GeometryHelper Class Reference

#include <GeometryHelper.hpp>

Inheritance diagram for GeometryHelper:

Static Public Member Functions
static void	rotationGetSinCos (double angle, double *cosa, double *sina)
static void	rotationMatrixIdentityInPlace (int ndim, VectorDouble &rot)
static void	rotation2DMatrixInPlace (double angle, VectorDouble &rot)
static void	rotation3DMatrixInPlace (double alpha, double beta, double gamma, VectorDouble &rot)
static void	rotationMatrixInPlace (int ndim, const VectorDouble &angles, VectorDouble &rot)
static VectorDouble	rotationMatrix (int ndim, const VectorDouble &angles)
static void	rotationGetAnglesInPlace (int ndim, const double *rot, double *angles)
static void	rotationGetAnglesInPlace (const VectorDouble &rot, VectorDouble &angles)
static void	rotationCopy (int ndim, const double *rotin, double *rotout)
static bool	rotationIsIdentity (int ndim, const double *rot, double eps=EPSILON10)
static MatrixSquareGeneral	EulerToRotation (const VectorDouble &angles, const ERotation &convrot=ERotation::fromKey("SXYZ"))
static void	rotationGetRandomDirection (double ct, double st, const double *a, double *codir)
static void	rotationGetDirection2D (const VectorDouble &angles, VectorDouble &codir)
static void	rotationGetDirectionDefault (int ndim, VectorDouble &codir)
static void	rotationGetAnglesFromCodirInPlace (const VectorDouble &codir, VectorDouble &angles)
static VectorDouble	rotationGetAngles (const VectorDouble &codir, bool flagResize=false)
static VectorDouble	rotationToEuler (const MatrixSquareGeneral &mat, const ERotation &convrot=ERotation::fromKey("SXYZ"), double eps=EPSILON10)
static double	distancePointToSegment (double x0, double y0, double x1, double y1, double x2, double y2, double *xd, double *yd, int *nint)
static bool	segmentIntersect (double xd1, double yd1, double xe1, double ye1, double xd2, double yd2, double xe2, double ye2, double *xint, double *yint)
static double	geodeticAngularDistance (double long1, double lat1, double long2, double lat2, double radius=1.)
static void	geodeticAngles (double long1, double lat1, double long2, double lat2, double long3, double lat3, double *a, double *b, double *c, double *A, double *B, double *C)
static double	geodeticTrianglePerimeter (double long1, double lat1, double long2, double lat2, double long3, double lat3)
static double	geodeticTriangleSurface (double long1, double lat1, double long2, double lat2, double long3, double lat3)
static bool	isInSphericalTriangle (double *coor, double surface, double *pts1, double *pts2, double *pts3, double *wgts, double eps=EPSILON6)
static bool	isInSphericalTriangleOptimized (const double *coor, double *ptsa, double *ptsb, double *ptsc, double *wgts, double eps=EPSILON6)
static VectorVectorDouble	convertLongLat (const VectorDouble &longitude, const VectorDouble &latitude, double dilate=1., double radius_arg=1.)
static void	convertCart2Sph (double x, double y, double z, double *rlong, double *rlat, double radius_arg=1.)
static void	convertSph2Cart (double rlong, double rlat, double *x, double *y, double *z, double radius_arg=1.)
static MatrixSquareGeneral	gradXYToRotmat (double dzoverdx, double dzoverdy)
static MatrixRectangular *	getDirectionsInR3 (const MatrixRectangular *U)
static MatrixRectangular *	getDirectionsInRn (const MatrixRectangular *U)
static double	formatAngle (double anglein, double basis=360.)
static VectorDouble	formatAngles (const VectorDouble &anglesin, double basis=360.)
static VectorDouble	rayTriangleIntersect (const VectorDouble &dir, const VectorDouble &v0, const VectorDouble &v1, const VectorDouble &v2)
static VectorVectorDouble	sphBarCoord (const VectorVectorDouble &sphPts, const MatrixRectangular &apices, const MatrixInt &meshes)
static double	getCosineAngularTolerance (double tolang)
static VectorVectorDouble	getEllipse (const VectorDouble &center, double rx, double ry, double theta, int count=360)

Member Function Documentation

convertCart2Sph()

void GeometryHelper::convertCart2Sph ( double  x, double  y, double  z, double *  rlong, double *  rlat, double  radius_arg = 1.  )

static

Convert the cartesian coordinates into spherical coordinates

Parameters

[in]	x	First cartesian coordinate
[in]	y	Second cartesian coordinate
[in]	z	Third cartesian coordinate
[in]	radius_arg	Radius of the sphere (Earth if TEST)
[out]	rlong	Longitude (in degrees)
[out]	rlat	Latitude (in degrees)

convertLongLat()

VectorVectorDouble GeometryHelper::convertLongLat ( const VectorDouble &  longitude, const VectorDouble &  latitude, double  dilate = 1., double  radius_arg = 1.  )

static

Returns the Vector of Sample coordinates in 3-D from Longitude-Latitude

Parameters

longitude	Array of longitude values
latitude	Array of latitude values
dilate	Dilation applied to radius
radius_arg	Radius (if note defined, taken from variety definition)

Returns

convertSph2Cart()

void GeometryHelper::convertSph2Cart ( double  rlong, double  rlat, double *  x, double *  y, double *  z, double  radius_arg = 1.  )

static

Convert the spherical coordinates into cartesian coordinates

Parameters

[in]	rlong	Longitude (in degrees)
[in]	rlat	Latitude (in degrees)
[in]	radius_arg	radius of the sphere (Earth if TEST)
[out]	x	First cartesian coordinate
[out]	y	Second cartesian coordinate
[out]	z	Third cartesian coordinate

distancePointToSegment()

double GeometryHelper::distancePointToSegment ( double  x0, double  y0, double  x1, double  y1, double  x2, double  y2, double *  xd, double *  yd, int *  nint  )

static

Find the shortest distance between the point (x0,y0) and the segment with the two end points (x1,y1) and (x2,y2)

Returns

Minimum algebraic distance (positive or negative)

Parameters

[in]	x0,y0	Coordinates of the target point
[in]	x1,y1	Coordinate of the first end-point of the segment
[in]	x2,y2	Coordinate of the second end-point of the segment
[out]	xd,yd	Coordinates of the closest point
[out]	nint	=1 if the projection belongs to the segment =0 if it is set to one of the segment vertices

EulerToRotation()

MatrixSquareGeneral GeometryHelper::EulerToRotation ( const VectorDouble &  angles, const ERotation &  convrot = ERotation::fromKey("SXYZ")  )

static

Returns the Rotation matrix, starting from the Euler angles

Parameters

angles	Ordered list of Euler angles
convrot	Rotation convention

Returns

Remarks

The code is coming from the following reference (BSD license)

https://github.com/matthew-brett/transforms3d/blob/master/transforms3d/euler.py

formatAngle()

double GeometryHelper::formatAngle ( double  anglein, double  basis = 360.  )

static

Format an Angle to be lying in [0, basis]

Parameters

anglein	Input angle value
basis	Basis (should be 360 by default; could be 180 for variogram or covariance)

Returns

formatAngles()

VectorDouble GeometryHelper::formatAngles ( const VectorDouble &  anglesin, double  basis = 360.  )

static

geodeticAngles()

void GeometryHelper::geodeticAngles ( double  long1, double  lat1, double  long2, double  lat2, double  long3, double  lat3, double *  a, double *  b, double *  c, double *  A, double *  B, double *  C  )

static

Calculate all geodetic angles from a spherical triangle

Parameters

[in]	long1	Longitude of the first point (in degrees)
[in]	lat1	Latitude of the first point (in degrees)
[in]	long2	Longitude of the second point (in degrees)
[in]	lat2	Latitude of the second point (in degrees)
[in]	long3	Longitude of the third point (in degrees)
[in]	lat3	Latitude of the third point (in degrees)
[out]	a	Angle (P2,O,P3)
[out]	b	Angle (P3,O,P1)
[out]	c	Angle (P1,O,P2)
[out]	A	Angle (P2,P1,P3)
[out]	B	Angle (P3,P2,P1)
[out]	C	Angle (P1,P3,P2)

geodeticAngularDistance()

double GeometryHelper::geodeticAngularDistance ( double  long1, double  lat1, double  long2, double  lat2, double  radius = 1.  )

static

Calculate the geodetic angular distance between two points on the sphere

Returns

Angular distance

Parameters

[in]	long1	Longitude of the first point (in degrees)
[in]	lat1	Latitude of the first point (in degrees)
[in]	long2	Longitude of the second point (in degrees)
[in]	lat2	Latitude of the second point (in degrees)
[in]	radius	Radius of the sphere

geodeticTrianglePerimeter()

double GeometryHelper::geodeticTrianglePerimeter ( double  long1, double  lat1, double  long2, double  lat2, double  long3, double  lat3  )

static

Calculate the perimeter of the spherical triangle

Returns

The Perimeter of the spherical triangle

Parameters

[in]	long1	Longitude of the first point (in degrees)
[in]	lat1	Latitude of the first point (in degrees)
[in]	long2	Longitude of the second point (in degrees)
[in]	lat2	Latitude of the second point (in degrees)
[in]	long3	Longitude of the third point (in degrees)
[in]	lat3	Latitude of the third point (in degrees)

geodeticTriangleSurface()

double GeometryHelper::geodeticTriangleSurface ( double  long1, double  lat1, double  long2, double  lat2, double  long3, double  lat3  )

static

Calculate the surface of the spherical triangle

Returns

The Surface of the spherical triangle (with unit radius)

Parameters

[in]	long1	Longitude of the first point (in degrees)
[in]	lat1	Latitude of the first point (in degrees)
[in]	long2	Longitude of the second point (in degrees)
[in]	lat2	Latitude of the second point (in degrees)
[in]	long3	Longitude of the third point (in degrees)
[in]	lat3	Latitude of the third point (in degrees)

getCosineAngularTolerance()

double GeometryHelper::getCosineAngularTolerance ( double  tolang )

static

Returns the cosine of the angular tolerance

Parameters

[in]

tolang

Angular tolerance

getDirectionsInR3()

MatrixRectangular * GeometryHelper::getDirectionsInR3 ( const MatrixRectangular *  U )

static

getDirectionsInRn()

MatrixRectangular * GeometryHelper::getDirectionsInRn ( const MatrixRectangular *  U )

static

Function to compute directions in Rd

Parameters

U	a matrix [n, d] of uniform values between [0,1]. 'n' is the number of direction and 'd' is the dimension of the space

Returns

A vector of a matrix [n, d] of the coordinates of the 'n' directions in the Euclidean space Rd.

getEllipse()

VectorVectorDouble GeometryHelper::getEllipse ( const VectorDouble &  center, double  rx, double  ry, double  theta, int  count = 360  )

static

gradXYToRotmat()

MatrixSquareGeneral GeometryHelper::gradXYToRotmat ( double  dzoverdx, double  dzoverdy  )

static

Calculate the rotation matrix starting from the partial derivatives along X and Y of a tilted plane

Parameters

dzoverdx	Partial derivative along X
dzoverdy	Partial derivative along Y

isInSphericalTriangle()

bool GeometryHelper::isInSphericalTriangle ( double *  coor, double  surface, double *  pts1, double *  pts2, double *  pts3, double *  wgts, double  eps = EPSILON6  )

static

Is a point inside a spherical triangle

Returns

1 if the point belongs to the spherical triangle; 0 otherwise

Parameters

[in]	coor	Coordinates of the target point (long,lat)
[in]	surface	Surface of the spherical triangle
[in]	pts1	Coordinates of the first point of the triangle
[in]	pts2	Coordinates of the second point of the triangle
[in]	pts3	Coordinates of the third point of the triangle
[in]	eps	Tolerance
[out]	wgts	Array of weights

isInSphericalTriangleOptimized()

bool GeometryHelper::isInSphericalTriangleOptimized ( const double *  coor, double *  ptsa, double *  ptsb, double *  ptsc, double *  wgts, double  eps = EPSILON6  )

static

Is a point inside a spherical triangle

Returns

True if the point belongs to the spherical triangle; False otherwise

Parameters

[in]	coor	Coordinates of the target point (long,lat)
[in]	ptsa	Coordinates of the first point of the triangle
[in]	ptsb	Coordinates of the second point of the triangle
[in]	ptsc	Coordinates of the third point of the triangle
[in]	eps	Tolerance
[out]	wgts	Array of weights

rayTriangleIntersect()

VectorDouble GeometryHelper::rayTriangleIntersect ( const VectorDouble &  dir, const VectorDouble &  v0, const VectorDouble &  v1, const VectorDouble &  v2  )

static

rotation2DMatrixInPlace()

void GeometryHelper::rotation2DMatrixInPlace ( double  angle, VectorDouble &  rot  )

static

Calculates the 2-D rotation matrix

Parameters

[in]	angle	Rotation angle (in degrees)
[out]	rot	Rotation matrix (Dimension = 4)

rotation3DMatrixInPlace()

void GeometryHelper::rotation3DMatrixInPlace ( double  alpha, double  beta, double  gamma, VectorDouble &  rot  )

static

Calculates the 3-D rotation matrix

Parameters

[in]	alpha	angle (in degrees) / oz
[in]	beta	angle (in degrees) / oy'
[in]	gamma	angle (in degrees) / ox''
[out]	rot	direct rotation matrix (Dimension = 9)

rotationCopy()

void GeometryHelper::rotationCopy ( int  ndim, const double *  rotin, double *  rotout  )

static

Copy a rotation matrix

Parameters

[in]	ndim	Space dimension
[in]	rotin	Input rotation matrix
[out]	rotout	Output rotation matrix (already allocated)

rotationGetAngles()

VectorDouble GeometryHelper::rotationGetAngles ( const VectorDouble &  codir, bool  flagResize = false  )

static

From the vector of direction coefficients (codir) returns the vector of angles

Parameters

codir	Input vector giving the direction coefficients
flagResize	When TRUE (and if in 2-D) the returned vector is resized to 1

Returns

rotationGetAnglesFromCodirInPlace()

void GeometryHelper::rotationGetAnglesFromCodirInPlace ( const VectorDouble &  codir, VectorDouble &  angles  )

static

Calculates the rotation angle from the direction coefficient

Parameters

[in]	codir	Direction vector (Dimension = ndim)
[out]	angles	Rotation angles (Dimension = ndim)

rotationGetAnglesInPlace() [1/2]

void GeometryHelper::rotationGetAnglesInPlace ( const VectorDouble &  rot, VectorDouble &  angles  )

static

rotationGetAnglesInPlace() [2/2]

void GeometryHelper::rotationGetAnglesInPlace ( int  ndim, const double *  rot, double *  angles  )

static

Calculates the rotation angles from the rotation matrix

Parameters

[in]	ndim	Space dimension
[in]	rot	Rotation matrix (Dimension = 9)
[out]	angles	Rotation angles (Dimension = ndim)

rotationGetDirection2D()

void GeometryHelper::rotationGetDirection2D ( const VectorDouble &  angles, VectorDouble &  codir  )

static

Convert angles to a set of Directions

Parameters

[in]	angles	Vector giving the angles characteristics (in degrees) As this provides rotation in 2D, 'angles' is dimensioned to 'ndir' (one angle requires a single value)
[out]	codir	Vector of the direction (Dim: ndir * ndim)

Remarks

'ndir' is given by the dimension of 'angles', 'ndim' is given by 'codir'

rotationGetDirectionDefault()

void GeometryHelper::rotationGetDirectionDefault ( int  ndim, VectorDouble &  codir  )

static

Create a Direction (used as default)

Parameters

[in]	ndim	Number of space dimensions
[out]	codir	Vector of the direction (Dim: ndim)

rotationGetRandomDirection()

void GeometryHelper::rotationGetRandomDirection ( double  ct, double  st, const double *  a, double *  codir  )

static

Rotation of a Direction in 3-D

Parameters

[in]	ct,st	Cosine and Sine of the rotation angle
[in]	a	Random direction
[in,out]	codir	Direction to be rotated

rotationGetSinCos()

void GeometryHelper::rotationGetSinCos ( double  angle, double *  cosa, double *  sina  )

static

Calculates the trigonometric features

Parameters

[in]	angle	input angle (in degrees)
[out]	cosa	cosine function
[out]	sina	sine function

rotationIsIdentity()

bool GeometryHelper::rotationIsIdentity ( int  ndim, const double *  rot, double  eps = EPSILON10  )

static

Starting from a rotation matrix, check it is different from the Identity

Returns

False if a rotation is defined; True if it is an Identity

Parameters

[in]	ndim	Space dimension
[in]	rot	Rotation matrix
[in]	eps	Tolerance

rotationMatrix()

VectorDouble GeometryHelper::rotationMatrix ( int  ndim, const VectorDouble &  angles  )

static

Calculates the rotation matrix. Returns the rotation matrix as a VectorDouble

Parameters

[in]	ndim	Space dimension
[in]	angles	Array of angles

rotationMatrixIdentityInPlace()

void GeometryHelper::rotationMatrixIdentityInPlace ( int  ndim, VectorDouble &  rot  )

static

Initialize a rotation matrix

Parameters

[in]	ndim	Space dimension
[out]	rot	Rotation matrix

rotationMatrixInPlace()

void GeometryHelper::rotationMatrixInPlace ( int  ndim, const VectorDouble &  angles, VectorDouble &  rot  )

static

Calculates the rotation matrix

Parameters

[in]	ndim	Space dimension
[in]	angles	Array of angles
[out]	rot	direct rotation matrix (dimensionned to ndim*ndim)

rotationToEuler()

VectorDouble GeometryHelper::rotationToEuler ( const MatrixSquareGeneral &  M, const ERotation &  convrot = ERotation::fromKey(                                          "SXYZ"), double  eps = EPSILON10  )

static

Returns the Euler angles, starting from a rotation matrix

Parameters

M	Input matrix
convrot	Rotation convention
eps	Tolerance

Returns

Remarks

The code is coming from the following reference (BSD license)

https://github.com/matthew-brett/transforms3d/blob/master/transforms3d/euler.py

segmentIntersect()

bool GeometryHelper::segmentIntersect ( double  xd1, double  yd1, double  xe1, double  ye1, double  xd2, double  yd2, double  xe2, double  ye2, double *  xint, double *  yint  )

static

Check if two 2-D segments intersect

Returns

True if there is an intersection; False otherwise

Parameters

[in]	xd1,yd1	Starting point for the first segment
[in]	xe1,ye1	Ending point for the first segment
[in]	xd2,yd2	Starting point for the second segment
[in]	xe2,ye2	Ending point for the second segment
[out]	xint,yint	Coordinates of the intersection

sphBarCoord()

VectorVectorDouble GeometryHelper::sphBarCoord ( const VectorVectorDouble &  sphPts, const MatrixRectangular &  apices, const MatrixInt &  meshes  )

static

Calculate the Barycenter coordinates of points with in the Spherical Meshing

Parameters

sphPts	Coordinates of target samples (dim = np * 3)
apices	Coordinates of the apices of the Meshing
meshes	Mesh information of the Meshing

Returns

A vector of barycenters (dimension = 4 * np) where

• 1: rank of the triangle
• 2, 3, 4: barycentric coordinates

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The documentation for this class was generated from the following files:

• include/Geometry/GeometryHelper.hpp
• src/Geometry/GeometryHelper.cpp