#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 GEOMETRY_TEST_EXACT	IsVertexConvexExact (const Vector &vertex, const Vector &next, const Vector &pred, const Vector &up=Vector(0, 1, 0), Float epsilon=GeomConstants::EPSILON4)

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

static MAXON_METHOD Result< void >	CalculateMeanValueCoordinatesWeights (const Vector &point, const Block< const Vector > &points, const Block< const UInt32 > &outlineIndices, const Vector &normal, WritableArrayInterface< Float > &weights)

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

static MAXON_METHOD GEOMETRY_TEST_EXACT	IsVertexConvexExact2D (const Vector2d &vertex, const Vector2d &next, const Vector2d &pred, Float epsilon=GeomConstants::EPSILON4)

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 Bool	PointInOutlineRobust2D (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	SegmentRayIntersectionTest2D (const Vector2d &segmentPoint1, const Vector2d &segmentPoint2, const Vector2d &rayStartPoint, const Vector2d &rayDirection)

static MAXON_METHOD Bool	IntersectSegments2D (const Vector2d &segment1Point1, const Vector2d &segment1Point2, const Vector2d &segment2Point1, const Vector2d &segment2Point2, Vector2d &intersectionPoint, Float tolerance=0.0_f)

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)

static MAXON_METHOD Float	CalculatePerimeterLength2D (const Block< const Vector2d > &outlinePoints)

static MAXON_METHOD Result< Bool >	IsWoundClockwise2D (const Block< const Vector2d > &outlinePoints)

static MAXON_METHOD Vector2d	CalculateOutlineCentroidAndArea2D (const Block< const Vector2d > &outlinePoints, Float area=nullptr, Bool windingPolarity=nullptr)

static MAXON_METHOD Result< Vector2d >	CalculateMultiOutlineCentroidAndAreas2D (const Block< const Vector2d > &loopVertices, const Block< const Int > &loopVertexCounts, Bool includeHolesInCogCalcs, Float overallArea=nullptr, BaseArray< Float > loopSoloAreas=nullptr, BaseArray< Bool > *windingPolarity=nullptr)

static MAXON_METHOD Result< BaseArray< Int > >	CalculateConvexHull2D (const Block< const Vector2d > &outlinePoints)

static MAXON_METHOD Result< BaseArray< BaseArray< Int > > >	CalculateConvexDecomposition2D (const Block< const Vector2d > &outlinePoints)

static MAXON_METHOD Result< Bool >	CleanLoop2DInPlace (BaseArray< Vector2d > &outlinePoints, Bool maintainStart)

static MAXON_METHOD Result< BaseArray< Vector2d > >	CalculateNoFitPolygonForConvex (const Block< const Vector2d > &outlinePointsA, const Block< const Vector2d > &outlinePointsB, Bool relativeBToA=true)

static MAXON_METHOD Result< BaseArray< Vector2d > >	CalculateNoFitPolygonUsingSliding (const Block< const Vector2d > &outlinePointsA, const Block< const Vector2d > &outlinePointsB, Bool relativeBToA=true)

static MAXON_METHOD Result< BaseArray< Vector2d > >	CalculateInnerFitPolygonUsingSliding (const Block< const Vector2d > &outlinePointsCcwA, const Block< const Vector2d > &outlinePointsB)

static MAXON_METHOD Result< BaseArray< Vector2d > >	CalculateNoFitPolygonForConvex (const Block< const Vector2d > &outlinePointsA, const Block< const Vector2d > &outlinePointsB, const Matrix2d &transformA, const Matrix2d &transformB, Bool relativeBToA=true)

static MAXON_METHOD Result< BaseArray< Vector2d > >	CalculateNoFitPolygonUsingSliding (const Block< const Vector2d > &outlinePointsA, const Block< const Vector2d > &outlinePointsB, const Matrix2d &transformA, const Matrix2d &transformB, Bool relativeBToA=true)

static MAXON_METHOD Result< BaseArray< BaseArray< Vector2d > > >	CalculateUnionOfPolygons (const Block< const Vector2d > &outlinePointsA, const Block< const Vector2d > &outlinePointsB, Bool includeHolesInResult, Bool createOuterLoop=true)

static MAXON_METHOD Bool	IntersectsSegmentsExact2D (const Vector2d &segment1Point1, const Vector2d &segment1Point2, const Vector2d &segment2Point1, const Vector2d &segment2Point2, Vector2d &intersectionPoint, Bool &areParallel, Vector2d *intersectionPoint2=nullptr, Float tolerance=0.0_f)

static MAXON_METHOD LOOP_OVERLAP_STATE	GetContainmentStateForNonIntersectingLoops (const Block< const Vector2d > &outlinePointsA, const Block< const Vector2d > &outlinePointsB)

static MAXON_METHOD Bool	AreLoopsEqualToWithinTolerance (const Block< const Vector2d > &loopA, const Block< const Vector2d > &loopB, Bool allowCyclicRotation=true, Bool ignoreTranslationOffset=true, maxon::Float tol=maxon::GeomConstants::EPSILON5)

static MAXON_METHOD void	CalculateBoundingBoxIndices (const Block< const Vector2d > &verts, Int &minIdxX, Int &maxIdxX, Int &minIdxY, Int &maxIdxY, Bool findMostCounterClockwise)

static MAXON_METHOD Bool	ArePointsCoLinearWithinTolerance (const Block< const Vector > &points, maxon::Float tol=maxon::GeomConstants::EPSILON5)

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.

◆ IsVertexConvexExact()

static MAXON_METHOD GEOMETRY_TEST_EXACT IsVertexConvexExact	(	const Vector &	vertex,
		const Vector &	next,
		const Vector &	pred,
		const Vector &	up = `Vector(0, 1, 0)`,
		Float	epsilon = `GeomConstants::EPSILON4`
	)

static

A convexity test for vertex in between 2 other vertices in 3D space. This is the same test as IsVertexConvex, but explicitly reports degenerate cases.

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: The detectected state

◆ CalculateMeanValueCoordinatesWeights() [1/3]

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. This internally calculates the normal of the outline and is thus more expensive than the other version that takes the normal as additional input.

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.

◆ CalculateMeanValueCoordinatesWeights() [2/3]

static MAXON_METHOD Result<void> CalculateMeanValueCoordinatesWeights	(	const Vector &	point,
		const Block< const Vector > &	points,
		const Block< const UInt32 > &	outlineIndices,
		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]	points	A list of points that the outlineIndices reference to.
[in]	outlineIndices	The indices of 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.

◆ 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.

◆ IsVertexConvexExact2D()

static MAXON_METHOD GEOMETRY_TEST_EXACT IsVertexConvexExact2D	(	const Vector2d &	vertex,
		const Vector2d &	next,
		const Vector2d &	pred,
		Float	epsilon = `GeomConstants::EPSILON4`
	)

static

A convexity test for vertex in between 2 other vertices in 2D This is the same test as IsVertexConvex, but explicitly reports degenerate cases.

Parameters

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

Returns: The detectected state

◆ 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.

◆ PointInOutlineRobust2D()

static MAXON_METHOD Bool PointInOutlineRobust2D	(	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.

◆ SegmentRayIntersectionTest2D()

static MAXON_METHOD Bool SegmentRayIntersectionTest2D	(	const Vector2d &	segmentPoint1,
		const Vector2d &	segmentPoint2,
		const Vector2d &	rayStartPoint,
		const Vector2d &	rayDirection
	)

static

Checks if a segment is intersected by a ray in 2D space.

Parameters

[in]	segmentPoint1	Segment point 1.
[in]	segmentPoint2	Segment point 2.
[in]	rayStartPoint	Line start point.
[in]	rayDirection	Line Direction.

Returns: True if the segments intersect in 2D.

◆ IntersectSegments2D()

static MAXON_METHOD Bool IntersectSegments2D	(	const Vector2d &	segment1Point1,
		const Vector2d &	segment1Point2,
		const Vector2d &	segment2Point1,
		const Vector2d &	segment2Point2,
		Vector2d &	intersectionPoint,
		Float	tolerance = `0.0_f`
	)

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() [3/3]

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.

◆ CalculatePerimeterLength2D()

static MAXON_METHOD Float CalculatePerimeterLength2D ( const Block< const Vector2d > & outlinePoints )

static

Calculates the perimeter length for an outline defined by a loop of points in outlinePoints.

Parameters

[in] outlinePoints An array with a point sequence defining the perimeter.

Returns: The perimeter

◆ IsWoundClockwise2D()

static MAXON_METHOD Result<Bool> IsWoundClockwise2D ( const Block< const Vector2d > & outlinePoints )

static

Determines whether outline defined by a loop of points is would clockwise or not This is only meaningful if the loop has no self crossings.

Parameters

[in] outlinePoints An array with a point sequence defining the perimeter.

Returns: Whether loop is wound clockwise

◆ CalculateOutlineCentroidAndArea2D()

static MAXON_METHOD Vector2d CalculateOutlineCentroidAndArea2D	(	const Block< const Vector2d > &	outlinePoints,
		Float *	area = `nullptr`,
		Bool *	windingPolarity = `nullptr`
	)

static

Calculates the centroid coordinates for an outline defined by a loop of points in outlinePoints.

Parameters

[in]	outlinePoints	An array with a point sequence.
[out]	area	If non-null, then pointed value is set to the enclosed area.
[out]	windingPolarity	If non-null, then pointed value contains the winding direction of the loop.

Returns: The centroid coordinates.

◆ CalculateMultiOutlineCentroidAndAreas2D()

static MAXON_METHOD Result<Vector2d> CalculateMultiOutlineCentroidAndAreas2D	(	const Block< const Vector2d > &	loopVertices,
		const Block< const Int > &	loopVertexCounts,
		Bool	includeHolesInCogCalcs,
		Float *	overallArea = `nullptr`,
		BaseArray< Float > *	loopSoloAreas = `nullptr`,
		BaseArray< Bool > *	windingPolarity = `nullptr`
	)

static

Calculates the centroid coordinates for an outline with optional holes, defined by loop(s) of vertices.

Parameters

[in]	loopVertices	An array with one or more point sequences which define perimeter loop followed by any hole loops. All loops are ASSUMED to neither overlap nor intersect, and first loop must enclose all others.
[in]	loopVertexCounts	An array containing the number of vertices in each loop. If no holes, then this will be a single value equal to the number of entries in loopVertices.
[in]	includeHolesInCogCalcs	If true, the holes are considered in calculation of the centroid position. If false, only the first loop (outer perimeter) is considered.
[out]	overallArea	If non-null, then pointed value is set to the enclosed area. Holes are ALWAYS considered in this calculation.
[out]	loopSoloAreas	If non-null, then pointed array contains the areas enclosed by each loop in isolation. Overall area is then the first value minus the sum of the rest.
[out]	windingPolarity	If non-null, then pointed array contains the winding direction of each loop.

Returns: The centroid coordinates.

◆ CalculateConvexHull2D()

static MAXON_METHOD Result<BaseArray<Int> > CalculateConvexHull2D ( const Block< const Vector2d > & outlinePoints )

static

Calculates the convex hull for an outline, defined by a loop of vertices Note that the polygon is assumed to be non-self intersecting, and with edges formed by the vertices in order. In particular, the vertices are NOT treated as a 'sea of points' - but instead as defining edges; order matters!

Parameters

[in] outlinePoints An array with a point sequence representing the perimeter of the polgon

Returns: BaseArray containing the indices of the input array corresponding to the vertices of the convex hull of the polygon.

◆ CalculateConvexDecomposition2D()

static MAXON_METHOD Result<BaseArray<BaseArray<Int> > > CalculateConvexDecomposition2D ( const Block< const Vector2d > & outlinePoints )

static

Decomposes an outline defined by a loop of vertices into a set of convex parts Note that the polygon is assumed to be non-self intersecting, and with edges formed by the vertices in order. In particular, the vertices are NOT treated as a 'sea of points' - but instead as defining edges; order matters!

Parameters

[in] outlinePoints An array with a point sequence representing the perimeter of the polgon

Returns: BaseArray containing BaseArray of indices of the input array corresponding to the vertices of each of the convex parts of.

◆ CleanLoop2DInPlace()

static MAXON_METHOD Result<Bool> CleanLoop2DInPlace	(	BaseArray< Vector2d > &	outlinePoints,
		Bool	maintainStart
	)

static

Given a loop of vertices, this performs in-place cleaning operations.

Duplicated consecutive vertices are removed.

Colinear and anti-colinear vertices are removed.

Parameters

[in]	outlinePoints	An array with a point sequence representing the perimeter of the polgon
[in]	maintainStart	If false, then vertex order is rotated such that the first vertex lies on the convex hull. (If it is true, then starting vertex remains unchanged, unless that vertex was removed during cleaning. In this case the new start vertex is the first vertex after that which survived.)

Returns: Whether any changes were made.

◆ CalculateNoFitPolygonForConvex() [1/2]

static MAXON_METHOD Result<BaseArray<Vector2d> > CalculateNoFitPolygonForConvex	(	const Block< const Vector2d > &	outlinePointsA,
		const Block< const Vector2d > &	outlinePointsB,
		Bool	relativeBToA = `true`
	)

static

Given two loops of vertices which represent two convex polygons, this calculates the corresponding No-Fit Polygon NFP of convex polygons never contain internal holes, only the main perimeter, hence only ever a single returned edge loop.

Parameters

[in]	outlinePointsA	An array with a point sequence representing the perimeter of the first convex polygon
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second convex polygon
[in]	relativeBToA	If true, returned NFP is the result of moving polygon B relative to polygon A. If false then A relative to B.

Returns: The resulting NoFit polygon

◆ CalculateNoFitPolygonUsingSliding() [1/2]

static MAXON_METHOD Result<BaseArray<Vector2d> > CalculateNoFitPolygonUsingSliding	(	const Block< const Vector2d > &	outlinePointsA,
		const Block< const Vector2d > &	outlinePointsB,
		Bool	relativeBToA = `true`
	)

static

Given two loops of vertices which represent two polygons, this calculates the corresponding No-Fit Polygon using the sliding method. Internal holes are NOT generated, only the main perimeter, hence only ever a single returned edge loop.

Parameters

[in]	outlinePointsA	An array with a point sequence representing the perimeter of the first polygon
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second polygon
[in]	relativeBToA	If true, returned NFP is the result of moving polygon B relative to polygon A. If false then A relative to B.

Returns: The resulting NoFit polygon

◆ CalculateInnerFitPolygonUsingSliding()

static MAXON_METHOD Result<BaseArray<Vector2d> > CalculateInnerFitPolygonUsingSliding	(	const Block< const Vector2d > &	outlinePointsCcwA,
		const Block< const Vector2d > &	outlinePointsB
	)

static

Given two loops of vertices which represent two polygons, this calculates the corresponding Inner-Fit Polygon using the sliding method. Internal holes are NOT generated, only the main perimeter, hence only ever a single returned edge loop.

Parameters

[in]	outlinePointsCcwA	An array with a point sequence representing the perimeter of the first polygon. This must be counterclockwise wound.
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second polygon. This must be clockwise wound.

Returns: The resulting Inner-Fit polygon

◆ CalculateNoFitPolygonForConvex() [2/2]

static MAXON_METHOD Result<BaseArray<Vector2d> > CalculateNoFitPolygonForConvex	(	const Block< const Vector2d > &	outlinePointsA,
		const Block< const Vector2d > &	outlinePointsB,
		const Matrix2d &	transformA,
		const Matrix2d &	transformB,
		Bool	relativeBToA = `true`
	)

static

Given two loops of vertices which represent two convex polygons, this calculates the corresponding No-Fit Polygon NFP of convex polygons never contain internal holes, only the main perimeter, hence only ever a single returned edge loop.

Parameters

[in]	outlinePointsA	An array with a point sequence representing the perimeter of the first convex polygon
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second convex polygon
[in]	transformA	Transformation to be applied to vertices in A prior to calculation.
[in]	transformB	Transformation to be applied to vertices in B prior to calculation.
[in]	relativeBToA	If true, returned NFP is the result of moving polygon B relative to polygon A. If false then A relative to B.

Returns: The resulting NoFit polygon

◆ CalculateNoFitPolygonUsingSliding() [2/2]

static MAXON_METHOD Result<BaseArray<Vector2d> > CalculateNoFitPolygonUsingSliding	(	const Block< const Vector2d > &	outlinePointsA,
		const Block< const Vector2d > &	outlinePointsB,
		const Matrix2d &	transformA,
		const Matrix2d &	transformB,
		Bool	relativeBToA = `true`
	)

static

Given two loops of vertices which represent two polygons, this calculates the corresponding No-Fit Polygon using the sliding method. Internal holes are NOT generated, only the main perimeter, hence only ever a single returned edge loop.

Parameters

[in]	outlinePointsA	An array with a point sequence representing the perimeter of the first polygon
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second polygon
[in]	transformA	Transformation to be applied to vertices in A prior to calculation.
[in]	transformB	Transformation to be applied to vertices in B prior to calculation.
[in]	relativeBToA	If true, returned NFP is the result of moving polygon B relative to polygon A. If false then A relative to B.

Returns: The resulting NoFit polygon

◆ CalculateUnionOfPolygons()

static MAXON_METHOD Result<BaseArray<BaseArray<Vector2d> > > CalculateUnionOfPolygons	(	const Block< const Vector2d > &	outlinePointsA,
		const Block< const Vector2d > &	outlinePointsB,
		Bool	includeHolesInResult,
		Bool	createOuterLoop = `true`
	)

static

Given two loops of vertices which represent two polygon outlines, this calculates the union.

Parameters

[in]	outlinePointsA	An array with a point sequence representing the perimeter of the first polygon
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second polygon
[in]	includeHolesInResult	If true, then if union shape contains holes, then these are also calculated and returned. If false then only the outer perimeter is returned.
[in]	createOuterLoop	If true, then attempt to generate an outer loop before looking for holes. Otherwise just generate holes.

Returns: The resulting union. If this contains multiple loops the first is the outer perimeter and all others represent internal loops (holes). If this is empty, then the outlines do not overlap.

◆ IntersectsSegmentsExact2D()

static MAXON_METHOD Bool IntersectsSegmentsExact2D	(	const Vector2d &	segment1Point1,
		const Vector2d &	segment1Point2,
		const Vector2d &	segment2Point1,
		const Vector2d &	segment2Point2,
		Vector2d &	intersectionPoint,
		Bool &	areParallel,
		Vector2d *	intersectionPoint2 = `nullptr`,
		Float	tolerance = `0.0_f`
	)

static

Checks if two segment intersect in 2D space and calculates the intersection point (if any). If the lines are parallel and intersect: If intersectionPoint2 is nullptr then the midpoint of the intersection range will be returned via 'intersectionPoint' If intersectionPoint2 is non-null, then the start of the intersection range will be returned via 'intersectionPoint', and the end via '*intersectionPoint2'

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. For parallel intersection segments this is the start or mid-point of the overlapping region - see above.
[out]	areParallel	If non null, routine sets to true or false to indicate whether the line segments were detected to be parallel.
[out]	intersectionPoint2	If non null, and segments are colinear and overlapping, then is the end of the overlapping region.
[in]	tolerance	Geometric tolerance for the operation.

Returns: True if the segments intersect in 2D.

◆ GetContainmentStateForNonIntersectingLoops()

static MAXON_METHOD LOOP_OVERLAP_STATE GetContainmentStateForNonIntersectingLoops	(	const Block< const Vector2d > &	outlinePointsA,
		const Block< const Vector2d > &	outlinePointsB
	)

static

Given two boundary loops of vertices WHICH ARE KNOWN TO CONTAIN NO INTERSECTIONS, this determines the relative containment state of the two loops.

Parameters

[in]	outlinePointsA	An array with a point sequence representing the perimeter of the first polygon
[in]	outlinePointsB	An array with a point sequence representing the perimeter of the second polygon

Returns: The containment state

◆ AreLoopsEqualToWithinTolerance()

static MAXON_METHOD Bool AreLoopsEqualToWithinTolerance	(	const Block< const Vector2d > &	loopA,
		const Block< const Vector2d > &	loopB,
		Bool	allowCyclicRotation = `true`,
		Bool	ignoreTranslationOffset = `true`,
		maxon::Float	tol = `maxon::GeomConstants::EPSILON5`
	)

static

Given two boundary loops of vertices, this determines whether the two loops are the same shape. They are deemed to be the same if there are the same number of vertices, and the pairwise vertices have the same coordinates to within the tolerance distance.

Parameters

[in]	loopA	An array with a point sequence representing the first loop
[in]	loopB	An array with a point sequence representing the second loop
[in]	allowCyclicRotation	If true, then cyclically rotated loops are considered equivalent, i.e. the loops don't have to start on the same vertices for a match to be found. Loops which match, but have opposing winding directions are also considered to be a match when this is true. If false then vertices with the same indices must have the same coordinates to declare a match.
[in]	ignoreTranslationOffset	If true then any translational offset between the loops is ignored. I.e. the same shapes at different offsets will be considered to match.
[in]	tol	The position tolerance. If vertices differ by more than this in either x or y then they are considered to be different and non-matching.

Returns: Whether the loops represent the same shape.

◆ CalculateBoundingBoxIndices()

static MAXON_METHOD void CalculateBoundingBoxIndices	(	const Block< const Vector2d > &	verts,
		Int &	minIdxX,
		Int &	maxIdxX,
		Int &	minIdxY,
		Int &	maxIdxY,
		Bool	findMostCounterClockwise
	)

static

Given a set of vertices, returns indices of vertices which lie on each of the maximal extents.

Parameters

[in]	verts	The set of vertices
[out]	minIdxX	The index of a vertex with minimum X extent
[out]	maxIdxX	The index of a vertex with maximum X extent
[out]	minIdxY	The index of a vertex with minimum Y extent
[out]	maxIdxY	The index of a vertex with minimum Y extent
[in]	findMostCounterClockwise	If true then when multiple vertices lie on the same extent, the most counterclockwise one will be the one whose index is returned.

◆ ArePointsCoLinearWithinTolerance()

static MAXON_METHOD Bool ArePointsCoLinearWithinTolerance	(	const Block< const Vector > &	points,
		maxon::Float	tol = `maxon::GeomConstants::EPSILON5`
	)

static

Given a set of vertices, this determines whether the vertices are co-linear (lie in the same line) They are deemed not to be co-linear if there exists a triangle whose area is greater than the given tolerance.

Parameters

[in]	points	The set of vertices.
[in]	tol	The triangle area tolerance. If area of the triangle formed by three vertices is greater than the tolerance, the vertices are not co-linear.

Returns: Whether the loops are co-linear.

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()

◆ IsVertexConvexExact()

◆ CalculateMeanValueCoordinatesWeights() [1/3]

◆ CalculateMeanValueCoordinatesWeights() [2/3]

◆ IsVertexConvex2D()

◆ IsVertexConvexExact2D()

◆ CalculateBarycentricCoordinate()

◆ CalculateBarycentricCoordinate3D()

◆ PointInTriangle()

◆ PointInTriangle2D()

◆ GetPointInPolygonWindingNumber2D() [1/2]

◆ GetPointInPolygonWindingNumber2DExact()

◆ GetPointInPolygonWindingNumber2D() [2/2]

◆ GetPointInPolygonWindingNumber() [1/2]

◆ GetPointInPolygonWindingNumber() [2/2]

◆ PointInOutline2D()

◆ PointInOutlineRobust2D()

◆ CalculateBisector()

◆ CalculateCircumcenter2D()

◆ CalculateCircumcenter()

◆ SegmentsIntersectionTest2D()

◆ SegmentRayIntersectionTest2D()

◆ IntersectSegments2D()

◆ 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() [3/3]

◆ CalculatePerimeterLength2D()

◆ IsWoundClockwise2D()

◆ CalculateOutlineCentroidAndArea2D()

◆ CalculateMultiOutlineCentroidAndAreas2D()

◆ CalculateConvexHull2D()

◆ CalculateConvexDecomposition2D()

◆ CleanLoop2DInPlace()

◆ CalculateNoFitPolygonForConvex() [1/2]