HMath.Geometry

Module index · Numerical conventions

Description

Checked Cartesian geometry and bounded CPU reference algorithms. Coordinates are finite with absolute value <=1e50; ND dimensions are 1..16. Raw primitive constructors are convenient for pattern matching, so every checked operation revalidates its inputs. Boundaries are included unless an API returns an explicit Location. Two-dimensional positive orientation is counterclockwise; three-dimensional coordinates are right-handed.

Polygon Boolean output rings preserve hole orientation. Constrained Delaunay constraints are noncrossing edges, not a polygon-domain/hole specification. Spatial queries expose exact/budget-exhaustion status. Collision support APIs operate on planar convex hulls; camera transforms follow OpenGL depth rules. Each algorithm documents its finite reference budget in the defining module.

On this page

API	Purpose
Point2	Cartesian two-dimensional point, also used for vectors.
P2	Declaration and type contract below.
Point3	Cartesian right-handed three-dimensional point/vector.
P3	Declaration and type contract below.
PointND	A point of dimension 1..16.
PointND	Declaration and type contract below.
point2	Given x,y, construct Point2 after bounded finite-coordinate validation.
point3	Given x,y,z, construct Point3 after bounded finite-coordinate validation.
pointND	Construct a checked ND point from 1..16 bounded finite coordinates.
Line	Parametric line origin+t*direction; direction must be nonzero.
Line	Declaration and type contract below.
Ray	Parametric ray origin+t*direction, t>=0.
Ray	Declaration and type contract below.
Segment	Closed segment with two endpoints; zero length is valid.
Segment	Declaration and type contract below.
Plane	Plane normal dot x = offset, with a nonzero normal.
Plane	Declaration and type contract below.
Triangle	Closed triangle; zero-area triangles are rejected by triangle operations.
Triangle	Declaration and type contract below.
Rectangle	Axis-aligned rectangle with ordered corners.
Rectangle	Declaration and type contract below.
Circle	Circle with nonnegative radius.
Circle	Declaration and type contract below.
Ellipse	Rotated ellipse: positive semiaxes, counterclockwise angle in radians.
Ellipse	Declaration and type contract below.
Polygon	Simple polygon; vertices are implicitly closed and no duplicate endpoint is needed.
Polygon	Declaration and type contract below.
Sphere	Closed sphere, including a zero radius.
Sphere	Declaration and type contract below.
AABB	Ordered, closed axis-aligned bounds in 1..16 dimensions.
AABB	Declaration and type contract below.
OBB	Oriented three-dimensional box: center, three orthonormal axes, half-extents.
OBB	Declaration and type contract below.
Capsule	Capsule around the closed axis segment.
Capsule	Declaration and type contract below.
Cylinder	Finite cylinder with endpoint centers and radius; endpoints must differ.
Cylinder	Declaration and type contract below.
Cone	Finite cone with apex, base center, and radius; axis must be nonzero.
Cone	Declaration and type contract below.
Frustum	Convex frustum represented by six inward half-spaces n dot x >= offset.
Frustum	Declaration and type contract below.
Orientation	Sign of an exact predicate on the input Double values.
Clockwise	Declaration and type contract below.
Collinear	Declaration and type contract below.
Counterclockwise	Declaration and type contract below.
Location	Point position with boundary reported separately.
Outside	Declaration and type contract below.
Boundary	Declaration and type contract below.
Inside	Declaration and type contract below.

Documentation

Point2

data Point2 Source #

Cartesian two-dimensional point, also used for vectors.

Constructors

P2 Double Double

Instances

Instances details

Show Point2 Source #
Instance details Defined in HMath.Geometry.Internal Methods showsPrec :: Int -> Point2 -> ShowS # show :: Point2 -> String # showList :: [Point2] -> ShowS #
Eq Point2 Source #
Instance details Defined in HMath.Geometry.Internal Methods (==) :: Point2 -> Point2 -> Bool # (/=) :: Point2 -> Point2 -> Bool #
Ord Point2 Source #
Instance details Defined in HMath.Geometry.Internal Methods compare :: Point2 -> Point2 -> Ordering # (<) :: Point2 -> Point2 -> Bool # (<=) :: Point2 -> Point2 -> Bool # (>) :: Point2 -> Point2 -> Bool # (>=) :: Point2 -> Point2 -> Bool # max :: Point2 -> Point2 -> Point2 # min :: Point2 -> Point2 -> Point2 #

Point3

data Point3 Source #

Cartesian right-handed three-dimensional point/vector.

Constructors

P3 Double Double Double

Instances

Instances details

Show Point3 Source #
Instance details Defined in HMath.Geometry.Internal Methods showsPrec :: Int -> Point3 -> ShowS # show :: Point3 -> String # showList :: [Point3] -> ShowS #
Eq Point3 Source #
Instance details Defined in HMath.Geometry.Internal Methods (==) :: Point3 -> Point3 -> Bool # (/=) :: Point3 -> Point3 -> Bool #
Ord Point3 Source #
Instance details Defined in HMath.Geometry.Internal Methods compare :: Point3 -> Point3 -> Ordering # (<) :: Point3 -> Point3 -> Bool # (<=) :: Point3 -> Point3 -> Bool # (>) :: Point3 -> Point3 -> Bool # (>=) :: Point3 -> Point3 -> Bool # max :: Point3 -> Point3 -> Point3 # min :: Point3 -> Point3 -> Point3 #

PointND

newtype PointND Source #

A point of dimension 1..16.

Constructors

PointND [Double]

Instances

Instances details

Show PointND Source #
Instance details Defined in HMath.Geometry.Internal Methods showsPrec :: Int -> PointND -> ShowS # show :: PointND -> String # showList :: [PointND] -> ShowS #
Eq PointND Source #
Instance details Defined in HMath.Geometry.Internal Methods (==) :: PointND -> PointND -> Bool # (/=) :: PointND -> PointND -> Bool #
Ord PointND Source #
Instance details Defined in HMath.Geometry.Internal Methods compare :: PointND -> PointND -> Ordering # (<) :: PointND -> PointND -> Bool # (<=) :: PointND -> PointND -> Bool # (>) :: PointND -> PointND -> Bool # (>=) :: PointND -> PointND -> Bool # max :: PointND -> PointND -> PointND # min :: PointND -> PointND -> PointND #

point2

point2 :: Double -> Double -> Either MathError Point2 Source #

Given x,y, construct Point2 after bounded finite-coordinate validation. Invalid values return DomainError.

point3

point3 :: Double -> Double -> Double -> Either MathError Point3 Source #

Given x,y,z, construct Point3 after bounded finite-coordinate validation. Invalid values return DomainError.

pointND

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

Construct a checked ND point from 1..16 bounded finite coordinates. Invalid dimension/value returns DomainError.

Line

data Line Source #

Parametric line origin+t*direction; direction must be nonzero.

Constructors

Line PointND PointND

Instances

Instances details

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

Ray

data Ray Source #

Parametric ray origin+t*direction, t>=0.

Constructors

Ray Point3 Point3

Instances

Instances details

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

Segment

data Segment Source #

Closed segment with two endpoints; zero length is valid.

Constructors

Segment PointND PointND

Instances

Instances details

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

Plane

data Plane Source #

Plane normal dot x = offset, with a nonzero normal.

Constructors

Plane Point3 Double

Instances

Instances details

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

Triangle

data Triangle Source #

Closed triangle; zero-area triangles are rejected by triangle operations.

Constructors

Triangle Point2 Point2 Point2

Instances

Instances details

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

Rectangle

data Rectangle Source #

Axis-aligned rectangle with ordered corners.

Constructors

Rectangle Point2 Point2

Instances

Instances details

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

Circle

data Circle Source #

Circle with nonnegative radius.

Constructors

Circle Point2 Double

Instances

Instances details

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

Ellipse

data Ellipse Source #

Rotated ellipse: positive semiaxes, counterclockwise angle in radians.

Constructors

Ellipse Point2 Double Double Double

Instances

Instances details

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

Polygon

newtype Polygon Source #

Simple polygon; vertices are implicitly closed and no duplicate endpoint is needed.

Constructors

Polygon [Point2]

Instances

Instances details

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

Sphere

data Sphere Source #

Closed sphere, including a zero radius.

Constructors

Sphere Point3 Double

Instances

Instances details

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

AABB

data AABB Source #

Ordered, closed axis-aligned bounds in 1..16 dimensions.

Constructors

AABB PointND PointND

Instances

Instances details

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

OBB

data OBB Source #

Oriented three-dimensional box: center, three orthonormal axes, half-extents.

Constructors

OBB Point3 [Point3] Point3

Instances

Instances details

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

Capsule

data Capsule Source #

Capsule around the closed axis segment.

Constructors

Capsule Point3 Point3 Double

Instances

Instances details

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

Cylinder

data Cylinder Source #

Finite cylinder with endpoint centers and radius; endpoints must differ.

Constructors

Cylinder Point3 Point3 Double

Instances

Instances details

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

Cone

data Cone Source #

Finite cone with apex, base center, and radius; axis must be nonzero.

Constructors

Cone Point3 Point3 Double

Instances

Instances details

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

Frustum

newtype Frustum Source #

Convex frustum represented by six inward half-spaces n dot x >= offset.

Constructors

Frustum [Plane]

Instances

Instances details

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

Orientation

data Orientation Source #

Sign of an exact predicate on the input Double values.

Constructors

Clockwise
Collinear
Counterclockwise

Instances

Instances details

Show Orientation Source #
Instance details Defined in HMath.Geometry.Internal Methods showsPrec :: Int -> Orientation -> ShowS # show :: Orientation -> String # showList :: [Orientation] -> ShowS #
Eq Orientation Source #
Instance details Defined in HMath.Geometry.Internal Methods (==) :: Orientation -> Orientation -> Bool # (/=) :: Orientation -> Orientation -> Bool #
Ord Orientation Source #
Instance details Defined in HMath.Geometry.Internal Methods compare :: Orientation -> Orientation -> Ordering # (<) :: Orientation -> Orientation -> Bool # (<=) :: Orientation -> Orientation -> Bool # (>) :: Orientation -> Orientation -> Bool # (>=) :: Orientation -> Orientation -> Bool # max :: Orientation -> Orientation -> Orientation # min :: Orientation -> Orientation -> Orientation #

Location

data Location Source #

Point position with boundary reported separately.

Constructors

Outside
Boundary
Inside

Instances

Instances details

Show Location Source #
Instance details Defined in HMath.Geometry.Internal Methods showsPrec :: Int -> Location -> ShowS # show :: Location -> String # showList :: [Location] -> ShowS #
Eq Location Source #
Instance details Defined in HMath.Geometry.Internal Methods (==) :: Location -> Location -> Bool # (/=) :: Location -> Location -> Bool #
Ord Location Source #
Instance details Defined in HMath.Geometry.Internal Methods compare :: Location -> Location -> Ordering # (<) :: Location -> Location -> Bool # (<=) :: Location -> Location -> Bool # (>) :: Location -> Location -> Bool # (>=) :: Location -> Location -> Bool # max :: Location -> Location -> Location # min :: Location -> Location -> Location #

module HMath.Geometry.Primitives

module HMath.Geometry.Polygon

module HMath.Geometry.Triangulation

module HMath.Geometry.Spatial

module HMath.Geometry.Collision

module HMath.Geometry.Transform