ImFusion::Geometry Namespace Reference

Classes to represent geometric primitives like lines or polygons, as well as functions dealing exclusively with such objects. More...

Detailed Description

Classes to represent geometric primitives like lines or polygons, as well as functions dealing exclusively with such objects.

Note

This namespace contains improved versions of what is in the original and now deprecated GeometryLegacy namespace.

See also

ImFusionGeometry

Classes
class	AlignedBox
	Class representing an axis aligned rectangular cuboid in 3D space. More...
class	AlignedRectangle2D
	Class representing an axis aligned rectangle in 2D space. More...
class	Circle
	Class representing a circle (actually a disk, so including the inner part) in 3D space. More...
class	Ellipse2D
	Class representing an ellipse in 2D space. More...
class	Line
	Class representing a full line, i.e. More...
class	LineBase
	Common interface of Line and LineSegment. More...
class	LineSegment
	Class representing a line segment, i.e. More...
class	Plane
	Class representing an oriented plane in 3D space defined by a base point and a normal direction. More...
class	Polygon2D
	Class representing a planar polygon. More...
class	Rectangle
	Arbitrary rectangle in 3D space. More...
struct	SpherePivotResult
class	Triangle
	Class representing a triangle in 3D space. More...

Functions
std::ostream &	operator<< (std::ostream &o, const AlignedBox &b)
int	fitCircle (const std::vector< vec2 > &pts, vec2 &center, double &radius, bool fixed[3], double *res=0, bool outlierRejection=false)
	Fit circle to points, using the Levenberg-Marquardt algorithm.
double	fitCircleRANSAC (const std::vector< vec2 > &pts, vec3 &circleOut, std::vector< vec2 > &inliersOut, double inlierThreshold=1.0, double diameter=-1)
double	fitCircleLeastSquares (const std::vector< vec2 > &pts, vec2 &center, double &radius)
	Fit circle to points, using a linear least squares fit.
int	fitCircle3D (const std::vector< vec3 > &pts, vec3 &outCenter, double &outRadius, mat3 &outR, double *outRes=0, bool rejectOutliers=false)
	Fit circle in 3D to points.
int	fitSphere (const std::vector< vec3 > &pts, vec3 &center, double &radius, bool fixed[4], double *res=0)
	Fit sphere to points.
double	fitSphereRANSAC (const std::vector< vec3 > &pts, vec4 &circleOut, std::vector< vec3 > &inliersOut, double inlierThreshold, double diameter=-1)
SpherePivotResult	fitSpherePivotingPoses (const std::vector< mat4 > &pivotPoses)
int	fitConic (const std::vector< vec2 > &pts, mat3 &C, double *res=0)
	Fit conic to points.
int	fitCylinder (const std::vector< vec3 > &pts, vec3 &center, double &radius, mat3 &R, double *res=0)
	Fit cylinder to points.
int	fitPlane (const std::vector< vec3 > &pts_, vec4 *plane, double *res=0, bool rejectOutliers=false)
	Fit plane to points.
double	fitPlaneRANSAC (const std::vector< vec3 > &pts, vec4 &planeOut, std::vector< vec3 > &inliersOut, double inlierThreshold, int maxIter=100)
void	fitAxesPCA (const std::vector< vec3 > &pts_, vec3 &outCentroid_, vec4(&outPlanes_)[3], bool scalePoints=true, vec3 *outEigenvalues=nullptr)
	Performs a PCA to fit the principal component axes to points.
int	fitLine (const std::vector< vec2 > &pts_, vec3 *line, double *res=0)
	Fit line to points.
double	fitLineRANSAC (const std::vector< vec2 > &pts, vec3 &lineOut, std::vector< vec2 > &inliersOut, double inlierThreshold)
double	fitLineRANSAC (const std::vector< vec3 > &pts, vec3 &lineOutOrigin, vec3 &lineOutDir, std::vector< vec3 > &inliersOut, double inlierThreshold)
	Fit line to inlier points.
int	fitLine (const std::vector< vec3 > &pts_, vec3 &lineOutOrigin, vec3 &lineOutDir, double *res=0)
std::optional< Geometry::Ellipse2D >	fitEllipse (const std::vector< vec2 > &pts)
	Fit ellipse to points using least squares.
std::vector< vec3 >	uniformDistributedPointsOnSphere (const int N)
	Picks uniform distributed points on the sphere, i.e.
std::vector< vec2 >	uniformDistributedPointsOnCircle (const int N)
	Picks uniform distributed points on the circle, i.e.

Find intersection points or overlapping parts
If the result has the same type as one of the arguments, it is a copy of the first such argument. In all other cases, the choice of variables that do not change the represented object (e.g. sign of normal) is arbitrary. Objects involving NAN or infinity will never intersect.
Utils::Variant< Line, vec3, std::nullptr_t >	intersection (const Line &l1, const Line &l2)
	Compute the intersection between two Lines or LineSegments.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Line &l1, const LineSegment &l2)
	Compute the intersection between two Lines or LineSegments.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const LineSegment &l1, const Line &l2)
	Compute the intersection between two Lines or LineSegments.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const LineSegment &l1, const LineSegment &l2)
	Compute the intersection between two Lines or LineSegments.
Utils::Variant< Line, vec3, std::nullptr_t >	intersection (const Line &l, const Plane &p)
	Compute the intersection between a Line or LineSegment and a Plane.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const LineSegment &l, const Plane &p)
	Compute the intersection between a Line or LineSegment and a Plane.
Utils::Variant< Line, vec3, std::nullptr_t >	intersection (const Plane &p, const Line &l)
	Compute the intersection between a Line or LineSegment and a Plane.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Plane &p, const LineSegment &l)
	Compute the intersection between a Line or LineSegment and a Plane.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Line &l, const Triangle &p)
	Compute the intersection between a Line or LineSegment and a Triangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const LineSegment &l, const Triangle &p)
	Compute the intersection between a Line or LineSegment and a Triangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Triangle &t, const Line &l)
	Compute the intersection between a Line or LineSegment and a Triangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Triangle &t, const LineSegment &l)
	Compute the intersection between a Line or LineSegment and a Triangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Line &l, const AlignedBox &c)
	Compute the intersection between a Line or LineSegment and a AlignedBox.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const LineSegment &l, const AlignedBox &c)
	Compute the intersection between a Line or LineSegment and a AlignedBox.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const AlignedBox &c, const Line &l)
	Compute the intersection between a Line or LineSegment and a AlignedBox.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const AlignedBox &c, const LineSegment &l)
	Compute the intersection between a Line or LineSegment and a AlignedBox.
std::vector< vec3 >	intersection (const AlignedBox &cuboid, const Plane &plane)
	Compute the intersection between a AlignedBox and a Plane.
std::vector< vec3 >	intersection (const Plane &plane, const AlignedBox &cuboid)
	Compute the intersection between a AlignedBox and a Plane.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Rectangle &p, const LineSegment &l)
	Compute the intersection between a LineSegment and a Rectangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const LineSegment &l, const Rectangle &p)
	Compute the intersection between a LineSegment and a Rectangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Rectangle &p, const Line &l)
	Compute the intersection between a Line and a Rectangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersection (const Line &l, const Rectangle &p)
	Compute the intersection between a Line and a Rectangle.
Utils::Variant< std::vector< vec3 >, LineSegment, vec3, std::nullptr_t >	intersection (const Rectangle &l, const Rectangle &p)
	Compute the intersection between two Rectangles.
Utils::Variant< AlignedBox, LineSegment, vec3, std::nullptr_t >	intersection (const AlignedBox &c, const AlignedBox &c2)
	Returns intersection between 2 boxes or nullptr in case of no intersection.
Utils::Variant< Plane, Line, std::nullptr_t >	intersection (const Plane &p1, const Plane &p2)
	Compute the intersection between multiple planes.
Utils::Variant< Plane, Line, vec3, std::nullptr_t >	intersection (const Plane &p1, const Plane &p2, const Plane &p3)
	Compute the intersection between multiple planes.
Utils::Variant< Triangle, LineSegment, vec3, std::nullptr_t >	intersection (const Plane &p, const Triangle &t)
	Compute the intersection between a Plane and a Triangle.
Utils::Variant< Triangle, LineSegment, vec3, std::nullptr_t >	intersection (const Triangle &t, const Plane &p)
	Compute the intersection between a Plane and a Triangle.
Utils::Variant< AlignedRectangle2D, vec3, std::nullptr_t >	intersection (const AlignedRectangle2D &r1, const AlignedRectangle2D &r2)
	Returns the intersection of 2 rectangles.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersectionFast (const Line &l, const Triangle &t)
	Compute the intersection between a Line and a Triangle.
Utils::Variant< LineSegment, vec3, std::nullptr_t >	intersectionFast (const Triangle &t, const Line &l)
	Compute the intersection between a Line and a Triangle.

Check if, but not how, a pair of objects intersects
Touching at a single point counts as intersection for the purpose of these functions. These are faster than computing the full intersection. Objects involving NAN or infinity will never intersect.
bool	intersects (const AlignedRectangle2D &r1, const AlignedRectangle2D &r2)
	Checks if the two rectangles intersect.
bool	intersects (const AlignedBox &c, const Triangle &t)
	Checks if the box and triangle intersect.
bool	intersects (const AlignedBox &c, const AlignedBox &c2)
	Checks if the two boxes intersect.
bool	intersects (const AlignedBox &cub, const Plane &plane)
	Checks if the box and plane intersect.

Function Documentation

fitCircle()

int fitCircle	(	const std::vector< vec2 > &	pts,
		vec2 &	center,
		double &	radius,
		bool	fixed[3],
		double *	res = 0,
		bool	outlierRejection = false )

Fit circle to points, using the Levenberg-Marquardt algorithm.

Parameters

pts	input points
center	estimated center
radius	estimated radius
fixed	fixed parameters (center x, y, radius)
res	residual

Returns

0 if successful

fitCircleLeastSquares()

double fitCircleLeastSquares	(	const std::vector< vec2 > &	pts,
		vec2 &	center,
		double &	radius )

Fit circle to points, using a linear least squares fit.

Parameters

pts	input points
center	estimated center
radius	estimated radius

Returns

The residual

Note

See https://dtcenter.org/met/users/docs/write_ups/circle_fit.pdf for technical details.

fitCircle3D()

int fitCircle3D	(	const std::vector< vec3 > &	pts,
		vec3 &	outCenter,
		double &	outRadius,
		mat3 &	outR,
		double *	outRes = 0,
		bool	rejectOutliers = false )

Fit circle in 3D to points.

Parameters

pts	input points
outCenter	estimated center
outRadius	estimated radius
outR	estimated rotation matrix which transforms the circle normal to the z unit vector
outRes	residual

Returns

0 if successful, -1 otherwise

fitSphere()

int fitSphere	(	const std::vector< vec3 > &	pts,
		vec3 &	center,
		double &	radius,
		bool	fixed[4],
		double *	res = 0 )

Fit sphere to points.

Parameters

pts	input points
center	estimated center and initial guess
radius	estimated radius and initial guess
fixed	fixed parameters (center x, y, z, radius)
res	residual

Returns

0 if successful

fitConic()

int fitConic	(	const std::vector< vec2 > &	pts,
		mat3 &	C,
		double *	res = 0 )

Fit conic to points.

Parameters

pts	input points
C	conic
res	residual

Returns

0 if successful

fitCylinder()

int fitCylinder	(	const std::vector< vec3 > &	pts,
		vec3 &	center,
		double &	radius,
		mat3 &	R,
		double *	res = 0 )

Fit cylinder to points.

Parameters

pts	input points
center	estimated center
radius	estimated radius
R	rotation matrix
res	residual

Returns

0 if successful

fitPlane()

int fitPlane	(	const std::vector< vec3 > &	pts_,
		vec4 *	plane,
		double *	res = 0,
		bool	rejectOutliers = false )

Fit plane to points.

Parameters

pts_	input points
plane	estimated plane
res	residual

Returns

0 if successful

For any point pt on the plane, plane.dot(pt.homogeneous()) == 0.0 holds, i.e. plane[3] is -d from the Hesse normal form

fitAxesPCA()

void fitAxesPCA	(	const std::vector< vec3 > &	pts_,
		vec3 &	outCentroid_,
		vec4(&)	outPlanes_[3],
		bool	scalePoints = true,
		vec3 *	outEigenvalues = nullptr )

Performs a PCA to fit the principal component axes to points.

Parameters

pts_	input points
outCentroid_	estimated centroid
outPlanes_	estimated planes in homogeneous convenion (see fitPlane())
scalePoints	whether to scale the points
outEigenvalues	estimated eigenvalues

The first three components of each estimated plane contain the normal vector, i.e. the principal component axis. fitPlane() returns the last of these planes.

fitLine()

int fitLine	(	const std::vector< vec2 > &	pts_,
		vec3 *	line,
		double *	res = 0 )

Fit line to points.

Parameters

pts_	input points
line	estimated line in general form: a*x + b*y + c = 0
res	residual

Returns

0 if successful

fitLineRANSAC()

double fitLineRANSAC	(	const std::vector< vec3 > &	pts,
		vec3 &	lineOutOrigin,
		vec3 &	lineOutDir,
		std::vector< vec3 > &	inliersOut,
		double	inlierThreshold )

Fit line to inlier points.

Parameters

pts	input points
lineOutOrigin	point belonging to the line
lineOutDir	direction of the line, thus any point on the line can be estimated as: <x, y, z> = lineOutOrigin + t*lineOutDir
inliersOut	input points that lie within inlierThreshold distance from the estimated line
inlierThreshold	threshold for distance between an inlier point and an estimated line

Returns

average distance between inlier point and the line

fitEllipse()

std::optional< Geometry::Ellipse2D > fitEllipse

(

const std::vector< vec2 > &

pts

)

Fit ellipse to points using least squares.

Parameters

pts	input points
ellipse	output fitted ellipse

Returns

true if successful, false otherwise

uniformDistributedPointsOnSphere()

std::vector< vec3 > uniformDistributedPointsOnSphere

(

const int

N

)

Picks uniform distributed points on the sphere, i.e.

unit vectors in 3D

Parameters

N	number of points to be picked

Returns

Vector of N uniform distributed unit vectors

uniformDistributedPointsOnCircle()

std::vector< vec2 > uniformDistributedPointsOnCircle

(

const int

N

)

Picks uniform distributed points on the circle, i.e.

unit vectors in 2D

Parameters

N	number of points to be picked

Returns

Vector of N uniform distributed unit vectors