersectionPoint	Declaration and type contract below.
OverlapSegment	Declaration and type contract below.
CoincidentLine	Declaration and type contract below.
segmentIntersection	Closed segment intersection with exact degeneracy predicates.
lineIntersection	Infinite-line intersection from origins and nonzero direction vectors.
linePlaneIntersection	Lineplane result: Nothing paralleldisjoint, Just Nothing coincident, Just (Just p) a unique intersection.
planeIntersection	Plane intersection: same nested convention as linePlaneIntersection, with the unique intersection represented by a line.
rayTriangle	Moller-Trumbore ray intersection; coplanar rays return Nothing because their hit set is not a unique transverse surface crossing.
rayBox	Slab intersection interval [entry,exit], clipped to the ray t>=0.
raySphere	Ray-sphere near/far nonnegative parameters; tangent gives equal roots.
CircleIntersection	Circle intersections: coincidence is distinct from disjointness and tangency.
DisjointCircles	Declaration and type contract below.
CoincidentCircles	Declaration and type contract below.
CirclePoints	Declaration and type contract below.
circleIntersection	Given two circles, return DisjointCircles, CoincidentCircles, or CirclePoints for their intersection.
triangleIntersection	Closed triangle overlap polygon, including isolated tangencies as vertices.
sphereSDF	Sphere signed distance (negative inside).
boxSDF	Axis-aligned box exact signed Euclidean distance in 1..16 dimensions.
obbSDF	Oriented box distance after validating its orthonormal axes.
capsuleSDF	Capsule distance from its closed axis minus radius.
cylinderSDF	Exact capped finite-cylinder signed distance.
coneSDF	Exact finite-cone distance by reducing to its radial/axial cross-section.

Documentation

Metric

data Metric Source #

Minkowski p must be finite and at least one.

Constructors

Euclidean
Manhattan
Chebyshev
Minkowski Double

Instances

Instances details

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

distance

distance :: Metric -> PointND -> PointND -> Either MathError Double Source #

Euclidean, L1, Linfinity, or scaled Lp distance.

cosineDistance

cosineDistance :: PointND -> PointND -> Either MathError Double Source #

One minus cosine similarity; zero vectors are undefined.

hammingDistance

hammingDistance :: Eq a => [a] -> [a] -> Either MathError Int Source #

Number of unequal positions (not normalized).

jaccardDistance

jaccardDistance :: Eq a => [a] -> [a] -> Either MathError Double Source #

Set Jaccard distance; two empty sets have distance zero.

hausdorffDistance

hausdorffDistance :: [PointND] -> [PointND] -> Either MathError Double Source #

Symmetric Hausdorff distance on two nonempty finite clouds, at most 1024 each.

mahalanobisDistance

mahalanobisDistance :: [[Double]] -> PointND -> PointND -> Either MathError Double Source #

Mahalanobis distance using a checked symmetric positive-definite covariance. A Cholesky triangular solve avoids an explicit inverse.

pointLineDistance

pointLineDistance :: PointND -> Line -> Either MathError Double Source #

Distance to an infinite line; a zero direction is an error.

pointSegmentDistance

pointSegmentDistance :: PointND -> Segment -> Either MathError Double Source #

Distance to a closed segment, including a zero-length segment.

pointPlaneDistance

pointPlaneDistance :: Point3 -> Plane -> Either MathError Double Source #

Unsigned perpendicular plane distance.

orientation

orientation :: Point2 -> Point2 -> Point2 -> Either MathError Orientation Source #

Exact orientation of the represented finite Double coordinates.

incircle

incircle :: Point2 -> Point2 -> Point2 -> Point2 -> Either MathError Ordering Source #

Exact in-circle sign, orientation-independent: positive means inside. A collinear defining triangle is rejected.

polygonLocation

polygonLocation :: Polygon -> Point2 -> Either MathError Location Source #

Simple polygon position, with boundary separate from interior.

triangleLocation

triangleLocation :: Triangle -> Point2 -> Either MathError Location Source #

Triangle position using exact orientation signs.

sphereContains

sphereContains :: Sphere -> Point3 -> Either MathError Bool Source #

Closed sphere containment.

boxContains

boxContains :: AABB -> PointND -> Either MathError Bool Source #

Closed axis-aligned box containment.

ellipseContains

ellipseContains :: Ellipse -> Point2 -> Either MathError Bool Source #

Closed ellipse containment after rotation to its principal axes.

triangleBarycentric

triangleBarycentric :: Triangle -> Point2 -> Either MathError [Double] Source #

Weights (a,b,c) summing to one; valid outside the triangle as well.

circumcenter

circumcenter :: Triangle -> Either MathError Point2 Source #

Circumcenter, obtained from exact rational perpendicular-bisector equations.

incenter

incenter :: Triangle -> Either MathError Point2 Source #

Incenter weighted by opposite side lengths.

Intersection2

data Intersection2 Source #

Two-dimensional intersection, with a coincident line or overlapping segment explicit.

Constructors

NoIntersection
IntersectionPoint Point2
OverlapSegment Point2 Point2
CoincidentLine

Instances

Instances details

Show Intersection2 Source #
Instance details Defined in HMath.Geometry.Primitives Methods showsPrec :: Int -> Intersection2 -> ShowS # show :: Intersection2 -> String # showList :: [Intersection2] -> ShowS #
Eq Intersection2 Source #
Instance details Defined in HMath.Geometry.Primitives Methods (==) :: Intersection2 -> Intersection2 -> Bool # (/=) :: Intersection2 -> Intersection2 -> Bool #

segmentIntersection

segmentIntersection :: Point2 -> Point2 -> Point2 -> Point2 -> Either MathError Intersection2 Source #

Closed segment intersection with exact degeneracy predicates.

lineIntersection

lineIntersection :: Point2 -> Point2 -> Point2 -> Point2 -> Either MathError Intersection2 Source #

Infinite-line intersection from origins and nonzero direction vectors.

linePlaneIntersection

linePlaneIntersection :: Line -> Plane -> Either MathError (Maybe (Maybe Point3)) Source #

Lineplane result: Nothing paralleldisjoint, Just Nothing coincident, Just (Just p) a unique intersection. The line must have dimension three.

planeIntersection

planeIntersection :: Plane -> Plane -> Either MathError (Maybe (Maybe Line)) Source #

Plane intersection: same nested convention as linePlaneIntersection, with the unique intersection represented by a line.

rayTriangle

rayTriangle :: Ray -> (Point3, Point3, Point3) -> Either MathError (Maybe Double) Source #

Moller-Trumbore ray intersection; coplanar rays return Nothing because their hit set is not a unique transverse surface crossing. Degenerate triangles fail.

rayBox

rayBox :: Ray -> AABB -> Either MathError (Maybe (Double, Double)) Source #

Slab intersection interval [entry,exit], clipped to the ray t>=0.

raySphere

raySphere :: Ray -> Sphere -> Either MathError (Maybe (Double, Double)) Source #

Ray-sphere near/far nonnegative parameters; tangent gives equal roots.

CircleIntersection

data CircleIntersection Source #

Circle intersections: coincidence is distinct from disjointness and tangency.

Constructors

DisjointCircles
CoincidentCircles
CirclePoints [Point2]

Instances

Instances details

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

circleIntersection

circleIntersection :: Circle -> Circle -> Either MathError CircleIntersection Source #

Given two circles, return DisjointCircles, CoincidentCircles, or CirclePoints for their intersection. Require valid finite centers and nonnegative bounded radii. Tangency yields one point; identical zero-radius circles yield their single center.