Vector with x,y,z components. More...

#include <dvec3d.h>

Inheritance diagram for DVec3d:

Public Member Functions
void	InitFromArray (double const *pXyz)
	Copies doubles from a 3 component array to the x,y, and z components of a DVec3d. More...

void	Init (double ax, double ay, double az)
	Sets the x,y, and z components of a vector. More...

void	Init (double ax, double ay)
	Sets the x, and y components of a vector. More...

void	Init (DPoint3dCR point)
	Initialize a vector from a point (treating the point as a vector from its origin). More...

double	Normalize (DVec3dCR vector)
	Normalizes (scales) a vector to length 1. More...

bool	TryNormalize (DVec3dCR source, double &magnitude)
	initialize this vector to unit vector in the direction of source. More...

ValidatedDVec3d	ValidatedNormalize () const
	return a (possibly invalid) unit vector in the direction of the calling instance. More...

double	Normalize ()
	Replaces a vector by a unit vector in the same direction, and returns the original length. More...

double	ScaleToLength (DVec3dCR vector, double length)
	Scales a vector to specified length. More...

double	ScaleToLength (double length)
	Scales a vector to a specified length, and returns the prior length. More...

double	NormalizedDifference (DPoint3dCR target, DPoint3dCR origin)
	Computes a unit vector in the direction of the difference of the vectors or vectors (Second parameter vector is subtracted from the first parameter vector, exactly as in the subtract function.) More...

void	DifferenceOf (DVec3dCR vector1, DVec3dCR vector2)
	Subtract coordinates of two vectors. More...

void	DifferenceOf (DPoint3dCR target, DPoint3dCR base)
	Subtract coordinates of two points. More...

void	Subtract (DVec3dCR vector2)
	Subtract two vectors, and return the result in place of the first. More...

void	InitFromXYAngleAndMagnitude (double theta, double magnitude)
	Sets a vector from given angle and distance in xy plane. More...

void	InitFromColumn (RotMatrixCR matrix, int col)
	Extracts a column of a matrix. More...

void	InitFromRow (RotMatrixCR matrix, int row)
	Extracts a row of a matrix. More...

void	Multiply (RotMatrixCR matrix, DVec3dCR vector)
	Returns the product of a matrix times a vector. More...

void	MultiplyTranspose (RotMatrixCR matrix, DVec3dCR vector)
	Returns the product of a matrix transpose times a vector. More...

void	Multiply (RotMatrixCR matrix, double x, double y, double z)
	Returns the product of a matrix times a vector, with the vector given as separate components. More...

void	MultiplyTranspose (RotMatrixCR matrix, double x, double y, double z)
	Returns the product P = [x,y,z]*M where M is the input matrix and P is the product vector. More...

void	XyzOf (DPoint4dCR hPoint)
	Sets the x,y, and z components of a DVec3d structure from the corresponding parts of a DPoint4d. More...

void	CrossProduct (DVec3dCR vector1, DVec3dCR vector2)
	Returns the (vector) cross product of two vectors. More...

void	CrossProduct (DVec3dCR vector1, DPoint3dCR point2)
	Returns the (vector) cross product of two vectors. More...

void	CrossProduct (DPoint3dCR point1, DVec3dCR vector2)
	Returns the (vector) cross product of two vectors. More...

void	CrossProductToPoints (DPoint3dCR origin, DPoint3dCR target1, DPoint3dCR target2)
	Sets the instance to the (vector) cross product of two vectors. More...

double	NormalizedCrossProduct (DVec3dCR vector1, DVec3dCR vector2)
	Compute the normalized cross product of two vectors and return the length of the unnormalized cross product. More...

double	SizedCrossProduct (DVec3dCR vector1, DVec3dCR vector2, double productLength)
	Computes the cross product of the two parameter vectors and scales it to a given length. More...

double	GeometricMeanCrossProduct (DVec3dCR vector1, DVec3dCR vector2)
	Computes the cross product of two vectors and scales it to the geometric mean of the lengths of the two vectors. More...

void	RotateXY (DVec3dCR vector, double theta)
	Rotate a vector around the z axis. More...

void	RotateXY (double theta)
	Rotate a vector around the z axis. More...

bool	UnitPerpendicularXY (DVec3dCR vector)
	Compute a unit vector perpendicular to the xy parts of given vector. More...

void	Interpolate (DVec3dCR vector0, double fractionParameter, DVec3dCR vector1)
	Computes a vector whose position is given by a fractional argument and two vectors. More...

void	SumOf (DVec3dCR vector1, DVec3dCR vector2)
	Compute the sum of two vectors. More...

void	Add (DVec3dCR vector)
	Adds a vector to a pointer or vector, returns the result in place. More...

void	SumOf (DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2)
	Compute the sum of two vectors with scale factors. More...

void	SumOf (DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2, DVec3dCR vector3, double scale3)
	Compute the sum of three vectors with scale factors. More...

void	SumOf (DVec3dCR origin, DVec3dCR vector, double scale)
	Adds an origin and a scaled vector. More...

void	SumOf (DVec3dCR origin, DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2)
	Adds an origin and two scaled vectors. More...

void	SumOf (DVec3dCR origin, DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2, DVec3dCR vector3, double scale3)
	Adds an origin and three scaled vectors. More...

void	Scale (DVec3dCR vector, double scale)
	Multiplies a vector by a scale factor. More...

void	Scale (double scale)
	Multiplies a vector (in place) by a scale factor. More...

bool	SafeDivide (DVec3dCR vector, double denominator)
	Try to divide each component of a vector by a scalar. More...

void	Negate (DVec3dCR vector)
	Computes a negated (opposite) vector. More...

void	Negate ()
	Negate a vector in place. More...

void	WeightedDifferenceOf (DPoint4dCR hPoint1, DPoint4dCR hPoint2)
	Scale each (homogeneous) point by the other's weight and subtract, i.e. More...

void	WeightedDifferenceCrossProduct (DPoint4dCR basePoint, DPoint4dCR target1, DPoint4dCR target2)
	Form the cross product of the weighted differences from base poitn to two targets. More...

double	DotProduct (DVec3dCR vector2) const
	Returns the (scalar) dot product of two vectors. More...

double	DotProductXY (DVec3dCR vector2) const
	Returns the (scalar) dot product of xy parts of two vectors. More...

double	DotProduct (double ax, double ay, double az) const
	Computes the dot product of one vector given as a vector structure and another given as xyz components. More...

double	DotProduct (DPoint3dCR point2) const
	Returns the (scalar) dot product of two vectors. More...

double	DotProductRow (RotMatrixCR matrix, int index) const
	Returns the (scalar) dot product of this vector and a row of a matrix. More...

double	DotProductColumn (RotMatrixCR matrix, int index) const
	Returns the (scalar) dot product of this vector and a column of a matrix. More...

double	DotProductMatrixRow (TransformCR matrix, int index) const
	Returns the (scalar) dot product of this vector and a row of the matrix part of the transform. More...

double	DotProductMatrixColumn (TransformCR matrix, int index) const
	Returns the (scalar) dot product of this vector and a column of the matrix part of the transform. More...

double	TripleProduct (DVec3dCR vector2, DVec3dCR vector3) const
	Computes the triple product of three vectors. More...

double	Magnitude () const
	Computes the magnitude of a vector. More...

double	MagnitudeSquared () const
	Computes the squared magnitude of a vector. More...

double	SafeOneOverMagnitudeSquared (double defaultValue) const
	Returns 1 over the squared magnitude, or caller supplied default if squared magnitude is too small. More...

ValidatedDouble	ValidatedFractionOfProjection (DVec3dCR vectorToProject, double defaultValue=0.0) const
	Returns fraction at which other projects onto this, in ValidatedDouble which records if the division was safe. More...

double	MagnitudeXY () const
	Computes the magnitude of the xy part of a vector. More...

double	MagnitudeSquaredXY () const
	Computes the squared magnitude of the xy part of a vector. More...

double	MaxAbs () const
	Finds the largest absolute value among the components of a vector. More...

double	Distance (DVec3dCR vector2) const
	Computes the (cartesian) distance between two vectors. More...

double	DistanceSquared (DVec3dCR vector2) const
	Computes the squared distance between two vectors. More...

double	DistanceSquaredXY (DVec3dCR vector2) const
	Computes the squared distance between two vectors, using only the xy parts. More...

double	DistanceXY (DVec3dCR vector2) const
	Computes the distance between two vectors, using only x and y components. More...

double	CrossProductMagnitude (DVec3dCR other) const
	Compute the cross product with other and return is magnitude (but the cross product is not returned) More...

double	CrossProductXY (DVec3dCR vector2) const
	Return the (scalar) cross product of the xy parts of two vectors. More...

void	SetComponent (double a, int index)
	Set one of three components (x,y,z) of the vector. More...

double	GetComponent (int index) const
	Gets a single component of a vector. More...

void	GetComponents (double &xCoord, double &yCoord, double &zCoord) const
	Copies x,y,z components from a vector to individual variables. More...

bool	GetTriad (DVec3dR xAxis, DVec3dR yAxis, DVec3dR zAxis) const
	Sets three vectors so that they are mutually perpendicular, the third (Z) vector is identical to the given axis vector, and all have the same length. More...

bool	GetNormalizedTriad (DVec3dR xAxis, DVec3dR yAxis, DVec3dR zAxis) const
	Sets three vectors so that they are mutually perpendicular unit vectors with the third (Z) vector in the direction of the given axis vector. More...

bool	ProjectToVector (DVec3dCR targetVector, double &fraction) const
	Find the fraction at which the instance projects to a vector. More...

bool	ProjectToPlane (DVec3dCR vectorU, DVec3dCR vectorV, DPoint2dR uv) const
	Find the projection of the instance vector to a plane defined by two vectors. More...

bool	GetPerpendicularParts (DVec3dCR hypotenuse, double &fraction, DVec3dR parallelPart, DVec3dR perpendicularPart) const
	Decompose hypotenuse into a vector parallel to the instance and a vector perpendicular to the instance. More...

double	AngleTo (DVec3dCR vector2) const
	Returns the angle between two vectors. More...

double	AngleToXY (DVec3dCR vector2) const
	Returns the angle from Vector1 to Vector2 using only xy parts. More...

double	SmallerUnorientedAngleTo (DVec3dCR vector2) const
	Returns the angle between two vectors, choosing the smaller of the two possible angles when both the vectors and their negations are considered. More...

double	SmallerUnorientedAngleToXY (DVec3dCR vector2) const
	Returns the angle between two vectors, considering both the vectors and their negations and choosing the smaller. More...

double	AngleFromPerpendicular (DVec3dCR vector2) const
	Returns the angle that two vectors deviate from being perpendicular. More...

double	SignedAngleTo (DVec3dCR vector2, DVec3dCR orientationVector) const
	Computes the signed angle from one vector to another, in the plane of the two vectors. More...

double	PlanarAngleTo (DVec3dCR vector2, DVec3dCR planeNormal) const
	Computes the signed angle between the projection of two vectors onto a plane with given normal. More...

bool	AngleAndAxisOfRotationFromVectorToVector (DVec3dCR target, DVec3dR axis, double &radians) const
	Compute an axis and angle to rotate from the instance vector to a target. More...

bool	IsVectorInSmallerSector (DVec3dCR vector0, DVec3dCR vector1) const
	Test a vector is "between" vector0 and vector1. More...

bool	IsVectorInCCWSector (DVec3dCR vector0, DVec3dCR vector1, DVec3dCR upVector) const
	Test if the test vector vector is "between" vector0 and vector1, with CCW direction resolved by an up vector. More...

bool	IsVectorInCCWXYSector (DVec3dCR vector0, DVec3dCR vector1) const
	Test if the instance vector vector is "between" vector0 and vector1, with CCW direction using only xy parts. More...

bool	IsParallelTo (DVec3dCR vector2) const
	Tests if two vectors are parallel (opposites are considered parallel!) More...

bool	IsPositiveParallelTo (DVec3dCR vector2) const
	Tests if two vectors are parallel and have positive dot product (opposites are NOT considered parallel) More...

bool	IsPerpendicularTo (DVec3dCR vector2) const
	Tests if two vectors are perpendicular. More...

bool	IsEqual (DVec3dCR vector2) const
	Test for exact equality between all components of two vectors. More...

bool	IsEqual (DVec3dCR vector2, double tolerance) const
	Test if the x, y, and z components of two vectors are equal within tolerance. More...

bool	AlmostEqual (DVec3d const &dataB) const
	test if two points are equal. More...

bool	IsZero ()
	checks if the vector has all zeros More...

Public Member Functions inherited from DPoint3d
void	Swap (DPoint3dR other)
	Swap contents of instance, other. More...

double	CrossProductToPointsXY (DPoint3dCR target1, DPoint3dCR target2) const
	Returns the (scalar) cross product of the xy parts of two vectors. More...

double	DotProductToPoints (DPoint3dCR target1, DPoint3dCR target2) const
	Returns the (scalar) dot product of two vectors. More...

double	DotProductToPointsXY (DPoint3dCR target1, DPoint3dCR target2) const
	Returns the (scalar) dot product of xy parts of two vectors. More...

double	DotDifference (DPoint3dCR origin, DVec3dCR vector) const
	Returns the (scalar) dot product of a two vectors. More...

double	TripleProductToPoints (DPoint3dCR target1, DPoint3dCR target2, DPoint3dCR target3) const
	Computes the triple product of vectors from a base point three target points. More...

void	Zero ()
	Sets all components of a point or vector to zero. More...

void	One ()
	Returns a point or vector with all components 1.0. More...

void	InitFromArray (const double *pXyz)
	Copies doubles from a 3 component array to the x,y, and z components of a DPoint3d. More...

void	Init (DPoint2dCR source)
	Copy from a 2d point setting z to zero. More...

void	Init (double ax, double ay, double az)
	Sets the x,y, and z components of a point. More...

void	Init (double ax, double ay)
	Sets the x, and y components of a point. More...

void	XyzOf (DPoint4dCR hPoint)
	Sets the x,y, and z components of a DPoint3d structure from the corresponding parts of a DPoint4d. More...

void	SetComponent (double a, int index)
	Set one of three components (x,y,z) of the point. More...

double	GetComponent (int index) const
	Gets a single component of a point. More...

void	GetComponents (double &xCoord, double &yCoord, double &zCoord) const
	Copies x,y,z components from a point to individual variables. More...

void	Interpolate (DPoint3dCR point0, double fractionParameter, DPoint3dCR point1)
	Computes a point whose position is given by a fractional argument and two endpoints. More...

bool	IsPointInSmallerSector (DPoint3dCR origin, DPoint3dCR target1, DPoint3dCR target2) const
	Form vectors from the origin to the test point and the two boundary vectors. More...

bool	IsPointInCCWector (DPoint3dCR origin, DPoint3dCR target0, DPoint3dCR target1, DVec3dCR upVector) const
	Test if a point is within the counter-clockwise sector defined by an origin and two boundary points, with an up vector to determine which direction is counter clockwise. More...

double	Distance (DPoint3dCR point2) const
	Computes the (cartesian) distance between two points. More...

double	DistanceSquared (DPoint3dCR point2) const
	Computes the squared distance between two points. More...

double	DistanceSquaredXY (DPoint3dCR point2) const
	Computes the squared distance between two points, using only the xy parts. More...

double	DistanceXY (DPoint3dCR point2) const
	Computes the distance between two points, using only x and y components. More...

bool	DistanceXY (DPoint3dCR otherPoint, DMatrix4dCP matrix, double &distance) const
	Computes the distance between two points, using only x and y components, optionally applying a transform into view space. More...

double	MaxAbs () const
	Finds the largest absolute value among the components of a point or vector. More...

double	MinAbs () const
	Finds the smallest absolute value among the components of a point or vector. More...

int	MaxAbsIndex () const
	return in the index of the MaxAbs () value. More...

int	MinAbsIndex () const
	return in the index of the MinAbs () value More...

DRange1d	ComponentRange () const

bool	IsEqual (DPoint3dCR point2) const
	Test for exact equality between all components of two points or vectors. More...

bool	IsEqual (DPoint3dCR point2, double tolerance) const
	Test if the x, y, and z components of two points or vectors are equal within tolerance. More...

void	NpcCoordinatesOf (DPoint3dCR point, DRange3dCR cube)
	Computes the coordinates of point under the translation and scaling that puts 000 at cube>low and 111 at cube>high. More...

bool	IsDisconnect () const

void	InitDisconnect ()
	Initialize a point with all coordinates as the disconnect value. More...

void	Init (DVec3dCR vector)
	Initialize a point by copying x,y,z from a vector. More...

void	Subtract (DPoint3dCR base, DVec3dCR vector)
	Subtract a vector from a point. More...

void	Add (DVec3dCR vector)
	Adds a vector to a pointer or vector, returns the result in place. More...

void	SumOf (DPoint3dCR origin, DVec3dCR vector, double scale)
	Adds an origin and a scaled vector. More...

void	SumOf (DPoint3dCR origin, DVec3dCR point1, double scale1, DVec3dCR point2, double scale2)
	Adds an origin and two scaled vectors. More...

void	SumOf (DPoint3dCR origin, DVec3dCR point1, double scale1, DVec3dCR point2, double scale2, DVec3dCR point3, double scale3)
	Adds an origin and three scaled vectors. More...

void	CrossProduct (DPoint3dCR point1, DPoint3dCR point2)
	Returns the cross (vector) cross product of two vectors. More...

void	CrossProductToPoints (DPoint3dCR origin, DPoint3dCR target1, DPoint3dCR target2)
	Returns the (vector) cross product of two vectors. More...

double	CrossProductXY (DPoint3dCR point2) const
	Return the (scalar) cross product of the xy parts of two vectors. More...

double	NormalizedCrossProduct (DPoint3dCR point1, DPoint3dCR point2)
	Compute the normalized cross product of two vectors and return the length of the unnormalized cross product. More...

double	SizedCrossProduct (DPoint3dCR point1, DPoint3dCR point2, double productLength)
	Computes the cross product of the two parameter vectors and scales it to a given length. More...

double	GeometricMeanCrossProduct (DPoint3dCR point1, DPoint3dCR point2)
	Computes the cross product of two vectors and scales it to the geometric mean of the lengths of the two vectors. More...

double	DotProduct (DPoint3dCR point2) const
	Returns the (scalar) dot product of two vectors. More...

double	DotProductXY (DPoint3dCR point2) const
	Returns the (scalar) dot product of xy parts of two vectors. More...

double	DotProduct (double ax, double ay, double az) const
	Computes the dot product of one vector given as a point structure and another given as xyz components. More...

double	NormalizedDifference (DPoint3dCR target, DPoint3dCR origin)
	Computes a unit vector in the direction of the difference of the points or vectors (Second parameter vector is subtracted from the first parameter vector, exactly as in the subtract function.) More...

double	AngleTo (DPoint3dCR point2) const
	Returns the angle between two vectors. More...

double	AngleXY () const
	Computes the (signed) angle from xy axis to the vector, using only xy parts. More...

double	SmallerUnorientedAngleTo (DPoint3dCR point2) const
	Returns the angle between two vectors, choosing the smaller of the two possible angles when both the vectors and their negations are considered. More...

bool	IsVectorInSmallerSector (DPoint3dCR point0, DPoint3dCR point1) const
	Test a vector is "between" point0 and point1. More...

bool	IsVectorInCCWSector (DPoint3dCR point0, DPoint3dCR point1, DPoint3dCR upVector) const
	Test if the test vector vector is "between" point0 and point1, with CCW direction resolved by an up vector. More...

double	AngleToXY (DPoint3dCR point2) const
	Returns the angle from Vector1 to Vector2 using only xy parts. More...

double	SmallerUnorientedAngleToXY (DPoint3dCR point2) const
	Returns the angle between two vectors, considering both the vectors and their negations and choosing the smaller. More...

void	RotateXY (DPoint3dCR vector, double theta)
	Rotate vector around the z axis, return as calling instance. More...

void	RotateXY (double theta)
	Rotate the calling instance around the z axis. More...

double	SignedAngleTo (DPoint3dCR point2, DPoint3dCR orientationVector) const
	Computes the signed from one vector to another, in the plane of the two vectors. More...

double	PlanarAngleTo (DPoint3dCR point2, DPoint3dCR planeNormal) const
	Computes the signed angle between the projection of two vectors onto a plane with given normal. More...

void	WeightedDifferenceOf (DPoint4dCR point1, DPoint4dCR point2)
	Scale each point by the other's weight and subtract, i.e. More...

void	WeightedDifferenceCrossProduct (DPoint4dCR basePoint, DPoint4dCR target1, DPoint4dCR target2)
	Form the cross product of the weighted differences from point0 to point1 and point2. More...

double	MagnitudeSquared () const
	Computes the squared magnitude of a vector. More...

double	MagnitudeXY () const
	Computes the magnitude of the xy part of a vector. More...

double	MagnitudeSquaredXY () const
	Computes the squared magnitude of the xy part of a vector. More...

bool	UnitPerpendicularXY (DPoint3dCR vector)
	Compute a unit vector perpendicular to the xy parts of given vector. More...

double	Magnitude () const
	Computes the magnitude of a vector. More...

void	Scale (DPoint3dCR vector, double scale)
	Multiplies a vector by a scale factor. More...

void	Scale (double scale)
	Multiplies a vector (in place) by a scale factor. More...

void	Negate (DPoint3dCR vector)
	Computes a negated (opposite) vector. More...

void	Negate ()
	Negate a vector in place. More...

double	Normalize (DPoint3dCR vector)
	Normalizes (scales) a vector to length 1. More...

double	ScaleToLength (DPoint3dCR vector, double length)
	Scales a vector to specified length. More...

double	ScaleToLength (double length)
	Scales a vector to a specified length, and returns the prior length. More...

double	Normalize ()
	Replaces a vector by a unit vector in the same direction, and returns the original length. More...

bool	IsParallelTo (DPoint3dCR point2) const
	Tests if two vectors are parallel. More...

bool	IsPerpendicularTo (DPoint3dCR point2) const
	Tests if two vectors are perpendicular. More...

bool	SafeDivide (DPoint3dCR vector, double denominator)
	Try to divide each component of a vector by a scalar. More...

double	TripleProduct (DPoint3dCR point2, DPoint3dCR point3) const
	Computes the triple product of three vectors. More...

void	Subtract (DPoint3dCR point2)
	Subtract two points or vectors, and return the result in place of the first. More...

void	DifferenceOf (DPoint3dCR point1, DPoint3dCR point2)
	Subtract coordinates of two vectors or points. More...

void	SumOf (DPoint3dCR origin, DPoint3dCR vector, double scale)
	Adds an origin and a scaled vector. More...

void	SumOf (DPoint3dCR origin, DPoint3dCR point1, double scale1, DPoint3dCR point2, double scale2)
	Adds an origin and two scaled vectors. More...

void	SumOf (DPoint3dCR origin, DPoint3dCR point1, double scale1, DPoint3dCR point2, double scale2, DPoint3dCR point3, double scale3)
	Adds an origin and three scaled vectors. More...

void	SumOf (DPoint3dCR point1, double a1, DPoint3dCR point2, double a2)
	Componentwise linear combination. More...

void	SumOf (DPoint3dCR point1, double a1, DPoint3dCR point2, double a2, DPoint3dCR point3, double a3)
	Componentwise linear combination. More...

void	Add (DPoint3dCR vector)
	Adds a vector to a pointer or vector, returns the result in place. More...

void	SumOf (DPoint3dCR point1, DPoint3dCR point2)
	Compute the sum of two points or vectors. More...

bool	AlmostEqual (DPoint3d const &dataB) const
	test if two points are equal. More...

bool	AlmostEqualXY (DPoint3d const &dataB) const
	test if two points are equal. More...

bool	AlmostEqual (DPoint3d const &dataB, double abstol) const
	test if two points are equal. More...

bool	AlmostEqualXY (DPoint3d const &dataB, double abstol) const
	test if two points are equal. More...

Static Public Member Functions
static DVec3d	FromArray (const double *pXyz)
	Returns a DVec3d with 3 component array of double. More...

static DVec3d	UnitX ()
	unit X vector More...

static DVec3d	UnitY ()
	unit Y vector More...

static DVec3d	UnitZ ()
	unit Z vector More...

static DVec3d	From (double ax, double ay, double az=0.0)
	Returns a DVec3d with given x,y, and z components of a vector. More...

static DVec3d	From (DPoint3dCR point)
	Returns a DVec3d from a point (treating the point as a vector from its origin). More...

static DVec3d	From (DVec2dCR vector)
	Returns a DVec3d from a 2d vector (with 0 z) More...

static DVec3d	FromStartEnd (DPoint3dCR start, DPoint3dCR end)
	Returns the unnormalized (full length) DVec3d between start and end. More...

static DVec3d	FromStartEnd (TransformCR start, DPoint3dCR target)
	Returns the unnormalized (full length) DVec3d from the frame origin to the target point. More...

static DVec3d	FromStartEndNormalize (DPoint3dCR start, DPoint3dCR end)
	Returns a vector from start towards end, normalized if nonzero. More...

static DVec3d	FromCCWPerpendicularXY (DVec3d source)
	return a vector same length as source but rotate 90 degrees CCW More...

static DVec3d	FromRotate90Towards (DVec3dCR source, DVec3dCR target)
	return a vector same length as source but rotate 90 degrees towards target More...

static DVec3d	FromRotate90Around (DVec3dCR source, DVec3dCR axis)
	return a vector same length as source but rotate 90 degrees around axis More...

static DVec3d	FromXYAngleAndMagnitude (double theta, double magnitude)
	Returns a DVec3d from given angle and distance in xy plane. More...

static DVec3d	FromTranslation (TransformCR source)
	return the translation xyz as a DVec3d (which you can pass as a DPoint3d where needed.) More...

static DVec3d	FromMatrixColumn (TransformCR transform, int i)
	return a (cyclically indexed) column of the matrix part of a transform. More...

static DVec3d	FromMatrixRow (TransformCR transform, int i)
	return a (cyclically indexed) row of the matrix part of a transform. More...

static DVec3d	FromColumn (RotMatrixCR matrix, int i)
	return a (cyclically indexed) column of the matrix. More...

static DVec3d	FromRow (RotMatrixCR matrix, int i)
	return a (cyclically indexed) row of the matrix. More...

static DVec3d	FromStartEnd (DPoint4dCR start, DPoint4dCR end)
	Returns DVec3d pseudo difference start.wend - end.wstart. More...

static DVec3d	FromCrossProduct (DVec3dCR vector0, DVec3dCR vector1)
	return the cross product of vectors More...

static DVec3d	FromCrossProductToPoints (DPoint3dCR origin, DPoint3dCR target1, DPoint3dCR target2)
	Returns the (vector) cross product of two vectors. More...

static DVec3d	FromNormalizedCrossProductToPoints (DPoint3dCR origin, DPoint3dCR target1, DPoint3dCR target2)
	Returns the (normalized vector) cross product of two vectors. More...

static DVec3d	FromNormalizedCrossProduct (DVec3dCR vector0, DVec3dCR vector1)
	return the normalized cross product of vectors More...

static DVec3d	FromCrossProduct (double x0, double y0, double z0, double x1, double y1, double z1)
	return the cross product of vectors presented as explicit components More...

static DVec3d	FromMatrixColumnCrossProduct (TransformCR transform, int i, int j)
	return the cross product of vectors found in columns of (the matrix part of) a transform. More...

static DVec3d	FromColumnCrossProduct (RotMatrixCR matrix, int i, int j)
	return the cross product of vectors found in columns a matrix More...

static ValidatedDVec3d	FromUnitPerpendicularXY (DVec3dCR vector)
	Compute a unit vector perpendicular to the xy parts of given vector. More...

static DVec3d	FromInterpolate (DVec3dCR vector0, double fraction, DVec3dCR vector1)
	Returns an interpolated vector. More...

static DVec3d	FromInterpolateBilinear (DVec3dCR vector00, DVec3dCR vector10, DVec3dCR vector01, DVec3dCR vector11, double u, double v)
	Returns a bilinear interpolation from corners (00)(10)(01)(11) More...

static DVec3d	FromSumOf (DVec3dCR vector0, DVec3dCR vector1)
	Returns a sum of vectors. More...

static DVec3d	FromSumOf (DVec3dCR vector0, double scale0, DVec3dCR vector1, double scale1)
	Returns a linear combination of vectors. More...

static DVec3d	FromSumOf (DVec3dCR vector0, double scale0, DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2)
	Returns a linear combination of vectors. More...

static DVec3d	FromSumOf (DVec3dCR vector0, DVec3dCR vector1, double scale1)
	Returns a linear combination of vectors. More...

static DVec3d	FromSumOf (DVec3dCR vector0, DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2)
	Returns a linear combination of vectors. More...

static DVec3d	FromSumOf (DVec3dCR vector0, DVec3dCR vector1, double scale1, DVec3dCR vector2, double scale2, DVec3dCR vector3, double scale3)
	Returns a linear combination of vectors. More...

static DVec3d	FromScale (DVec3dCR vector, double scale)
	Returns a scalar multiple of a DVec3d. More...

static DVec3d	FromWeightedDifferenceOf (DPoint4dCR hPoint1, DPoint3dCR point2)
	Promote point2 to homogeneous and form (point1 point2.w - point2 point1.w). More...

Static Public Member Functions inherited from DPoint3d
static DPoint3d	From (double x, double y, double z=0.0)
	Return a DPoint3d with given xyz. More...

static DPoint3d	From (DPoint2dCR xy)
	Return a DPoint3d with given xy, z = 0;. More...

static DPoint3d	FromZero ()
	Return a DPoint3d with xyz = 0. More...

static DPoint3d	FromOne ()
	Return a DPoint3d with xyz = 1. More...

static DPoint3d	FromArray (const double *pXyz)
	Simple initialization from 3 coordinates in array. More...

static void	AddToArray (DPoint3dP points, int n, DPoint3dCR delta)
	Add translation to all points. More...

static void	MultiplyArrayByScales (DPoint3dP pDest, DPoint3dCP pSource, double *pScales, int n)
	Multiply each point in an array by its corresponding scale factor. More...

static void	DivideArrayByScales (DPoint3dP pDest, DPoint3dCP pSource, double *pScales, int n)
	Divide each point in an array by its corresponding scale factor. More...

static DPoint3d	FromProduct (TransformCR transform, double x, double y, double z)
	return product of transform times point given as components. More...

static DPoint3d	FromProduct (TransformCR transform, DPoint3dCR point)
	return product of transform times point More...

static DPoint3d	FromInterpolate (DPoint3dCR pointA, double fraction, DPoint3dCR pointB)
	interpolate between points. More...

static DPoint3d	FromInterpolateBilinear (DPoint3dCR point00, DPoint3dCR point10, DPoint3dCR point01, DPoint3dCR point11, double u, double v)
	Returns a bilinear interpolation from corners (00)(10)(01)(11) More...

static DPoint3d	FromSumOf (DPoint3dCR origin, DPoint3dCR vector)
	Add a point and a vector. More...

static DPoint3d	FromSumOf (DPoint3dCR origin, DPoint3dCR vector, double scaleFactor)
	Add scaled vector from origin. More...

static DPoint3d	FromSumOf (DPoint3dCR origin, DPoint3dCR point0, double scaleFactor0, DPoint3dCR point1, double scaleFactor1)
	Add scaled vectors from an origin. More...

static DPoint3d	FromSumOf (DPoint3dCR origin, DPoint3dCR point0, double scaleFactor0, DPoint3dCR point1, double scaleFactor1, DPoint3dCR point2, double scaleFactor2)
	Add scaled vectors from origin. More...

static DPoint3d	FromScale (DPoint3d point, double scale)
	Returns a scalar multiple of a DPoint3d. More...

static DPoint3d	FromSumOf (DPoint3dCR point0, double scale0, DPoint3dCR point1, double scale1)
	Returns a linear combination of points. More...

static DPoint3d	FromSumOf (DPoint3dCR point0, double scale0, DPoint3dCR point1, double scale1, DPoint3dCR point2, double scale2)
	Returns a linear combination of points. More...

static DPoint3d	FromProduct (DPoint3dCR point, RotMatrixCR matrix, double x, double y, double z)
	Return {point + matrix * (x,y,z)}. More...

static DPoint3d	FromProduct (DPoint3dCR point, RotMatrixCR matrix, DVec3dCR vector)
	Return {point + matrix * vector}. More...

static bool	AlmostEqual (bvector< DPoint3d > const &left, bvector< DPoint3d > const &right, double tolerance=0.0)
	apply AlmostEqual test to corresponding points More...

static bool	AlmostEqualXY (bvector< DPoint3d > const &left, bvector< DPoint3d > const &right, double tolerance=0.0)
	apply AlmostEqualXY test to corresponding points More...

Additional Inherited Members
Public Attributes inherited from DPoint3d
double	x
	x coordinate More...

double	y
	y coordinate More...

double	z
	z coordinate More...

Detailed Description

Vector with x,y,z components.

>DVec3d Usage Summary
Method Invocation	Remarks
W.crossProduct(U,V)	W = U cross V
W.crossProductToPoints (A,B,C)	W = (B-A) cross (C-A)
W.normalizedCrossProduct (U,V)	W = normalize (U cross V)
W.sizedCrossProduct (U,V, a)	W = a * normalize (U cross V)
W.geometricMeanCrossProduct (U,V)	W = sqrt (mag(U) * mag(V)) * normalize(U cross V)
a = crossProductXY (U,V)	a = U cross V (xy only, scalar result)
a = tripleProduct (U,V,W)va = U cross V dot W
a = tripleProductToPoints (A,B,C,D)	a = (B-A) cross (C-A) dot (D-A)
a = dotProduct (U,V)	a = U dot V
a = dotProductXY (U,V)	a = U dot V, using only x and y parts
U.getTriad (&Vx ,&Vy, &Vz)	return Vz=U, Vx,Vy perpenidcular, same length
U.getNormalizedTriad (&Vx, &Vy, &Vz)	return Vz=normalize(U), Vx,Vy perpenidcular, all unit
U.normalizedDifference (A,B)	U = normalize (A-B)
a = U.angleTo (V)	Spatial angle from U to V. Range 0 to PI.
a = U.angleToXY (V)
a = U.smallerUnorientedAngleTo (V)
a = U.smallerUnorientedAngleToXY (V)
a = U.signedAngleTo (V, upVector)
U.isVectorInSmallerSector(V,W)	Test if U appears in the smaller sector between V and W, when viewed with V cross W as up vector.
U.isVectorInCCWSector (V,W, upVector))	Test if U appears in the sector from V counterclockwise towards W when viewed with upVector
U.planarAngleTo (V,W)	Anlge after projection to plane with nomral W.
U.rotateXY (V, theta)	rotate around z axis
U.rotateXY (theta)	Inplace rotation around z
U.unitPerpendicularXY (V)
U.scale (V,a)	U = V * a
U.scale (a)	U *= a
U.negate ()	U *= -1
U.negate(V)	U = - V
U.normalize (V)	U = V / V.magnitude ()
U.normalize ()	U /= U.magnitude ()
U.scaleToLength (V,a)	U = V * a / V.magnitude ()
U.isParallelTo(V)
U.isPerpendicularTo(V)
if (U.safeDivide) ... (V,a)	Divde by a, but return false if a is too close to zero
U.zero()	Sets all components to 0
U.one()	Sets all components to 1
U.init (x,y,z)
U.init (A)	copy from point
U.setComponent (a, i)	Set individual components
a = U.getComponent (i)	Get individual component
U.getComponents (U, &a, &b, &c)	Get all components as separate doubles
U.sumOf (V,W)	U = V + W
U.add (V)	U += V
U.subtract (V)	U -= V
U.sumOf (V, W, a)	U = V + a W
U.interpolate (V, a, W)	U = (1-a)V * a W
W.sumOf (U, V1, a1, V2, a2)	W = U + a1 * V1 + a2 * V2 + a3 * V3
W.sumOf (U, V1, a1, V2, a2, V2, a3)	W = U + a1 * V1 + a2 * V2 + a3 * V3
W.differenceOf (U,V)	W = U - V
W.differenceOf (A,B)	W = A - B
a = U.distance (V)	W = (V-U).magnitude ()
a = U.distanceSquared(V)
a = U.distanceXY (V)
a = U.distanceSquaredXY (V)
a = U.magnitudeSquared ()
a = U.magnitudeSquaredXY ()
a = U.magnitude ()
a = U.magnitudeXY ()
a = U.maxAbs()
U.isEqual(V)	Bitwise equality
U.isEqual (V, tol)	componentwise absolute difference
U.multiply (M,V)	U = M * V<
mutliplyArray (U[], M, V[], count)
U.multiply (M, x, y, z)	U = M * <x,y,z>
U.multiplyTranspose (M, V)	U = M^ * V
U.multiplyTranspose (M, x, y, z)	U = M' * <x,y,z>
Dvec3d::multiplyTransposeArray (U[], M, V[], count)

Member Function Documentation

void Add ( DVec3dCR vector )

Adds a vector to a pointer or vector, returns the result in place.

Parameters

[in] vector The vector to add.

bool AlmostEqual ( DVec3d const & dataB ) const

test if two points are equal.

Uses library "small angle" as both absolute and relative tolerance. points are equal if squared distance between is less than (squared abstol) plus (squared relTol) * sum of cmponent squares

Parameters

[in] dataB second DVec3d

Returns: true if within tolerance.

bool AngleAndAxisOfRotationFromVectorToVector	(	DVec3dCR	target,
		DVec3dR	axis,
		double &	radians
	)		const

Compute an axis and angle to rotate from the instance vector to a target.

Parameters

[out]	target	direction that the instance is to rotate towards.
[out]	axis	returned axis of rotation
[out]	radians	returned rotation angle

Returns: true if both vectors are nonzero.

double AngleFromPerpendicular ( DVec3dCR vector2 ) const

Returns the angle that two vectors deviate from being perpendicular.

double AngleTo ( DVec3dCR vector2 ) const

Returns the angle between two vectors.

This angle is between 0 and pi. Rotating the first vector by this angle around the cross product between the vectors aligns it with the second vector.

Parameters

[in] vector2 The second vector

Returns: The angle between the vectors.

double AngleToXY ( DVec3dCR vector2 ) const

Returns the angle from Vector1 to Vector2 using only xy parts.

This angle is between -pi and +pi.

Parameters

[in] vector2 The second vector

Returns: The angle between vectors.

void CrossProduct	(	DVec3dCR	vector1,
		DVec3dCR	vector2
	)

Returns the (vector) cross product of two vectors.

Parameters

[in]	vector1	The first vector
[in]	vector2	The second vector

void CrossProduct	(	DVec3dCR	vector1,
		DPoint3dCR	point2
	)

Returns the (vector) cross product of two vectors.

Parameters

[in]	vector1	The first vector
[in]	point2	The second vector, given as a point. The point's xyz are understood to be a vector from the origin.

void CrossProduct	(	DPoint3dCR	point1,
		DVec3dCR	vector2
	)

Returns the (vector) cross product of two vectors.

Parameters

[in]	point1	The first vector, givenn as a point. The point's xyz are understood to be a vector from the origin.
[in]	vector2	The second vector.

double CrossProductMagnitude ( DVec3dCR other ) const

Compute the cross product with other and return is magnitude (but the cross product is not returned)

Parameters

[in] other second vector of cross product

void CrossProductToPoints	(	DPoint3dCR	origin,
		DPoint3dCR	target1,
		DPoint3dCR	target2
	)

Sets the instance to the (vector) cross product of two vectors.

The vectors are computed from the Origin to Target1 and Target2.

Parameters

[in]	origin	The base point for computing vectors.
[in]	target1	The target point for the first vector.
[in]	target2	The target point for the second vector.

double CrossProductXY ( DVec3dCR vector2 ) const

Return the (scalar) cross product of the xy parts of two vectors.

Parameters

[in] vector2 The second vector

Returns: The 2d cross product.

void DifferenceOf	(	DVec3dCR	vector1,
		DVec3dCR	vector2
	)

Subtract coordinates of two vectors.

(Compute Vector1 - Vector2)

Parameters

[in]	vector1	The first vector
[in]	vector2	The second (subtracted) vector

void DifferenceOf	(	DPoint3dCR	target,
		DPoint3dCR	base
	)

Subtract coordinates of two points.

(Compute Point1 - Point2)

Parameters

[in]	target	The target point
[in]	base	The base point

double Distance ( DVec3dCR vector2 ) const

Computes the (cartesian) distance between two vectors.

Parameters

[in] vector2 The second vector

Returns: The distance between vector.

double DistanceSquared ( DVec3dCR vector2 ) const

Computes the squared distance between two vectors.

Parameters

[in] vector2 The second vector.

Returns: The squared distance between the vectors.

double DistanceSquaredXY ( DVec3dCR vector2 ) const

Computes the squared distance between two vectors, using only the xy parts.

Parameters

[in] vector2 The second vector

Returns: The squared distance between the XY projections of the two vectors. (i.e. any z difference is ignored)

double DistanceXY ( DVec3dCR vector2 ) const

Computes the distance between two vectors, using only x and y components.

Parameters

[in] vector2 The second vector

Returns: The distance between the XY projections of the two vectors. (i.e. any z difference is ignored)

double DotProduct ( DVec3dCR vector2 ) const

Returns the (scalar) dot product of two vectors.

Parameters

[in] vector2 The second vector

Returns: The dot product of the two vectors

double DotProduct	(	double	ax,
		double	ay,
		double	az
	)		const

Computes the dot product of one vector given as a vector structure and another given as xyz components.

Parameters

[in]	ax	The x component of second vector.
[in]	ay	The y component of second vector.
[in]	az	The z component of second vector.

Returns: The dot product of the vector with a vector with the given components

double DotProduct ( DPoint3dCR point2 ) const

Returns the (scalar) dot product of two vectors.

Parameters

[in] point2 The second vector, given as point. The point's xyz are understood to be a vector from the origin.

Returns: dot product of the two vectors.

double DotProductColumn	(	RotMatrixCR	matrix,
		int	index
	)		const

Returns the (scalar) dot product of this vector and a column of a matrix.

Parameters

[in]	matrix
[in]	index	column index.

Returns: The dot product of the two vectors

double DotProductMatrixColumn	(	TransformCR	matrix,
		int	index
	)		const

Returns the (scalar) dot product of this vector and a column of the matrix part of the transform.

Parameters

[in]	matrix
[in]	index	column index.

Returns: The dot product of the two vectors

double DotProductMatrixRow	(	TransformCR	matrix,
		int	index
	)		const

Returns the (scalar) dot product of this vector and a row of the matrix part of the transform.

Parameters

[in]	matrix
[in]	index	row index.

Returns: The dot product of the two vectors

double DotProductRow	(	RotMatrixCR	matrix,
		int	index
	)		const

Returns the (scalar) dot product of this vector and a row of a matrix.

Parameters

[in]	matrix
[in]	index	row index.

Returns: The dot product of the two vectors

double DotProductXY ( DVec3dCR vector2 ) const

Returns the (scalar) dot product of xy parts of two vectors.

Parameters

[in] vector2 The second vector

Returns: The dot product of the xy parts of the two vectors

static DVec3d From	(	double	ax,
		double	ay,
		double	az = `0.0`
	)

static

Returns a DVec3d with given x,y, and z components of a vector.

Parameters

[in]	ax	The x component.
[in]	ay	The y component.
[in]	az	The z component.

Referenced by DVec3d::UnitX(), DVec3d::UnitY(), and DVec3d::UnitZ().

static DVec3d From ( DPoint3dCR point )

static

Returns a DVec3d from a point (treating the point as a vector from its origin).

Parameters

[in] point the point.

static DVec3d From ( DVec2dCR vector )

static

Returns a DVec3d from a 2d vector (with 0 z)

Parameters

[in] vector the 2d vector

static DVec3d FromArray ( const double * pXyz )

static

Returns a DVec3d with 3 component array of double.

Parameters

[in] pXyz x, y, z components

static DVec3d FromCCWPerpendicularXY ( DVec3d source )

static

return a vector same length as source but rotate 90 degrees CCW

static DVec3d FromColumn	(	RotMatrixCR	matrix,
		int	i
	)

static

return a (cyclically indexed) column of the matrix.

Parameters

[in]	matrix	source
[in]	i	column index

static DVec3d FromColumnCrossProduct	(	RotMatrixCR	matrix,
		int	i,
		int	j
	)

static

return the cross product of vectors found in columns a matrix

Parameters

[in]	matrix	source transform
[in]	i	first column index
[in]	j	second column index

static DVec3d FromCrossProduct	(	DVec3dCR	vector0,
		DVec3dCR	vector1
	)

static

return the cross product of vectors

Parameters

[in]	vector0	first vector
[in]	vector1	second vector

static DVec3d FromCrossProduct	(	double	x0,
		double	y0,
		double	z0,
		double	x1,
		double	y1,
		double	z1
	)

static

return the cross product of vectors presented as explicit components

Parameters

[in]	x0	vector0 x component
[in]	y0	vector0 y component
[in]	z0	vector0 z component
[in]	x1	vector1 x component
[in]	y1	vector1 y component
[in]	z1	vector1 z component

static DVec3d FromCrossProductToPoints	(	DPoint3dCR	origin,
		DPoint3dCR	target1,
		DPoint3dCR	target2
	)

static

Returns the (vector) cross product of two vectors.

The vectors are computed from the Origin to Target1 and Target2.

Parameters

[in]	origin	The base point for computing vectors.
[in]	target1	The target point for the first vector.
[in]	target2	The target point for the second vector.

static DVec3d FromInterpolate	(	DVec3dCR	vector0,
		double	fraction,
		DVec3dCR	vector1
	)

static

Returns an interpolated vector.

Parameters

[in]	vector0	vector at fraction 0
[in]	fraction	fraction from interpolation.
[in]	vector1	vector at fraction 1

static DVec3d FromInterpolateBilinear	(	DVec3dCR	vector00,
		DVec3dCR	vector10,
		DVec3dCR	vector01,
		DVec3dCR	vector11,
		double	u,
		double	v
	)

static

Returns a bilinear interpolation from corners (00)(10)(01)(11)

Parameters

[in]	vector00	vector at (0,0)
[in]	vector10	vector at (1,0)
[in]	vector01	vector at (0,1)
[in]	vector11	vector at (1,1)
[in]	u	interpolation fraction for edges (vector00,vector10) and (vector01,vector11)
[in]	v	interpolation fraction for edges (vector00,vector10) and (vector10,vector11)

static DVec3d FromMatrixColumn	(	TransformCR	transform,
		int	i
	)

static

return a (cyclically indexed) column of the matrix part of a transform.

Parameters

[in]	transform	source transform
[in]	i	column index

static DVec3d FromMatrixColumnCrossProduct	(	TransformCR	transform,
		int	i,
		int	j
	)

static

return the cross product of vectors found in columns of (the matrix part of) a transform.

Parameters

[in]	transform	source transform
[in]	i	first column index
[in]	j	second column index

static DVec3d FromMatrixRow	(	TransformCR	transform,
		int	i
	)

static

return a (cyclically indexed) row of the matrix part of a transform.

Parameters

[in]	transform	source transform
[in]	i	row index

static DVec3d FromNormalizedCrossProduct	(	DVec3dCR	vector0,
		DVec3dCR	vector1
	)

static

return the normalized cross product of vectors

Parameters

[in]	vector0	first vector
[in]	vector1	second vector

static DVec3d FromNormalizedCrossProductToPoints	(	DPoint3dCR	origin,
		DPoint3dCR	target1,
		DPoint3dCR	target2
	)

static

Returns the (normalized vector) cross product of two vectors.

The vectors are computed from the Origin to Target1 and Target2. If the cross product is zero, a zero vector is returned.

Parameters

[in]	origin	The base point for computing vectors.
[in]	target1	The target point for the first vector.
[in]	target2	The target point for the second vector.

static DVec3d FromRotate90Around	(	DVec3dCR	source,
		DVec3dCR	axis
	)

static

return a vector same length as source but rotate 90 degrees around axis

static DVec3d FromRotate90Towards	(	DVec3dCR	source,
		DVec3dCR	target
	)

static

return a vector same length as source but rotate 90 degrees towards target

static DVec3d FromRow	(	RotMatrixCR	matrix,
		int	i
	)

static

return a (cyclically indexed) row of the matrix.

Parameters

[in]	matrix	source
[in]	i	row index

static DVec3d FromScale	(	DVec3dCR	vector,
		double	scale
	)

static

Returns a scalar multiple of a DVec3d.

Parameters

[in]	vector	input vector
[in]	scale	scale factor

static DVec3d FromStartEnd	(	DPoint3dCR	start,
		DPoint3dCR	end
	)

static

Returns the unnormalized (full length) DVec3d between start and end.

Parameters

[in]	start	start point
[in]	end	end point

static DVec3d FromStartEnd	(	TransformCR	start,
		DPoint3dCR	target
	)

static

Returns the unnormalized (full length) DVec3d from the frame origin to the target point.

Parameters

[in]	start	start point
[in]	target	end point

static DVec3d FromStartEnd	(	DPoint4dCR	start,
		DPoint4dCR	end
	)

static

Returns DVec3d pseudo difference start.w*end - end.w*start.

Parameters

[in]	start	start point
[in]	end	end point

static DVec3d FromStartEndNormalize	(	DPoint3dCR	start,
		DPoint3dCR	end
	)

static

Returns a vector from start towards end, normalized if nonzero.

Parameters

[in]	start	start point
[in]	end	end point

static DVec3d FromSumOf	(	DVec3dCR	vector0,
		DVec3dCR	vector1
	)

static

Returns a sum of vectors.

Parameters

[in]	vector0	first vector
[in]	vector1	second vector

static DVec3d FromSumOf	(	DVec3dCR	vector0,
		double	scale0,
		DVec3dCR	vector1,
		double	scale1
	)

static

Returns a linear combination of vectors.

Parameters

[in]	vector0	first vector
[in]	scale0	first scale
[in]	vector1	second vector
[in]	scale1	second scale

static DVec3d FromSumOf	(	DVec3dCR	vector0,
		double	scale0,
		DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2
	)

static

Returns a linear combination of vectors.

Parameters

[in]	vector0	first vector
[in]	scale0	first scale
[in]	vector1	second vector
[in]	scale1	second scale
[in]	vector2	third vector
[in]	scale2	third scale

static DVec3d FromSumOf	(	DVec3dCR	vector0,
		DVec3dCR	vector1,
		double	scale1
	)

static

Returns a linear combination of vectors.

Parameters

[in]	vector0	first vector
[in]	vector1	second vector
[in]	scale1	second scale

static DVec3d FromSumOf	(	DVec3dCR	vector0,
		DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2
	)

static

Returns a linear combination of vectors.

Parameters

[in]	vector0	first vector
[in]	vector1	second vector
[in]	scale1	second scale
[in]	vector2	third vector
[in]	scale2	third scale

static DVec3d FromSumOf	(	DVec3dCR	vector0,
		DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2,
		DVec3dCR	vector3,
		double	scale3
	)

static

Returns a linear combination of vectors.

Parameters

[in]	vector0	first vector
[in]	vector1	second vector
[in]	scale1	scale for vector1
[in]	vector2	third vector
[in]	scale2	scale fro vector2
[in]	vector3	fourth vector
[in]	scale3	scale for vector3

static DVec3d FromTranslation ( TransformCR source )

static

return the translation xyz as a DVec3d (which you can pass as a DPoint3d where needed.)

Parameters

[in] source source transform

static ValidatedDVec3d FromUnitPerpendicularXY ( DVec3dCR vector )

static

Compute a unit vector perpendicular to the xy parts of given vector.

Parameters

[in] vector The source vector

Returns: perpendicular vector, marked invalid if unable to divide.

static DVec3d FromWeightedDifferenceOf	(	DPoint4dCR	hPoint1,
		DPoint3dCR	point2
	)

static

Promote point2 to homogeneous and form (point1 *point2.w - point2 * point1.w).

The weight term vanishes. Copy the xyz parts back as a vector.

Parameters

[in]	hPoint1	The first homogeneous point
[in]	point2	The second point.

static DVec3d FromXYAngleAndMagnitude	(	double	theta,
		double	magnitude
	)

static

Returns a DVec3d from given angle and distance in xy plane.

Z part is set to zero.

Parameters

[in]	theta	Angle from X axis to the vector, in the xy plane.
[in]	magnitude	Vector magnitude

double GeometricMeanCrossProduct	(	DVec3dCR	vector1,
		DVec3dCR	vector2
	)

Computes the cross product of two vectors and scales it to the geometric mean of the lengths of the two vectors.

This is useful because it has the direction of the cross product (i.e. normal to the plane of the two vectors) and a size in between the two vectors.

Parameters

[in]	vector1	The first vector
[in]	vector2	The second vector

Returns: The The length of unscaled cross product.

double GetComponent ( int index ) const

Gets a single component of a vector.

If the index is out of range 0,1,2, it is interpreted cyclically.

Parameters

[in] index Indicates which component is accessed. The values are 0=x, 1=y, 2=z. Other values are treated cyclically.

Returns: The specified component of the vector.

void GetComponents	(	double &	xCoord,
		double &	yCoord,
		double &	zCoord
	)		const

Copies x,y,z components from a vector to individual variables.

Parameters

[out]	xCoord	x component
[out]	yCoord	y component
[out]	zCoord	z component

bool GetNormalizedTriad	(	DVec3dR	xAxis,
		DVec3dR	yAxis,
		DVec3dR	zAxis
	)		const

Sets three vectors so that they are mutually perpendicular unit vectors with the third (Z) vector in the direction of the given axis vector.

If the given axis vector contains only zeros, a (0,0,1) vector is used instead.

Parameters

[out]	xAxis	unit x direction vector
[out]	yAxis	unit y direction vector
[out]	zAxis	unit z direction vector

Returns: true unless given vector has zero length.

bool GetPerpendicularParts	(	DVec3dCR	hypotenuse,
		double &	fraction,
		DVec3dR	parallelPart,
		DVec3dR	perpendicularPart
	)		const

Decompose hypotenuse into a vector parallel to the instance and a vector perpendicular to the instance.

Parameters

[in]	hypotenuse	vector to decompose
[out]	fraction	position where hypotenuse projects onto the instance.
[out]	parallelPart	vector parallel to the instance
[out]	perpendicularPart	vector perpendicular to the instance

bool GetTriad	(	DVec3dR	xAxis,
		DVec3dR	yAxis,
		DVec3dR	zAxis
	)		const

Sets three vectors so that they are mutually perpendicular, the third (Z) vector is identical to the given axis vector, and all have the same length.

If the given axis vector contains only zeros, a (0,0,1) vector is used instead.

Parameters

[out]	xAxis	x direction of the coordinate system
[out]	yAxis	y direction of the coordinate system
[out]	zAxis	z direction of the coordinate system

Returns: true unless given vector is z zero vector.

void Init	(	double	ax,
		double	ay,
		double	az
	)

Sets the x,y, and z components of a vector.

Parameters

[in]	ax	The x component.
[in]	ay	The y component.
[in]	az	The z component.

void Init	(	double	ax,
		double	ay
	)

Sets the x, and y components of a vector.

Sets z to zero.

Parameters

[in]	ax	The x component.
[in]	ax	The x component.
[in]	ay	The y component

void Init ( DPoint3dCR point )

Initialize a vector from a point (treating the point as a vector from its origin).

Parameters

[in] point the point.

void InitFromArray ( double const * pXyz )

Copies doubles from a 3 component array to the x,y, and z components of a DVec3d.

Parameters

[in] pXyz x, y, z components

void InitFromColumn	(	RotMatrixCR	matrix,
		int	col
	)

Extracts a column of a matrix.

Parameters

[in]	matrix	The matrix.
[in]	col	column index. Columns are numbered 0,1,2. Others indices are reduced cyclically.

void InitFromRow	(	RotMatrixCR	matrix,
		int	row
	)

Extracts a row of a matrix.

Parameters

[in]	matrix	The matrix.
[in]	row	row index. Rows are numbered 0,1,2. Others indices are reduced cyclically.

void InitFromXYAngleAndMagnitude	(	double	theta,
		double	magnitude
	)

Sets a vector from given angle and distance in xy plane.

Z part is set to zero.

Parameters

[in]	theta	Angle from X axis to the vector, in the xy plane.
[in]	magnitude	Vector magnitude

void Interpolate	(	DVec3dCR	vector0,
		double	fractionParameter,
		DVec3dCR	vector1
	)

Computes a vector whose position is given by a fractional argument and two vectors.

Parameters

[in]	vector0	The vector corresponding to fractionParameter of 0.
[in]	fractionParameter	The fractional parametric coordinate. 0.0 is the start of the segment, 1.0 is the end, 0.5 is middle
[in]	vector1	The vector corresponding to fractionParameter of 1.

bool IsEqual ( DVec3dCR vector2 ) const

Test for exact equality between all components of two vectors.

Parameters

[in] vector2 The second vector

Returns: true if the vectors are identical.

bool IsEqual	(	DVec3dCR	vector2,
		double	tolerance
	)		const

Test if the x, y, and z components of two vectors are equal within tolerance.

Tests are done independently using the absolute value of each component differences (i.e. not the magnitude or sum of squared differences)

Parameters

[in]	vector2	The second vector.
[in]	tolerance	The tolerance.

Returns: true if all components are within given tolerance of each other.

bool IsParallelTo ( DVec3dCR vector2 ) const

Tests if two vectors are parallel (opposites are considered parallel!)

Parameters

[in] vector2 The second vector

Returns: true if the vectors are parallel within tolerance

bool IsPerpendicularTo ( DVec3dCR vector2 ) const

Tests if two vectors are perpendicular.

Parameters

[in] vector2 The second vector

Returns: true if vectors are perpendicular within tolerance

bool IsPositiveParallelTo ( DVec3dCR vector2 ) const

Tests if two vectors are parallel and have positive dot product (opposites are NOT considered parallel)

Parameters

[in] vector2 The second vector

Returns: true if the vectors are parallel within tolerance

bool IsVectorInCCWSector	(	DVec3dCR	vector0,
		DVec3dCR	vector1,
		DVec3dCR	upVector
	)		const

Test if the test vector vector is "between" vector0 and vector1, with CCW direction resolved by an up vector.

The cross product of vector0 and vector1 is considered the positive plane normal if its dot product with the up vector is positive.

Parameters

[in]	vector0	The boundary vector.
[in]	vector1	The boundary vector.
[in]	upVector	The out of plane vector.

Returns: true if test vector is within the angle.

bool IsVectorInCCWXYSector	(	DVec3dCR	vector0,
		DVec3dCR	vector1
	)		const

Test if the instance vector vector is "between" vector0 and vector1, with CCW direction using only xy parts.

Parameters

[in]	vector0	The boundary vector.
[in]	vector1	The boundary vector.

Returns: true if test vector is within the angle.

bool IsVectorInSmallerSector	(	DVec3dCR	vector0,
		DVec3dCR	vector1
	)		const

Test a vector is "between" vector0 and vector1.

If the vectors are coplanar and vector0 is neither parallel nor antiparallel to vector1, betweenness has the expected meaning: there are two angles between vector0 and vector1; one is less than 180; the test vector is tested to see if it is in the smaller angle. If the vectors are not coplanar, the test is based on the projection of the test vector into the plane of the other two vectors.

Zero testing is untoleranced, and is biased to all parallel conditions "false". That is, if any pair of the input vectors is parallel or antiparallel, the mathematical answer is false. Floating point tolerances will cause "nearby" cases to be unpredictable. It is assumed that if the caller considers the "parallel" cases important they will be checked explicitly.

Parameters

[in]	vector0	The first boundary vector.
[in]	vector1	The second boundary vector.

Returns: true if the test vector is within the angle.

bool IsZero ( )

checks if the vector has all zeros

double Magnitude ( ) const

Computes the magnitude of a vector.

Returns: The length of the vector

double MagnitudeSquared ( ) const

Computes the squared magnitude of a vector.

Returns: The squared magnitude of the vector.

double MagnitudeSquaredXY ( ) const

Computes the squared magnitude of the xy part of a vector.

Returns: The squared magnitude of the xy parts of the given vector.

double MagnitudeXY ( ) const

Computes the magnitude of the xy part of a vector.

Returns: The magnitude of the xy parts of the given vector.

double MaxAbs ( ) const

Finds the largest absolute value among the components of a vector.

Returns: The largest absolute value among vector coordinates.

void Multiply	(	RotMatrixCR	matrix,
		DVec3dCR	vector
	)

Returns the product of a matrix times a vector.

Parameters

[in]	matrix	The matrix.
[in]	vector	The known vector.

void Multiply	(	RotMatrixCR	matrix,
		double	x,
		double	y,
		double	z
	)

Returns the product of a matrix times a vector, with the vector given as separate components.

Parameters

[in]	matrix	The matrix to apply
[in]	x	The x component of input vector
[in]	y	The y component of input vector
[in]	z	The z component of input vector

void MultiplyTranspose	(	RotMatrixCR	matrix,
		DVec3dCR	vector
	)

Returns the product of a matrix transpose times a vector.

Parameters

[in]	matrix	The the matrix.
[in]	vector	The known vector.

void MultiplyTranspose	(	RotMatrixCR	matrix,
		double	x,
		double	y,
		double	z
	)

Returns the product P = [x,y,z]*M where M is the input matrix and P is the product vector.

Parameters

[in]	matrix	The matrix to apply
[in]	x	The x component
[in]	y	The y component
[in]	z	The z component

void Negate ( DVec3dCR vector )

Computes a negated (opposite) vector.

Parameters

[in] vector The vector to be negated.

void Negate ( )

Negate a vector in place.

double Normalize ( DVec3dCR vector )

Normalizes (scales) a vector to length 1.

Remarks: In the 0-length error case, the vector is set to (1,0,0) in the legacy microstation style.

Parameters

[in] vector The vector to be normalized.

Returns: The length prior to normalization

double Normalize ( )

Replaces a vector by a unit vector in the same direction, and returns the original length.

Remarks: In the 0-length error case, the vector is set to (1,0,0) in the legacy microstation style.

Returns: The length prior to normalization

double NormalizedCrossProduct	(	DVec3dCR	vector1,
		DVec3dCR	vector2
	)

Compute the normalized cross product of two vectors and return the length of the unnormalized cross product.

Parameters

[in]	vector1	The first vector
[in]	vector2	The second vector

Returns: The length of the original (prenormalization) cross product vector

double NormalizedDifference	(	DPoint3dCR	target,
		DPoint3dCR	origin
	)

Computes a unit vector in the direction of the difference of the vectors or vectors (Second parameter vector is subtracted from the first parameter vector, exactly as in the subtract function.)

Remarks: In the 0-length error case, the vector is set to (1,0,0) in the legacy microstation style.

Parameters

[in]	target	The target point.
[in]	origin	The origin point.

Returns: The length of original difference vector.

double PlanarAngleTo	(	DVec3dCR	vector2,
		DVec3dCR	planeNormal
	)		const

Computes the signed angle between the projection of two vectors onto a plane with given normal.

Parameters

[in]	vector2	The second vector
[in]	planeNormal	The plane normal vector

Returns: The angle in plane

bool ProjectToPlane	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		DPoint2dR	uv
	)		const

Find the projection of the instance vector to a plane defined by two vectors.

Parameters

[in]	vectorU	u-direction vector of the plane.
[in]	vectorV	v-direction vector of the plane.
[out]	uv	fractional coordinates on vectors.

Returns: false if plane vectors are not independent. In this case the method attempts to project to the longer plane vector, and sets the other fraction to 0. If that fails uv is 00.

bool ProjectToVector	(	DVec3dCR	targetVector,
		double &	fraction
	)		const

Find the fraction at which the instance projects to a vector.

Parameters

[in]	targetVector	target vector.
[out]	fraction	projection fraction

Returns: false if targetVector has zero length. In this case the fraction is zero.

void RotateXY	(	DVec3dCR	vector,
		double	theta
	)

Rotate a vector around the z axis.

Parameters

[in]	vector	vector to rotate.
[in]	theta	The rotation angle.

void RotateXY ( double theta )

Rotate a vector around the z axis.

Parameters

[in] theta The rotation angle.

bool SafeDivide	(	DVec3dCR	vector,
		double	denominator
	)

Try to divide each component of a vector by a scalar.

If the denominator near zero compared to any numerator component, return the original vector.

Parameters

[in]	vector	The initial vector.
[in]	denominator	The divisor.

Returns: true if division is numerically safe.

double SafeOneOverMagnitudeSquared ( double defaultValue ) const

Returns 1 over the squared magnitude, or caller supplied default if squared magnitude is too small.

void Scale	(	DVec3dCR	vector,
		double	scale
	)

Multiplies a vector by a scale factor.

Parameters

[in]	vector	The vector to be scaled.
[in]	scale	The scale factor.

void Scale ( double scale )

Multiplies a vector (in place) by a scale factor.

Parameters

[in] scale The scale

double ScaleToLength	(	DVec3dCR	vector,
		double	length
	)

Scales a vector to specified length.

Remarks: In the 0-length error case, the vector is set to (1,0,0) in the legacy microstation style.

Parameters

[in]	vector	The original vector.
[in]	length	The requested length.

Returns: The length prior to scaling.

double ScaleToLength ( double length )

Scales a vector to a specified length, and returns the prior length.

Remarks: In the 0-length error case, the vector is set to (1,0,0) in the legacy microstation style.

Parameters

[in] length The requested length

Returns: The length prior to scaling.

void SetComponent	(	double	a,
		int	index
	)

Set one of three components (x,y,z) of the vector.

Parameters

[in]	a	The component value.
[in]	index	Selects the the axis: 0=x, 1=y, 2=z, others cyclic.

double SignedAngleTo	(	DVec3dCR	vector2,
		DVec3dCR	orientationVector
	)		const

Computes the signed angle from one vector to another, in the plane of the two vectors.

Initial computation using only the two vectors yields two possible angles depending on which side of the plane of the vectors is viewed. To choose which side to view, go on the side whose normal has a positive dot product with the orientation vector. This angle can be between -pi and +pi.

Parameters

[in]	vector2	The second vector
[in]	orientationVector	The vector used to determine orientation.

Returns: The signed angle

double SizedCrossProduct	(	DVec3dCR	vector1,
		DVec3dCR	vector2,
		double	productLength
	)

Computes the cross product of the two parameter vectors and scales it to a given length.

The scaled vector is stored as the product vector, and the length of the original cross product vector is returned.

Parameters

[in]	vector1	The first vector
[in]	vector2	The second vector
[in]	productLength	The Desired length

Returns: The The length of unscaled cross product.

double SmallerUnorientedAngleTo ( DVec3dCR vector2 ) const

Returns the angle between two vectors, choosing the smaller of the two possible angles when both the vectors and their negations are considered.

This angle is between 0 and pi/2.

Parameters

[in] vector2 The second vector

Returns: The angle between the vectors.

double SmallerUnorientedAngleToXY ( DVec3dCR vector2 ) const

Returns the angle between two vectors, considering both the vectors and their negations and choosing the smaller.

This angle is between 0 and pi/2.

Parameters

[in] vector2 The second vector

Returns: The angle between vectors.

void Subtract ( DVec3dCR vector2 )

Subtract two vectors, and return the result in place of the first.

Parameters

[in] vector2 The vector to subtract.

void SumOf	(	DVec3dCR	vector1,
		DVec3dCR	vector2
	)

Compute the sum of two vectors.

Parameters

[in]	vector1	The the first vector
[in]	vector2	The second vector

void SumOf	(	DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2
	)

Compute the sum of two vectors with scale factors.

Parameters

[in]	vector1	The the first vector
[in]	scale1	first scale
[in]	vector2	The second vector
[in]	scale2	second scale

void SumOf	(	DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2,
		DVec3dCR	vector3,
		double	scale3
	)

Compute the sum of three vectors with scale factors.

Parameters

[in]	vector1	The the first vector
[in]	scale1	first scale
[in]	vector2	The second vector
[in]	scale2	second scale
[in]	vector3	The third vector
[in]	scale3	third scale

void SumOf	(	DVec3dCR	origin,
		DVec3dCR	vector,
		double	scale
	)

Adds an origin and a scaled vector.

Parameters

[in]	origin	Origin for the sum.
[in]	vector	The vector to be added.
[in]	scale	The scale factor.

void SumOf	(	DVec3dCR	origin,
		DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2
	)

Adds an origin and two scaled vectors.

Parameters

[in]	origin	The origin.
[in]	vector1	The first direction vector
[in]	scale1	The first scale factor
[in]	vector2	The second direction vector
[in]	scale2	The second scale factor

void SumOf	(	DVec3dCR	origin,
		DVec3dCR	vector1,
		double	scale1,
		DVec3dCR	vector2,
		double	scale2,
		DVec3dCR	vector3,
		double	scale3
	)

Adds an origin and three scaled vectors.

Parameters

[in]	origin	The origin.
[in]	vector1	The first direction vector
[in]	scale1	The first scale factor
[in]	vector2	The second direction vector
[in]	scale2	The second scale factor
[in]	vector3	The third direction vector
[in]	scale3	The third scale factor

double TripleProduct	(	DVec3dCR	vector2,
		DVec3dCR	vector3
	)		const

Computes the triple product of three vectors.

The following are equivalent definitions of the triple product of three vectors V1, V2, and V3:

(V1 cross V2) dot V3
V1 dot (V2 cross V3)
The determinant of the 3x3 matrix with the three vectors as its columns.
The determinant of the 3x3 matrix with the three vectors as its rows.
The (signed)volume of the parallelepiped whose 4 vertices are at the origin and at the ends of the 3 vectors placed at the origin.

Parameters

[in]	vector2	The second vector.
[in]	vector3	The third vector.

Returns: The triple product

bool TryNormalize	(	DVec3dCR	source,
		double &	magnitude
	)

initialize this vector to unit vector in the direction of source.

Remarks: In the 0-length error case, the vector is set to (1,0,0) in the legacy microstation style.

Parameters

[in]	source	The vector to be normalized.
[out]	magnitude	The orignal magnitude of the source vector;

Returns: true if the other vector length is large enough for DoubleOps::SafeDivide to compute 1/length.

bool UnitPerpendicularXY ( DVec3dCR vector )

Compute a unit vector perpendicular to the xy parts of given vector.

Parameters

[in] vector The source vector

Returns: true if the input vector has nonzero length

static DVec3d UnitX ( )

static

unit X vector

References DVec3d::From().

static DVec3d UnitY ( )

static

unit Y vector

References DVec3d::From().

static DVec3d UnitZ ( )

static

unit Z vector

References DVec3d::From().

ValidatedDouble ValidatedFractionOfProjection	(	DVec3dCR	vectorToProject,
		double	defaultValue = `0.0`
	)		const

Returns fraction at which other projects onto this, in ValidatedDouble which records if the division was safe.

ValidatedDVec3d ValidatedNormalize ( ) const

return a (possibly invalid) unit vector in the direction of the calling instance.

void WeightedDifferenceCrossProduct	(	DPoint4dCR	basePoint,
		DPoint4dCR	target1,
		DPoint4dCR	target2
	)

Form the cross product of the weighted differences from base poitn to two targets.

Parameters

[in]	basePoint	The common base point (second point for differences)
[in]	target1	The first target point.
[in]	target2	The second target point.

void WeightedDifferenceOf	(	DPoint4dCR	hPoint1,
		DPoint4dCR	hPoint2
	)

Scale each (homogeneous) point by the other's weight and subtract, i.e.

form (point1 * point2.w - point2 * point1.w). The weight term vanishes. Copy the xyz parts back as a vector.

Parameters

[in]	hPoint1	The first homogeneous point
[in]	hPoint2	The second homogeneous point.

void XyzOf ( DPoint4dCR hPoint )

Sets the x,y, and z components of a DVec3d structure from the corresponding parts of a DPoint4d.

Weight part of DPoint4d is not used.

Parameters

[in] hPoint The homogeneous point

The documentation for this struct was generated from the following file:

dvec3d.h

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