Geometric utility functions for 3D space. More...

Functions
double	GetAngleBetweenVectors (const CVector3d &v1, const CVector3d &v2)
	Calculate angle between two vectors in radians.

double	GetSignedAngleBetweenVectors (const CVector3d &v1, const CVector3d &v2, const CVector3d &axis)
	Calculate signed angle between two vectors around an axis.

double	GetDistance (const CVector3d &p1, const CVector3d &p2)
	Calculate distance between two points.

double	GetDistanceSq (const CVector3d &p1, const CVector3d &p2)
	Calculate squared distance between two points (faster).

double	GetDistance (const CVector3d &point, const CPlane3d &plane)
	Calculate distance from point to plane.

double	GetDistance (const CVector3d &point, const CLine3d &line)
	Calculate distance from point to line.

bool	AreIntersecting (const CLine3d &line1, const CLine3d &line2, double tolerance=I_BIG_EPSILON)
	Check if two lines intersect in 3D.

bool	GetIntersection (const CLine3d &line, const CPlane3d &plane, CVector3d &result, double tolerance=I_BIG_EPSILON)
	Find intersection point between line and plane.

double	GetClosestPoints (const CLine3d &line1, const CLine3d &line2, CVector3d &point1, CVector3d &point2)
	Find closest points between two lines.

bool	IsOnPositiveSide (const CVector3d &point, const CPlane3d &plane)
	Check if point is on the same side of plane as the plane's normal.

CVector3d	ProjectVectorOntoVector (const CVector3d &vector, const CVector3d &onto)
	Project vector onto another vector.

bool	GetBarycentricCoordinates (const CVector3d &point, const CVector3d &p1, const CVector3d &p2, const CVector3d &p3, double &u, double &v, double &w)
	Calculate barycentric coordinates of point relative to triangle.

bool	IsPointInTriangle (const CVector3d &point, const CVector3d &p1, const CVector3d &p2, const CVector3d &p3)
	Check if point is inside triangle.

CVector3d	GetTriangleNormal (const CVector3d &p1, const CVector3d &p2, const CVector3d &p3)
	Calculate normal vector of triangle.

double	GetTriangleArea (const CVector3d &p1, const CVector3d &p2, const CVector3d &p3)
	Calculate area of triangle.

Detailed Description

Geometric utility functions for 3D space.

Function Documentation

◆ AreIntersecting()

bool i3d::Geometry::AreIntersecting	(	const CLine3d &	line1,
		const CLine3d &	line2,
		double	tolerance = `I_BIG_EPSILON`
	)

Check if two lines intersect in 3D.

Parameters

line1	First line.
line2	Second line.
tolerance	Tolerance for intersection test.

Returns: True if lines intersect (or nearly intersect).

◆ GetAngleBetweenVectors()

double i3d::Geometry::GetAngleBetweenVectors	(	const CVector3d &	v1,
		const CVector3d &	v2
	)

inline

Calculate angle between two vectors in radians.

Parameters

v1	First vector.
v2	Second vector.

Returns: Angle in radians [0, PI].

Definition at line 28 of file Geometry.h.

References imath::TVector< Size, Element >::GetDotProduct(), and i3d::CVector3d::GetNormalized().

Referenced by GetSignedAngleBetweenVectors().

◆ GetBarycentricCoordinates()

bool i3d::Geometry::GetBarycentricCoordinates	(	const CVector3d &	point,
		const CVector3d &	p1,
		const CVector3d &	p2,
		const CVector3d &	p3,
		double &	u,
		double &	v,
		double &	w
	)

Calculate barycentric coordinates of point relative to triangle.

Parameters

point	Point to calculate barycentric coordinates for.
p1	First triangle vertex.
p2	Second triangle vertex.
p3	Third triangle vertex.
u	Output barycentric coordinate u.
v	Output barycentric coordinate v.
w	Output barycentric coordinate w (w = 1 - u - v).

Returns: True if calculation successful.

◆ GetClosestPoints()

double i3d::Geometry::GetClosestPoints	(	const CLine3d &	line1,
		const CLine3d &	line2,
		CVector3d &	point1,
		CVector3d &	point2
	)

Find closest points between two lines.

Parameters

line1	First line.
line2	Second line.
point1	Output closest point on line1.
point2	Output closest point on line2.

Returns: Distance between closest points.

◆ GetDistance() [1/3]

double i3d::Geometry::GetDistance	(	const CVector3d &	p1,
		const CVector3d &	p2
	)

inline

Calculate distance between two points.

Definition at line 64 of file Geometry.h.

References imath::TVector< Size, Element >::GetLength().

◆ GetDistance() [2/3]

double i3d::Geometry::GetDistance	(	const CVector3d &	point,
		const CLine3d &	line
	)

inline

Calculate distance from point to line.

Definition at line 91 of file Geometry.h.

References i3d::CLine3d::GetDistance().

◆ GetDistance() [3/3]

double i3d::Geometry::GetDistance	(	const CVector3d &	point,
		const CPlane3d &	plane
	)

inline

Calculate distance from point to plane.

Definition at line 82 of file Geometry.h.

References i3d::CPlane3d::GetDistance().

◆ GetDistanceSq()

double i3d::Geometry::GetDistanceSq	(	const CVector3d &	p1,
		const CVector3d &	p2
	)

inline

Calculate squared distance between two points (faster).

Definition at line 73 of file Geometry.h.

◆ GetIntersection()

bool i3d::Geometry::GetIntersection	(	const CLine3d &	line,
		const CPlane3d &	plane,
		CVector3d &	result,
		double	tolerance = `I_BIG_EPSILON`
	)

Find intersection point between line and plane.

Parameters

line	Line to intersect.
plane	Plane to intersect.
result	Output intersection point.
tolerance	Tolerance for parallel check.

Returns: True if intersection exists, false if line is parallel to plane.

◆ GetSignedAngleBetweenVectors()

double i3d::Geometry::GetSignedAngleBetweenVectors	(	const CVector3d &	v1,
		const CVector3d &	v2,
		const CVector3d &	axis
	)

inline

Calculate signed angle between two vectors around an axis.

Parameters

v1	First vector.
v2	Second vector.
axis	Axis to measure rotation around.

Returns: Signed angle in radians [-PI, PI].

Definition at line 44 of file Geometry.h.

References GetAngleBetweenVectors(), i3d::CVector3d::GetCrossProduct(), imath::TVector< Size, Element >::GetDotProduct(), and i3d::CVector3d::GetNormalized().

◆ GetTriangleArea()

double i3d::Geometry::GetTriangleArea	(	const CVector3d &	p1,
		const CVector3d &	p2,
		const CVector3d &	p3
	)

inline

Calculate area of triangle.

Definition at line 206 of file Geometry.h.

References i3d::CVector3d::GetCrossProduct(), and imath::TVector< Size, Element >::GetLength().

◆ GetTriangleNormal()

CVector3d i3d::Geometry::GetTriangleNormal	(	const CVector3d &	p1,
		const CVector3d &	p2,
		const CVector3d &	p3
	)

inline

Calculate normal vector of triangle.

Definition at line 195 of file Geometry.h.

References i3d::CVector3d::GetCrossProduct(), and i3d::CVector3d::GetNormalized().

◆ IsOnPositiveSide()

bool i3d::Geometry::IsOnPositiveSide	(	const CVector3d &	point,
		const CPlane3d &	plane
	)

inline

Check if point is on the same side of plane as the plane's normal.

Definition at line 132 of file Geometry.h.

References i3d::CPlane3d::GetSignedDistance().

◆ IsPointInTriangle()

bool i3d::Geometry::IsPointInTriangle	(	const CVector3d &	point,
		const CVector3d &	p1,
		const CVector3d &	p2,
		const CVector3d &	p3
	)

Check if point is inside triangle.

Parameters

point	Point to test.
p1	First triangle vertex.
p2	Second triangle vertex.
p3	Third triangle vertex.

Returns: True if point is inside or on triangle boundary.

◆ ProjectVectorOntoVector()

CVector3d i3d::Geometry::ProjectVectorOntoVector	(	const CVector3d &	vector,
		const CVector3d &	onto
	)

inline

Project vector onto another vector.

Parameters

vector	Vector to project.
onto	Vector to project onto.

Returns: Projection of vector onto 'onto'.

Definition at line 144 of file Geometry.h.

References imath::TVector< Size, Element >::GetDotProduct(), imath::TVector< Size, Element >::GetLength2(), and I_BIG_EPSILON.

Functions

Detailed Description

Function Documentation

◆ AreIntersecting()

◆ GetAngleBetweenVectors()

◆ GetBarycentricCoordinates()

◆ GetClosestPoints()

◆ GetDistance() [1/3]

◆ GetDistance() [2/3]

◆ GetDistance() [3/3]

◆ GetDistanceSq()

◆ GetIntersection()

◆ GetSignedAngleBetweenVectors()

◆ GetTriangleArea()

◆ GetTriangleNormal()

◆ IsOnPositiveSide()

◆ IsPointInTriangle()

◆ ProjectVectorOntoVector()