#include <geometryutils.h>

Detailed Description

2D and 3D geometrical utility functions.

Static Public Member Functions
static MAXON_METHOD Float	LinearRemapToRange (Float value, Float from1, Float to1, Float from2, Float to2)

static MAXON_METHOD Float	GetAngle2D (const Vector2d &direction1, const Vector2d &direction2)

static MAXON_METHOD Float	InterpolatePointOnSegment (const Vector &segmentPoint1, const Vector &segmentPoint2, const Vector &point, Bool clamp=true)

static MAXON_METHOD Float	InterpolatePointOnSegment2D (const Vector2d &segmentPoint1, const Vector2d &segmentPoint2, const Vector2d &point, Bool clamp=true)

static MAXON_METHOD Bool	CalculateBestFitPlane (const Block< const Vector > &pointCloud, Vector &centroid, Vector &normal, Int iterMax=500)

static MAXON_METHOD Result< void >	Points3Dto2D (const Block< const Vector > &points, const Vector &normal, Vector &basisVector0, Vector &basisVector1, Vector &translate, Bool checkDegenerated, WritableArrayInterface< Vector2d > &outPoints, Bool computeBasis=true)

static MAXON_METHOD Result< void >	Points3Dto2D (const Block< const Vector > &points, const Vector &normal, Bool checkDegenerated, WritableArrayInterface< Vector2d > &outPoints)

static MAXON_METHOD Vector	Point2Dto3D (const Vector2d &point, const Vector &basisVector0, const Vector &basisVector1, const Vector &translate)

static MAXON_METHOD Result< void >	Points2Dto3D (const Block< const Vector2d > &points, const Vector &basisVector0, const Vector &basisVector1, const Vector &translate, WritableArrayInterface< Vector > &outPoints)

static MAXON_METHOD Float	CalculateTriangleArea (const Vector &a, const Vector &b, const Vector &c)

static MAXON_METHOD Float	CalculateSignedTriangleArea (const Vector &a, const Vector &b, const Vector &c)

static MAXON_METHOD Float	CalculateQuadrangleArea (const Vector &a, const Vector &b, const Vector &c, const Vector &d)

static MAXON_METHOD Float	CalculateOutlineArea (const Block< const Vector > &outlinePoints)

static MAXON_METHOD Vector	CalculateOutlineNormal (const Block< const Vector > &points, const Block< const Int32 > &indices, Bool normalized=true)

static MAXON_METHOD Vector	CalculateOutlineNormal (const Block< const Vector > &points, Bool normalize=true)

static MAXON_METHOD Bool	IsVertexConvex (const Vector &vertex, const Vector &next, const Vector &pred, const Vector &up=Vector(0, 1, 0))

static MAXON_METHOD Result< void >	CalculateMeanValueCoordinatesWeights (const Vector &point, const Block< const Vector > &outline, WritableArrayInterface< Float > &weights)

static MAXON_METHOD Bool	IsVertexConvex2D (const Vector2d &vertex, const Vector2d &next, const Vector2d &pred)

static MAXON_METHOD Vector2d	CalculateBarycentricCoordinate (const Vector &point, const Vector &a, const Vector &b, const Vector &c)

static MAXON_METHOD Vector	CalculateBarycentricCoordinate3D (const Vector &point, const Vector &a, const Vector &b, const Vector &c)

static MAXON_METHOD Bool	PointInTriangle (const Vector &point, const Vector &a, const Vector &b, const Vector &c)

static MAXON_METHOD Bool	PointInTriangle2D (const Vector2d &point, const Vector2d &a, const Vector2d &b, const Vector2d &c)

static MAXON_METHOD Int	GetPointInPolygonWindingNumber2D (Vector2d point, const Block< const Vector2d > &outline)

static MAXON_METHOD Int	GetPointInPolygonWindingNumber2DExact (Vector2d point, const Block< const Vector2d > &outline)

static MAXON_METHOD Int	GetPointInPolygonWindingNumber2D (Vector2d point, const Block< const Vector2d > &outline, Int &edgeHit)

static MAXON_METHOD Int	GetPointInPolygonWindingNumber (Vector point, const Block< const Vector > &outline)

static MAXON_METHOD Int	GetPointInPolygonWindingNumber (Vector point, const Block< const Vector > &outline, Int &edgeHit)

static MAXON_METHOD Bool	PointInOutline2D (const Vector &point, const Block< const Vector2d > &outline)

static MAXON_METHOD Vector	CalculateBisector (const Vector &v1, const Vector &v2, const Vector &up=Vector(0, 1, 0), Float w1=1.0, Float w2=1.0)

static MAXON_METHOD Bool	CalculateCircumcenter2D (const Vector2d &a, const Vector2d &b, const Vector2d &c, Vector2d &center, Float &sqrRad, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	CalculateCircumcenter (const Vector &a, const Vector &b, const Vector &c, Vector &center, Float &rad, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	SegmentsIntersectionTest2D (const Vector2d &segment1Point1, const Vector2d &segment1Point2, const Vector2d &segment2Point1, const Vector2d &segment2Point2)

static MAXON_METHOD Bool	IntersectsSegments2D (const Vector2d &segment1Point1, const Vector2d &segment1Point2, const Vector2d &segment2Point1, const Vector2d &segment2Point2, Vector2d &intersectionPoint, Float tolerance=0.0)

static MAXON_METHOD Vector	LineLineDistance (const Vector &line1Point, const Vector &line1Dir, const Vector &line2Point, const Vector &line2Dir, Bool &parallel, Float &param1, Float &param2, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	PointInSegment2D (const Vector2d &point, const Vector2d &segmentPoint1, const Vector2d &segmentPoint2, Float tolerance)

static MAXON_METHOD Bool	PointInSegment (const Vector &point, const Vector &segmentPoint1, const Vector &segmentPoint2, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	PointInHalfLine (const Vector &point, const Vector &halfLineOrigin, const Vector &halfLineDir, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLines (const Vector &line1Point, const Vector &line1Dir, const Vector &line2Point, const Vector &line2Dir, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLineSegment (const Vector &linePoint, const Vector &lineDir, const Vector &segmentPoint1, const Vector &segmentPoint2, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectSegments (const Vector &segment1Point1, const Vector &segment1Point2, const Vector &segment2Point1, const Vector &segment2Point2, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectHalfLines (const Vector &halfLine1Origin, const Vector &halfLine1Dir, const Vector &halfLine2Origin, const Vector &halfLine2Dir, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLineHalfLine (const Vector &linePoint, const Vector &lineDir, const Vector &halfLineOrigin, const Vector &halfLineDir, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectHalfLineSegment (const Vector &halfLineOrigin, const Vector &halfLineDir, const Vector &segmentPoint1, const Vector &segmentPoint2, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectPlanes (const Vector &plane1Point, const Vector &plane1Normal, const Vector &plane2Point, const Vector &plane2Normal, Vector &resLinePoint, Vector &resLineDirection, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLinePlane (const Vector &linePoint, const Vector &lineDir, const Vector &planePoint, const Vector &planeNormal, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLinePlane (const Vector &linePoint, const Vector &lineDir, const Vector &planePoint, const Vector &planeNormal, Vector &intersectionPoint, Float &param, Bool &samePlane, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectSegmentPlane (const Vector &segmentPoint1, const Vector &segmentPoint2, const Vector &planePoint, const Vector &planeNormal, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectHalfLinePlane (const Vector &halfLinePoint, const Vector &halfLineDir, const Vector &planePoint, const Vector &planeNormal, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLineTriangle (const Vector &linePoint, const Vector &lineDir, const Vector &a, const Vector &b, const Vector &c, Vector &intersectionPoint, Vector2d *barycCoords=nullptr, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectHalfLineTriangle (const Vector &halfLineOrigin, const Vector &halfLineDir, const Vector &a, const Vector &b, const Vector &c, Vector &intersectionPoint, Vector2d *barycCoords=nullptr, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectLineQuadrangle (const Vector &linePoint, const Vector &lineDir, const Vector &a, const Vector &b, const Vector &c, const Vector &d, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectHalfLineQuadrangle (const Vector &halfLineOrigin, const Vector &halfLineDir, const Vector &a, const Vector &b, const Vector &c, const Vector &d, Vector &intersectionPoint, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	IntersectSegmentTriangle (const Vector &segmentPoint1, const Vector &segmentPoint2, const Vector &a, const Vector &b, const Vector &c, Vector &intersectionPoint, Vector *barycCoords=nullptr, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	TrianglesIntersectionTest (const Vector &t1a, const Vector &t1b, const Vector &t1c, const Vector &t2a, const Vector &t2b, const Vector &t2c, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD Bool	CalculatePolygonPointST (const Vector &point, const Vector &pa, const Vector &pb, const Vector &pc, const Vector &pd, Bool isQuad, Float &s, Float &t, Float tolerance=GeomConstants::EPSILON4)

static MAXON_METHOD void	InverseBilinarInterpolate (const Vector &pa, const Vector &pb, const Vector &pc, const Vector &pd, const Vector &point, Vector2d &bilinarVariables)

static MAXON_METHOD void	InverseBilinarInterpolateNewton (const Vector &pa, const Vector &pb, const Vector &pc, const Vector &pd, const Vector &point, Int32 iterations, Vector2d &bilinarVariables)

static MAXON_METHOD void	InverseBilinarInterpolate2D (const Vector2d &pa, const Vector2d &pb, const Vector2d &pc, const Vector2d &pd, const Vector2d &point, Vector2d &bilinarVariables)

static MAXON_METHOD void	InverseBilinarInterpolate2DNewton (const Vector2d &pa, const Vector2d &pb, const Vector2d &pc, const Vector2d &pd, const Vector2d &point, Int32 iterations, Vector2d &bilinarVariables)

static MAXON_METHOD Vector	BilinearInterpolate (const Vector &pa, const Vector &pb, const Vector &pc, const Vector &pd, const Float s, const Float t)

static MAXON_METHOD Float	CalculateSignedTriangleArea (const Vector &a, const Vector &b, const Vector &c, const Vector &normal)

static MAXON_METHOD Result< void >	CalculateMeanValueCoordinatesWeights (const Vector &point, const Block< const Vector > &outline, const Vector &normal, WritableArrayInterface< Float > &weights)

Private Member Functions
	MAXON_INTERFACE_NONVIRTUAL (GeometryUtilsInterface, MAXON_REFERENCE_NONE, "net.maxon.geom.geometryutils")

Member Function Documentation

◆ MAXON_INTERFACE_NONVIRTUAL()

MAXON_INTERFACE_NONVIRTUAL	(	GeometryUtilsInterface	,
		MAXON_REFERENCE_NONE	,
		"net.maxon.geom.geometryutils"
	)

private

◆ LinearRemapToRange()

static MAXON_METHOD Float LinearRemapToRange	(	Float	value,
		Float	from1,
		Float	to1,
		Float	from2,
		Float	to2
	)

static

Remaps a value from one range to another.

Parameters

[in]	value	The value to remap.
[in]	from1	First bound of source range.
[in]	to1	Second bound of source range.
[in]	from2	First bound of destination range.
[in]	to2	Second bound of destination range.

Returns: The remapped value.

◆ GetAngle2D()

static MAXON_METHOD Float GetAngle2D	(	const Vector2d &	direction1,
		const Vector2d &	direction2
	)

static

Gets the 2D angle between two direction vectors.

Parameters

[in]	direction1	First direction vector.
[in]	direction2	Second direction vector.

Returns: The angle value in between 0 and 2PI in radians.

◆ InterpolatePointOnSegment()

static MAXON_METHOD Float InterpolatePointOnSegment	(	const Vector &	segmentPoint1,
		const Vector &	segmentPoint2,
		const Vector &	point,
		Bool	clamp = `true`
	)

static

Calculates the normalized position of a point along a directed segment.

Parameters

[in]	segmentPoint1	First segment point.
[in]	segmentPoint2	Second segment point.
[in]	point	The point position along the segment line.
[in]	clamp	If true the resulting value will be clamped between 0 and 1.

Returns: The normalized position of the point on the segment.

◆ InterpolatePointOnSegment2D()

static MAXON_METHOD Float InterpolatePointOnSegment2D	(	const Vector2d &	segmentPoint1,
		const Vector2d &	segmentPoint2,
		const Vector2d &	point,
		Bool	clamp = `true`
	)

static

Calculates the normalized position of a 2D point along a directed segment.

Parameters

[in]	segmentPoint1	First segment point.
[in]	segmentPoint2	Second segment point.
[in]	point	The point position along the segment line.
[in]	clamp	If true the resulting value will be clamped between 0 and 1.

Returns: The normalized position of the point on the segment.

◆ CalculateBestFitPlane()

static MAXON_METHOD Bool CalculateBestFitPlane	(	const Block< const Vector > &	pointCloud,
		Vector &	centroid,
		Vector &	normal,
		Int	iterMax = `500`
	)

static

Calculates the the best fit plane centroid and normal from a point cloud.

Parameters

[in]	pointCloud	A block filled with point coordinates.
[out]	centroid	The resulting point cloud centroid.
[out]	normal	The resulting plane normal.
[in]	iterMax	Max iteration for computation.

Returns: True if successful otherwise false.

◆ Points3Dto2D() [1/2]

static MAXON_METHOD Result<void> Points3Dto2D	(	const Block< const Vector > &	points,
		const Vector &	normal,
		Vector &	basisVector0,
		Vector &	basisVector1,
		Vector &	translate,
		Bool	checkDegenerated,
		WritableArrayInterface< Vector2d > &	outPoints,
		Bool	computeBasis = `true`
	)

static

Projects 3D points as 2D points on a plane which is parallel to the points best fit plane and which passes through the origin of the world coordinate system.

Parameters

[in]	points	Points 3D positions to project.
[in]	normal	The normal vector of the plane onto which to project the points.
[in,out]	basisVector0	First basis vector of the 2D plane coordinate system.
[in,out]	basisVector1	Second basis vector of the 2D plane coordinate system.
[out]	translate	Translation vector between the projection plane origin (which is the world CS origin) and the best fit plane origin (which is the orthogonal projection of the world CS origin to the fit plane). In other words, translation vector is the distance vector between the projection plane an the best fit planes.
[in]	checkDegenerated	If true try to avoid cases where the resulting 2d outline contains coincident vertices.
[out]	outPoints	Array containing 2D projected points positions.
[out]	computeBasis	Compute basis vectors from the normal and the input points if enabled.

Returns: OK on success. DegeneratedInputError if input points are collapsed in one point.

◆ Points3Dto2D() [2/2]

static MAXON_METHOD Result<void> Points3Dto2D	(	const Block< const Vector > &	points,
		const Vector &	normal,
		Bool	checkDegenerated,
		WritableArrayInterface< Vector2d > &	outPoints
	)

static

Projects 3D points as 2D points on a plane. Overloaded function.

Parameters

[in]	points	Points 3D positions to project.
[in]	normal	The normal vector of the plane onto which to project the points.
[in]	checkDegenerated	If true try to avoid cases where the resulting 2d outline contains coincident vertices.
[out]	outPoints	Array containing 2D projected points positions.

Returns: OK on success. DegeneratedInputError if input points are collapsed in one point.

◆ Point2Dto3D()

static MAXON_METHOD Vector Point2Dto3D	(	const Vector2d &	point,
		const Vector &	basisVector0,
		const Vector &	basisVector1,
		const Vector &	translate
	)

static

Calculates 3D world point coordinates from its 2D local coordinates.

Parameters

[in]	point	Point 2D local coordinates.
[in]	basisVector0	First basis vector of the 2D local coordinate system.
[in]	basisVector1	Second basis vector of the 2D local coordinate system.
[in]	translate	Translation vector.

Returns: Point 3D world coordinates.

◆ Points2Dto3D()

static MAXON_METHOD Result<void> Points2Dto3D	(	const Block< const Vector2d > &	points,
		const Vector &	basisVector0,
		const Vector &	basisVector1,
		const Vector &	translate,
		WritableArrayInterface< Vector > &	outPoints
	)

static

Calculates 3D world points coordinates from its 2D local coordinates.

Parameters

[in]	points	Points 2D local coordinates.
[in]	basisVector0	First basis vector of the 2D local coordinate system.
[in]	basisVector1	Second basis vector of the 2D local coordinate system.
[in]	translate	Translation vector.
[out]	outPoints	Points 3D world coordinates.

◆ CalculateTriangleArea()

static MAXON_METHOD Float CalculateTriangleArea	(	const Vector &	a,
		const Vector &	b,
		const Vector &	c
	)

static

Calculates the area of a triangle.

Parameters

[in]	a	Triangle point A.
[in]	b	Triangle point B.
[in]	c	Triangle point C.

Returns: Unsigned triangle area.

◆ CalculateSignedTriangleArea() [1/2]

static MAXON_METHOD Float CalculateSignedTriangleArea	(	const Vector &	a,
		const Vector &	b,
		const Vector &	c
	)

static

Calculates the signed area of an oriented triangle. Sign is defined as the sign of the z coordinate of the triangle normal vector.

Parameters

[in]	a	Triangle point A.
[in]	b	Triangle point B.
[in]	c	Triangle point C.

Returns: Unsigned triangle area.

◆ CalculateQuadrangleArea()

static MAXON_METHOD Float CalculateQuadrangleArea	(	const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		const Vector &	d
	)

static

Calculates the area of a quadrangle.

Parameters

[in]	a	Quadrangle point A.
[in]	b	Quadrangle Point B.
[in]	c	Quadrangle Point C.
[in]	d	Quadrangle Point D.

Returns: Unsigned area of Quadrangle.

◆ CalculateOutlineArea()

static MAXON_METHOD Float CalculateOutlineArea ( const Block< const Vector > & outlinePoints )

static

Calculates the unsigned area of an outline defined by points in outlinePoints. If the points are not co-planar, they will be flattened on a "best fit" plane.

Parameters

[in] outlinePoints An array with a point sequence.

Returns: The outline area.

◆ CalculateOutlineNormal() [1/2]

static MAXON_METHOD Vector CalculateOutlineNormal	(	const Block< const Vector > &	points,
		const Block< const Int32 > &	indices,
		Bool	normalized = `true`
	)

static

Calculates the normal of an ngon outline.

Parameters

[in]	points	A list of points that includes the outline points.
[in]	indices	The indices in the points list for the outline points to use. The order is important.
[in]	normalized	If true, the output normal will be normalized.

Returns: The normal of the point outline.

◆ CalculateOutlineNormal() [2/2]

static MAXON_METHOD Vector CalculateOutlineNormal	(	const Block< const Vector > &	points,
		Bool	normalize = `true`
	)

static

Calculates the normal of an ngon outline.

Parameters

[in]	points	The correctly ordered points that include the points for the outline.
[in]	normalize	If true, the output normal will be normalized.

Returns: The normal of the point outline.

◆ IsVertexConvex()

static MAXON_METHOD Bool IsVertexConvex	(	const Vector &	vertex,
		const Vector &	next,
		const Vector &	pred,
		const Vector &	up = `Vector(0, 1, 0)`
	)

static

A convexity test for vertex in between 2 other vertices in 3D space.

Parameters

[in]	vertex	The vertex to check.
[in]	next	The next point.
[in]	pred	The prev point.
[in]	up	Up vector or the normal of the polygon.

Returns: True if vertex is convex otherwise false, in case of aligned point (angle == PI) return true.

◆ CalculateMeanValueCoordinatesWeights() [1/2]

static MAXON_METHOD Result<void> CalculateMeanValueCoordinatesWeights	(	const Vector &	point,
		const Block< const Vector > &	outline,
		WritableArrayInterface< Float > &	weights
	)

static

Calculates the mean value coordinates weights for a point inside an outline.

Parameters

[in]	point	The point for which to calculate weights.
[in]	outline	The outline.
[in]	weights	Array of weights. The amount of entries in the resulting array is the same amount of outline vertices.

Returns: OK on success.

◆ IsVertexConvex2D()

static MAXON_METHOD Bool IsVertexConvex2D	(	const Vector2d &	vertex,
		const Vector2d &	next,
		const Vector2d &	pred
	)

static

A convexity test for vertex in between two other vertices in 2D.

Parameters

[in]	vertex	The vertex to check.
[in]	next	The next point.
[in]	pred	The prev point.

Returns: True if vertex is convex otherwise false, in case of aligned point (angle == PI) return true.

◆ CalculateBarycentricCoordinate()

static MAXON_METHOD Vector2d CalculateBarycentricCoordinate	(	const Vector &	point,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c
	)

static

Calculates the barycentric UV coordinate of a point within a triangle.

Parameters

[in]	point	The point.
[in]	a	Triangle vertex A.
[in]	b	Triangle vertex B.
[in]	c	Triangle vertex C.

Returns: The barycentric point coordinate. 'x' component of the vector is the coordinate of the point c, 'y' component of the vector is the coordinate of the point b.

◆ CalculateBarycentricCoordinate3D()

static MAXON_METHOD Vector CalculateBarycentricCoordinate3D	(	const Vector &	point,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c
	)

static

Calculates the barycentric UVW coordinate of a point within a triangle.

Parameters

[in]	point	The point.
[in]	a	Triangle vertex A.
[in]	b	Triangle vertex B.
[in]	c	Triangle vertex C.

Returns: The barycentric point coordinate.

◆ PointInTriangle()

static MAXON_METHOD Bool PointInTriangle	(	const Vector &	point,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c
	)

static

Checks if a point is inside a triangle.

Parameters

[in]	point	The point to test.
[in]	a	Triangle vertex A.
[in]	b	Triangle vertex B.
[in]	c	Triangle vertex C.

Returns: True if point is inside the triangle.

◆ PointInTriangle2D()

static MAXON_METHOD Bool PointInTriangle2D	(	const Vector2d &	point,
		const Vector2d &	a,
		const Vector2d &	b,
		const Vector2d &	c
	)

static

Checks if a point is inside triangle in 2D.

Parameters

[in]	point	The point to test.
[in]	a	Triangle vertex A.
[in]	b	Triangle vertex B.
[in]	c	Triangle vertex C.

Returns: True if point is inside the triangle.

◆ GetPointInPolygonWindingNumber2D() [1/2]

static MAXON_METHOD Int GetPointInPolygonWindingNumber2D	(	Vector2d	point,
		const Block< const Vector2d > &	outline
	)

static

Checks if a point is inside an outline.

Parameters

[in]	point	The point ot test.
[in]	outline	The array with outline points.

Returns: The resulting winding number, 0 means point is outside.

◆ GetPointInPolygonWindingNumber2DExact()

static MAXON_METHOD Int GetPointInPolygonWindingNumber2DExact	(	Vector2d	point,
		const Block< const Vector2d > &	outline
	)

static

Checks if a point is inside an outline. Exact yet slower version.

Parameters

[in]	point	The point ot test.
[in]	outline	The array with outline points.

Returns: The resulting winding number, 0 means point is outside.

◆ GetPointInPolygonWindingNumber2D() [2/2]

static MAXON_METHOD Int GetPointInPolygonWindingNumber2D	(	Vector2d	point,
		const Block< const Vector2d > &	outline,
		Int &	edgeHit
	)

static

Checks if a point is inside an outline.

Parameters

[in]	point	The point ot test.
[in]	outline	The array with outline points.
[out]	edgeHit	In case point lies on an outline edge this will be filled with the edge index, otherwise maxon::InvalidArrayIndex.

Returns: The resulting winding number, 0 means point is outside.

◆ GetPointInPolygonWindingNumber() [1/2]

static MAXON_METHOD Int GetPointInPolygonWindingNumber	(	Vector	point,
		const Block< const Vector > &	outline
	)

static

Checks if a point is inside an outline. Accepts 3d vectors but assumes points to lie in xy plane.

Parameters

[in]	point	The point to test.
[in]	outline	The array with outline points.

Returns: The resulting winding number. 0 means point is outside.

◆ GetPointInPolygonWindingNumber() [2/2]

static MAXON_METHOD Int GetPointInPolygonWindingNumber	(	Vector	point,
		const Block< const Vector > &	outline,
		Int &	edgeHit
	)

static

Checks if a point is inside an outline. Accepts 3d vectors but assumes points to lie in xy plane.

Parameters

[in]	point	The point to test.
[in]	outline	The array with outline points.
[out]	edgeHit	In case point lies on an outline edge, this will be filled with the edge index. Otherwise the value maxon::InvalidArrayIndex is set.

Returns: The resulting winding number. 0 means point is outside.

◆ PointInOutline2D()

static MAXON_METHOD Bool PointInOutline2D	(	const Vector &	point,
		const Block< const Vector2d > &	outline
	)

static

Checks if a point is inside an outline.

Parameters

[in]	point	The point ot test.
[in]	outline	The array with outline points.

Returns: True if the point is inside the outline.

◆ CalculateBisector()

static MAXON_METHOD Vector CalculateBisector	(	const Vector &	v1,
		const Vector &	v2,
		const Vector &	up = `Vector(0, 1, 0)`,
		Float	w1 = `1.0`,
		Float	w2 = `1.0`
	)

static

Calculates the 3D bisector angle using an up vector to identify the sliding surface. A custom weight for each side can optionally be specified.

Parameters

[in]	v1	First vector.
[in]	v2	Second vector.
[in]	up	The up vector.
[in]	w1	Optional weight value for v1.
[in]	w2	Optional weight value for v2.

Returns: The bisector angle vector.

◆ CalculateCircumcenter2D()

static MAXON_METHOD Bool CalculateCircumcenter2D	(	const Vector2d &	a,
		const Vector2d &	b,
		const Vector2d &	c,
		Vector2d &	center,
		Float &	sqrRad,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Calculates the circumcenter and radius of a planar triangle.

Parameters

[in]	a	Triangle point A.
[in]	b	Triangle point B.
[in]	c	Triangle point C.
[out]	center	Triangle circumcenter.
[out]	sqrRad	Squared radius of the circle defined by the triangle points.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: False if the points are collinear or if the triangle is collapsed, true otherwise.

◆ CalculateCircumcenter()

static MAXON_METHOD Bool CalculateCircumcenter	(	const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		Vector &	center,
		Float &	rad,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Calculates the circumcenter and radius of a triangle.

Parameters

[in]	a	Triangle point A.
[in]	b	Triangle point B.
[in]	c	Triangle point C.
[out]	center	Triangle circumcenter.
[out]	rad	Radius of the circle defined by the triangle points.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: False if the points are collinear or if the triangle is collapsed, true otherwise.

◆ SegmentsIntersectionTest2D()

static MAXON_METHOD Bool SegmentsIntersectionTest2D	(	const Vector2d &	segment1Point1,
		const Vector2d &	segment1Point2,
		const Vector2d &	segment2Point1,
		const Vector2d &	segment2Point2
	)

static

Checks if two segments intersect in 2D space.

Parameters

[in]	segment1Point1	First segment point 1.
[in]	segment1Point2	First segment point 2.
[in]	segment2Point1	Second segment point 1.
[in]	segment2Point2	Second segment point 2.

Returns: True if the segments intersect in 2D.

◆ IntersectsSegments2D()

static MAXON_METHOD Bool IntersectsSegments2D	(	const Vector2d &	segment1Point1,
		const Vector2d &	segment1Point2,
		const Vector2d &	segment2Point1,
		const Vector2d &	segment2Point2,
		Vector2d &	intersectionPoint,
		Float	tolerance = `0.0`
	)

static

Checks if two segment intersect in 2D space and calculates the intersection point (if any).

Parameters

[in]	segment1Point1	First segment point.
[in]	segment1Point2	First segment point.
[in]	segment2Point1	Second segment point.
[in]	segment2Point2	Second segment point.
[out]	intersectionPoint	Calculated intersection point in xy plane.
[in]	tolerance	Geometric linear tolerance for the operation by default = 0.0.

Returns: True if the segments intersect in 2D.

◆ LineLineDistance()

static MAXON_METHOD Vector LineLineDistance	(	const Vector &	line1Point,
		const Vector &	line1Dir,
		const Vector &	line2Point,
		const Vector &	line2Dir,
		Bool &	parallel,
		Float &	param1,
		Float &	param2,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Calculates min distance for given lines, fill param1/param2 with parametrized distance form first point.

Parameters

[in]	line1Point	A point on first line.
[in]	line1Dir	First line direction vector.
[in]	line2Point	A point on second line.
[in]	line2Dir	Second line direction vector.
[out]	parallel	The function set it true if the tow line are parallel.
[out]	param1	Parametrized distance from fist line first point where the distance is calculated (p = line1Point + !line1Dir * param1)
[out]	param2	Parametrized distance from second line first point where the distance is calculated (p = line2Point + !line2Dir * param2)
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: Distance Vector.

◆ PointInSegment2D()

static MAXON_METHOD Bool PointInSegment2D	(	const Vector2d &	point,
		const Vector2d &	segmentPoint1,
		const Vector2d &	segmentPoint2,
		Float	tolerance
	)

static

Checks if a point is on a line segment in 2D. The tolerance value is used for the colinearity test only, not for the boundary test.

Parameters

[in]	point	The point to check.
[in]	segmentPoint1	1st Segment point.
[in]	segmentPoint2	2nd Segment point.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if point is on segment, otherwise false.

◆ PointInSegment()

static MAXON_METHOD Bool PointInSegment	(	const Vector &	point,
		const Vector &	segmentPoint1,
		const Vector &	segmentPoint2,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks if a point is on a line segment in 3D. The tolerance value is used for the colinearity test only, not for the boundary test.

Parameters

[in]	point	The point to check.
[in]	segmentPoint1	1st Segment point.
[in]	segmentPoint2	2nd Segment point.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if point is on segment, otherwise false.

◆ PointInHalfLine()

static MAXON_METHOD Bool PointInHalfLine	(	const Vector &	point,
		const Vector &	halfLineOrigin,
		const Vector &	halfLineDir,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks if a point is on a half line .

Parameters

[in]	point	The point to check.
[in]	halfLineOrigin	Half line origin.
[in]	halfLineDir	Half line direction.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if point is on half line, otherwise false.

◆ IntersectLines()

static MAXON_METHOD Bool IntersectLines	(	const Vector &	line1Point,
		const Vector &	line1Dir,
		const Vector &	line2Point,
		const Vector &	line2Dir,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for intersection between two lines and fills intersectionPoint with the intersection position.

Parameters

[in]	line1Point	A point on 1st line.
[in]	line1Dir	1st line direction vector.
[in]	line2Point	A point on 2nd line.
[in]	line2Dir	2nd line direction vector.
[out]	intersectionPoint	Resulting intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectLineSegment()

static MAXON_METHOD Bool IntersectLineSegment	(	const Vector &	linePoint,
		const Vector &	lineDir,
		const Vector &	segmentPoint1,
		const Vector &	segmentPoint2,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for line vs. segment intersection and fills intersection with the intersection position.

Parameters

[in]	linePoint	A point on the line.
[in]	lineDir	Line direction vector.
[in]	segmentPoint1	First segment point.
[in]	segmentPoint2	Second segment point.
[out]	intersectionPoint	Resulting intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectSegments()

static MAXON_METHOD Bool IntersectSegments	(	const Vector &	segment1Point1,
		const Vector &	segment1Point2,
		const Vector &	segment2Point1,
		const Vector &	segment2Point2,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for segment vs. segment intersection and fills intersection with the intersection position.

Parameters

[in]	segment1Point1	First Segment first point.
[in]	segment1Point2	First Segment second point.
[in]	segment2Point1	Second Segment first point.
[in]	segment2Point2	Second Segment second point.
[out]	intersectionPoint	Resulting intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectHalfLines()

static MAXON_METHOD Bool IntersectHalfLines	(	const Vector &	halfLine1Origin,
		const Vector &	halfLine1Dir,
		const Vector &	halfLine2Origin,
		const Vector &	halfLine2Dir,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for halfline/halfline intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	halfLine1Origin	Start point 1st half line.
[in]	halfLine1Dir	1st half line direction vector.
[in]	halfLine2Origin	Start point 2nd half line.
[in]	halfLine2Dir	2nd half line direction vector.
[out]	intersectionPoint	Resulting intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectLineHalfLine()

static MAXON_METHOD Bool IntersectLineHalfLine	(	const Vector &	linePoint,
		const Vector &	lineDir,
		const Vector &	halfLineOrigin,
		const Vector &	halfLineDir,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for line/halfline intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	linePoint	A point on the line.
[in]	lineDir	Line direction vector.
[in]	halfLineOrigin	Start point of Half line.
[in]	halfLineDir	Half line direction vector.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectHalfLineSegment()

static MAXON_METHOD Bool IntersectHalfLineSegment	(	const Vector &	halfLineOrigin,
		const Vector &	halfLineDir,
		const Vector &	segmentPoint1,
		const Vector &	segmentPoint2,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for halfLine/segment Intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	halfLineOrigin	Start point of Half line.
[in]	halfLineDir	Half line direction vector.
[in]	segmentPoint1	First Segment point.
[in]	segmentPoint2	Second Segment point.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectPlanes()

static MAXON_METHOD Bool IntersectPlanes	(	const Vector &	plane1Point,
		const Vector &	plane1Normal,
		const Vector &	plane2Point,
		const Vector &	plane2Normal,
		Vector &	resLinePoint,
		Vector &	resLineDirection,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for plane/plane intersection and fills the intersection line.

Parameters

[in]	plane1Point	Plane 1 point.
[in]	plane1Normal	Plane 1 normal.
[in]	plane2Point	Plane 2 point.
[in]	plane2Normal	Plane 2 normal.
[out]	resLinePoint	A point on the intersection line.
[out]	resLineDirection	Intersection line direction.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectLinePlane() [1/2]

static MAXON_METHOD Bool IntersectLinePlane	(	const Vector &	linePoint,
		const Vector &	lineDir,
		const Vector &	planePoint,
		const Vector &	planeNormal,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for plane/Line intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	linePoint	A point on line.
[in]	lineDir	Line direction vector.
[in]	planePoint	Plane point.
[in]	planeNormal	Plane normal.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false. (line is parallel or lie on the plane)

◆ IntersectLinePlane() [2/2]

static MAXON_METHOD Bool IntersectLinePlane	(	const Vector &	linePoint,
		const Vector &	lineDir,
		const Vector &	planePoint,
		const Vector &	planeNormal,
		Vector &	intersectionPoint,
		Float &	param,
		Bool &	samePlane,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for plane/line intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	linePoint	A point on line.
[in]	lineDir	Line direction vector.
[in]	planePoint	Plane point.
[in]	planeNormal	Plane normal.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false. (line is parallel or lie on the plane)

◆ IntersectSegmentPlane()

static MAXON_METHOD Bool IntersectSegmentPlane	(	const Vector &	segmentPoint1,
		const Vector &	segmentPoint2,
		const Vector &	planePoint,
		const Vector &	planeNormal,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for plane/segment intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	segmentPoint1	Segment point 1.
[in]	segmentPoint2	Segment point 2.
[in]	planePoint	Plane point.
[in]	planeNormal	Plane normal.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectHalfLinePlane()

static MAXON_METHOD Bool IntersectHalfLinePlane	(	const Vector &	halfLinePoint,
		const Vector &	halfLineDir,
		const Vector &	planePoint,
		const Vector &	planeNormal,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for plane/halfline intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	halfLinePoint	Half line Origin.
[in]	halfLineDir	Half line direction vector.
[in]	planePoint	Plane point.
[in]	planeNormal	Plane normal.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectLineTriangle()

static MAXON_METHOD Bool IntersectLineTriangle	(	const Vector &	linePoint,
		const Vector &	lineDir,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		Vector &	intersectionPoint,
		Vector2d *	barycCoords = `nullptr`,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for line/triangle intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	linePoint	A point on the line.
[in]	lineDir	The line direction vector.
[in]	a	Triangle vertex.
[in]	b	Triangle vertex.
[in]	c	Triangle vertex.
[out]	intersectionPoint	Intersection position if intersection happens.
[out]	barycCoords	In case of intersection the pointr is filled with barycentric coordinates of the hit point, can be nullptr.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectHalfLineTriangle()

static MAXON_METHOD Bool IntersectHalfLineTriangle	(	const Vector &	halfLineOrigin,
		const Vector &	halfLineDir,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		Vector &	intersectionPoint,
		Vector2d *	barycCoords = `nullptr`,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for halfline/triangle intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	halfLineOrigin	Half line origin point.
[in]	halfLineDir	The half line direction vector.
[in]	a	Triangle vertex.
[in]	b	Triangle vertex.
[in]	c	Triangle vertex.
[out]	intersectionPoint	Intersection position if intersection happens.
[out]	barycCoords	In case of intersection the pointr is filled with barycentric coordinates of the hit point, can be nullptr.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectLineQuadrangle()

static MAXON_METHOD Bool IntersectLineQuadrangle	(	const Vector &	linePoint,
		const Vector &	lineDir,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		const Vector &	d,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for line/quadrangle intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	linePoint	A point on the line.
[in]	lineDir	The line direction vector.
[in]	a	Quadrangle vertex.
[in]	b	Quadrangle vertex.
[in]	c	Quadrangle vertex.
[in]	d	Quadrangle vertex.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectHalfLineQuadrangle()

static MAXON_METHOD Bool IntersectHalfLineQuadrangle	(	const Vector &	halfLineOrigin,
		const Vector &	halfLineDir,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		const Vector &	d,
		Vector &	intersectionPoint,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for halfline/quadrangle intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	halfLineOrigin	Half line origin point.
[in]	halfLineDir	The half line direction vector.
[in]	a	Quadrangle vertex.
[in]	b	Quadrangle vertex.
[in]	c	Quadrangle vertex.
[in]	d	Quadrangle vertex.
[out]	intersectionPoint	Intersection position if intersection happens.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ IntersectSegmentTriangle()

static MAXON_METHOD Bool IntersectSegmentTriangle	(	const Vector &	segmentPoint1,
		const Vector &	segmentPoint2,
		const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		Vector &	intersectionPoint,
		Vector *	barycCoords = `nullptr`,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks for linesegment/triangle intersection and fills intersectionPoint with the intersection position.

Parameters

[in]	segmentPoint1	Segment point.
[in]	segmentPoint2	Segment point.
[in]	a	Triangle vertex.
[in]	b	Triangle vertex.
[in]	c	Triangle vertex.
[out]	intersectionPoint	Intersection position if intersection happens.
[out]	barycCoords	In case of intersection the pointr is filled with barycentric coordinates of the hit point, can be nullptr.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ TrianglesIntersectionTest()

static MAXON_METHOD Bool TrianglesIntersectionTest	(	const Vector &	t1a,
		const Vector &	t1b,
		const Vector &	t1c,
		const Vector &	t2a,
		const Vector &	t2b,
		const Vector &	t2c,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Checks if 2 triangles intersect.

Parameters

[in]	t1a	Triangle 1 vertex.
[in]	t1b	Triangle 1 vertex.
[in]	t1c	Triangle 1 vertex.
[in]	t2a	Triangle 2 vertex.
[in]	t2b	Triangle 2 vertex.
[in]	t2c	Triangle 2 vertex.
[in]	tolerance	Geometric linear tolerance for the operation.

Returns: True if an intersection happens otherwise false.

◆ CalculatePolygonPointST()

static MAXON_METHOD Bool CalculatePolygonPointST	(	const Vector &	point,
		const Vector &	pa,
		const Vector &	pb,
		const Vector &	pc,
		const Vector &	pd,
		Bool	isQuad,
		Float &	s,
		Float &	t,
		Float	tolerance = `GeomConstants::EPSILON4`
	)

static

Calculates a S/T coordinate for a given 3D point and polygon in the polygon plane. The 3D point needs to be on the plane that is defined by the polygon. The function is just a 2d evaluation so not coplanar polygons need to be evaluated by projecting vertex on best fit plane.

Parameters

[in]	point	The point to find s and t.
[in]	pa	Polygon point.
[in]	pb	Polygon point.
[in]	pc	Polygon point.
[in]	pd	Polygon point.
[in]	isQuad	If true evaluate using a quadrangle, otherwise ignore pd and use a triangle.
[out]	s	The resulting s coordinate, or MINVLAUE_FLOAT if the functions fail.
[out]	t	The resulting t coordinate, or MINVLAUE_FLOAT if the functions fail.
[in]	tolerance	Geometric linear tolerance for the operation, used to define if the point is inside of polygon or not.

Returns: True if the point is in the polygon boundary otherwise false (negative s or t values).

◆ InverseBilinarInterpolate()

static MAXON_METHOD void InverseBilinarInterpolate	(	const Vector &	pa,
		const Vector &	pb,
		const Vector &	pc,
		const Vector &	pd,
		const Vector &	point,
		Vector2d &	bilinarVariables
	)

static

Calculates the bilinear coordinates of a point in a quad. The quad is defined by the points pa, pb, pc and pd.

Parameters

[in]	pa	Polygon point.
[in]	pb	Polygon point.
[in]	pc	Polygon point.
[in]	pd	Polygon point.
[in]	point	The point to find the bilinear interpolation values for.
[out]	bilinarVariables	The resulting coordinates.

◆ InverseBilinarInterpolateNewton()

static MAXON_METHOD void InverseBilinarInterpolateNewton	(	const Vector &	pa,
		const Vector &	pb,
		const Vector &	pc,
		const Vector &	pd,
		const Vector &	point,
		Int32	iterations,
		Vector2d &	bilinarVariables
	)

static

Calculates the bilinear coordinates of a point in a quad with a Newton iteration method. The quad is defined by the points pa, pb, pc and pd.

Parameters

[in]	pa	Polygon point.
[in]	pb	Polygon point.
[in]	pc	Polygon point.
[in]	pd	Polygon point.
[in]	point	The point to find the bilinear interpolation values for.
[in]	iterations	The iteration count of the Newton iteration.
[out]	bilinarVariables	The resulting coordinates.

◆ InverseBilinarInterpolate2D()

static MAXON_METHOD void InverseBilinarInterpolate2D	(	const Vector2d &	pa,
		const Vector2d &	pb,
		const Vector2d &	pc,
		const Vector2d &	pd,
		const Vector2d &	point,
		Vector2d &	bilinarVariables
	)

static

Calculates the bilinear coordinates of a 2d point in a 2d quad. The quad is defined by the points pa, pb, pc and pd.

Parameters

[in]	pa	Polygon 2d point.
[in]	pb	Polygon 2d point.
[in]	pc	Polygon 2d point.
[in]	pd	Polygon 2d point.
[in]	point	The 2d point to find the bilinear interpolation values for.
[out]	bilinarVariables	The resulting coordinates.

◆ InverseBilinarInterpolate2DNewton()

static MAXON_METHOD void InverseBilinarInterpolate2DNewton	(	const Vector2d &	pa,
		const Vector2d &	pb,
		const Vector2d &	pc,
		const Vector2d &	pd,
		const Vector2d &	point,
		Int32	iterations,
		Vector2d &	bilinarVariables
	)

static

Calculates the bilinear coordinates of a 2d point in a 2d quad with a Newton iteration method. The quad is defined by the points pa, pb, pc and pd.

Parameters

[in]	pa	Polygon 2d point.
[in]	pb	Polygon 2d point.
[in]	pc	Polygon 2d point.
[in]	pd	Polygon 2d point.
[in]	point	The 2d point to find the bilinear interpolation values for.
[in]	iterations	The iteration count of the Newton iteration.
[out]	bilinarVariables	The resulting coordinates.

◆ BilinearInterpolate()

static MAXON_METHOD Vector BilinearInterpolate	(	const Vector &	pa,
		const Vector &	pb,
		const Vector &	pc,
		const Vector &	pd,
		const Float	s,
		const Float	t
	)

static

Calculates the bilinear interpolation within a quad. The quad is defined by the points pa, pb, pc and pd.

Parameters

[in]	pa	Polygon point.
[in]	pb	Polygon point.
[in]	pc	Polygon point.
[in]	pd	Polygon point.
[in]	s	The first bilinar coordinate.
[in]	t	The second bilinear coordinate.

Returns: The point in space with these bilinear coordinates relative to the quad pa, pb, pc and pd.

◆ CalculateSignedTriangleArea() [2/2]

static MAXON_METHOD Float CalculateSignedTriangleArea	(	const Vector &	a,
		const Vector &	b,
		const Vector &	c,
		const Vector &	normal
	)

static

Calculates the signed area of an oriented triangle. Sign is defined as the sign of the z coordinate of the triangle normal vector.

Parameters

[in]	a	Triangle point A.
[in]	b	Triangle point B.
[in]	c	Triangle point C.
[in]	normal	The reference normal to calculate the sign.

Returns: Unsigned triangle area.

◆ CalculateMeanValueCoordinatesWeights() [2/2]

static MAXON_METHOD Result<void> CalculateMeanValueCoordinatesWeights	(	const Vector &	point,
		const Block< const Vector > &	outline,
		const Vector &	normal,
		WritableArrayInterface< Float > &	weights
	)

static

Calculates the mean value coordinates weights for a point inside an outline.

Parameters

[in]	point	The point for which to calculate weights.
[in]	outline	The outline.
[in]	normal	The normal direction of the outline.
[in]	weights	Array of weights. The amount of entries in the resulting array is the same amount of outline vertices.

Returns: OK on success.

Detailed Description

Static Public Member Functions

Private Member Functions

Member Function Documentation

◆ MAXON_INTERFACE_NONVIRTUAL()

◆ LinearRemapToRange()

◆ GetAngle2D()

◆ InterpolatePointOnSegment()

◆ InterpolatePointOnSegment2D()

◆ CalculateBestFitPlane()

◆ Points3Dto2D() [1/2]

◆ Points3Dto2D() [2/2]

◆ Point2Dto3D()

◆ Points2Dto3D()

◆ CalculateTriangleArea()

◆ CalculateSignedTriangleArea() [1/2]

◆ CalculateQuadrangleArea()

◆ CalculateOutlineArea()

◆ CalculateOutlineNormal() [1/2]

◆ CalculateOutlineNormal() [2/2]

◆ IsVertexConvex()

◆ CalculateMeanValueCoordinatesWeights() [1/2]

◆ IsVertexConvex2D()

◆ CalculateBarycentricCoordinate()

◆ CalculateBarycentricCoordinate3D()

◆ PointInTriangle()

◆ PointInTriangle2D()

◆ GetPointInPolygonWindingNumber2D() [1/2]

◆ GetPointInPolygonWindingNumber2DExact()

◆ GetPointInPolygonWindingNumber2D() [2/2]

◆ GetPointInPolygonWindingNumber() [1/2]

◆ GetPointInPolygonWindingNumber() [2/2]

◆ PointInOutline2D()

◆ CalculateBisector()

◆ CalculateCircumcenter2D()

◆ CalculateCircumcenter()

◆ SegmentsIntersectionTest2D()

◆ IntersectsSegments2D()

◆ LineLineDistance()

◆ PointInSegment2D()

◆ PointInSegment()

◆ PointInHalfLine()

◆ IntersectLines()

◆ IntersectLineSegment()

◆ IntersectSegments()

◆ IntersectHalfLines()

◆ IntersectLineHalfLine()

◆ IntersectHalfLineSegment()

◆ IntersectPlanes()

◆ IntersectLinePlane() [1/2]

◆ IntersectLinePlane() [2/2]

◆ IntersectSegmentPlane()

◆ IntersectHalfLinePlane()

◆ IntersectLineTriangle()

◆ IntersectHalfLineTriangle()

◆ IntersectLineQuadrangle()

◆ IntersectHalfLineQuadrangle()

◆ IntersectSegmentTriangle()

◆ TrianglesIntersectionTest()

◆ CalculatePolygonPointST()

◆ InverseBilinarInterpolate()

◆ InverseBilinarInterpolateNewton()

◆ InverseBilinarInterpolate2D()

◆ InverseBilinarInterpolate2DNewton()

◆ BilinearInterpolate()

◆ CalculateSignedTriangleArea() [2/2]

◆ CalculateMeanValueCoordinatesWeights() [2/2]