Utils/Algebra3D.hpp File Reference

Utility functions for 3D vector operations and affine transformations. More...

#include <cmath>
#include <cstring>

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Namespaces
namespace	Utils::Algebra3D
	Utility functions for 3D vector operations and affine transformations.
Enumerations
enum	{ Utils::Algebra3D::Trans_NR_ENTRIES = 3, Utils::Algebra3D::Rot_NR_ENTRIES = 9, Utils::Algebra3D::TransRot_NR_ENTRIES = 12 }
	Numbers of entries for arrays representing 3D quantities. More...
Functions
Vector operations
static double	Utils::Algebra3D::VecDotProduct (const double v1[], const double v2[])
	Computes the dot product of vectors v1 and v2.
static void	Utils::Algebra3D::VecCrossProduct (const double v1[], const double v2[], double v[])
	Computes the cross product of vectors v1 and v2 and stores the result in v.
static double	Utils::Algebra3D::VecNormSquared (const double v[])
	Computes the norm squared of the vector v.
static double	Utils::Algebra3D::VecNorm (const double v[])
	Computes the norm of the vector v.
static void	Utils::Algebra3D::VecUnit (const double v[], double vunit[])
	Computes the unit vector of v and stores the result in vunit.
static void	Utils::Algebra3D::VecScale (const double v[], const double s, double vscaled[])
	Scales the vector v by the scalar s and stores the result in vscaled.
static void	Utils::Algebra3D::VecAdd (const double v1[], const double v2[], double v[])
	Adds vectors v1 and v2 and stores the result in v.
static void	Utils::Algebra3D::VecSubtract (const double v1[], const double v2[], double v[])
	Subtracts v2 from v1 and stores the result in v.
Identities for translations and rotations
static void	Utils::Algebra3D::IdentityAsTrans (double T[])
	T is set to the identity for translations.
static void	Utils::Algebra3D::IdentityAsRot (double R[])
	R is set to the identity for rotations.
static void	Utils::Algebra3D::IdentityAsTransRot (double TR[])
	TR is set to the identity for translations and rotations.
Determine if specified transformation represents the identity transformation
static bool	Utils::Algebra3D::IdentitySameAsTrans (const double T[])
	Determine if T is the same as the identity translation.
static bool	Utils::Algebra3D::IdentitySameAsRot (const double R[])
	Determine if R is the same as the identity rotation.
static bool	Utils::Algebra3D::IdentitySameAsTransRot (const double TR[])
	Determine if TR is the same as the identity translation and rotation.
Copy transformations
static void	Utils::Algebra3D::TransAsTrans (const double x, const double y, const double z, double Tresult[])
	Set Tresult to the translation given by (x, y, z).
static void	Utils::Algebra3D::TransAsTrans (const double T[], double Tresult[])
	Copy the translation T to Tresult.
static void	Utils::Algebra3D::RotAsRot (const double R[], double Rresult[])
	Copy the rotation R to Rresult.
static void	Utils::Algebra3D::TransRotAsTransRot (const double TR[], double TRresult[])
	Copy the transformation TR to TRresult.
Determine if specified transformations are the same
static bool	Utils::Algebra3D::TransSameAsTrans (const double Ta[], const double Tb[])
	Determine if the translations Ta and Tb are the same.
static bool	Utils::Algebra3D::RotSameAsRot (const double Ra[], const double Rb[])
	Determine if the rotations Ra and Rb are the same.
static bool	Utils::Algebra3D::TransRotSameAsTransRot (const double TRa[], const double TRb[])
	Determine if the transformations TRa and TRb are the same.
Apply transformation to point
static void	Utils::Algebra3D::TransMultPoint (const double T[], const double p[], double pnew[])
	Apply translation T to point p and store result in pnew.
static void	Utils::Algebra3D::TransMultInvPoint (const double T[], const double p[], double pnew[])
	Apply translation T to the inverse of point p and store result in pnew.
static void	Utils::Algebra3D::InvTransMultPoint (const double T[], const double p[], double pnew[])
	Apply the inverse of the translation T to point p and store result in pnew.
static void	Utils::Algebra3D::InvTransMultInvPoint (const double T[], const double p[], double pnew[])
	Apply the inverse translation T to the inverse of point p and store result in pnew.
static void	Utils::Algebra3D::RotMultPoint (const double R[], const double p[], double pnew[])
	Apply rotation R to point p and store result in pnew.
static void	Utils::Algebra3D::RotMultInvPoint (const double R[], const double p[], double pnew[])
	Apply rotation R to the inverse of point p and store result in pnew.
static void	Utils::Algebra3D::InvRotMultPoint (const double R[], const double p[], double pnew[])
	Apply the inverse of rotation R to point p and store result in pnew.
static void	Utils::Algebra3D::InvRotMultInvPoint (const double R[], const double p[], double pnew[])
	Apply the inverse or rotation R to the inverse of point p and store result in pnew.
static void	Utils::Algebra3D::TransRotMultPoint (const double TR[], const double p[], double pnew[])
	Apply transformation TR to point p and store result in pnew.
static void	Utils::Algebra3D::TransRotMultInvPoint (const double TR[], const double p[], double pnew[])
	Apply transformation TR to the inverse of point p and store result in pnew.
static void	Utils::Algebra3D::InvTransRotMultPoint (const double TR[], const double p[], double pnew[])
	Apply the inverse of the transformation TR to point p and store result in pnew.
static void	Utils::Algebra3D::InvTransRotMultInvPoint (const double TR[], const double p[], double pnew[])
	Apply the inverse of the transformation TR to the inverse of point p and store result in pnew.
Inverse transformations
static void	Utils::Algebra3D::InvTransAsTrans (const double T[], double Tresult[])
	Set Tresult as the inverse of the translation T.
static void	Utils::Algebra3D::InvRotAsRot (const double R[], double Rresult[])
	Set Rresult as the inverse of the rotation R.
static void	Utils::Algebra3D::InvTransRotAsTransRot (const double TR[], double TRresult[])
	Set TRresult as the inverse of the transformation TR.
Combine transformations
static void	Utils::Algebra3D::TransMultTransAsTrans (const double Ta[], const double Tb[], double T[])
	T <-- Ta + Tb.
static void	Utils::Algebra3D::TransMultRotAsTransRot (const double T[], const double R[], double TR[])
	TR <-- T * R.
static void	Utils::Algebra3D::TransMultTransRotAsTransRot (const double T[], const double TR[], double TRresult[])
	TRresult <-- T * TR.
void	Utils::Algebra3D::RotMultRotAsRot (const double Ra[], const double Rb[], double R[])
	R <-- Ra * Rb.
static void	Utils::Algebra3D::RotMultTransAsTransRot (const double R[], const double T[], double TR[])
	TR <-- R * T.
static void	Utils::Algebra3D::RotMultTransRotAsTransRot (const double R[], const double TR[], double TRresult[])
	TRresult <-- R * TR.
static void	Utils::Algebra3D::TransRotMultTransAsTransRot (const double TR[], const double T[], double TRresult[])
	TRresult <-- TR * T.
static void	Utils::Algebra3D::TransRotMultRotAsTransRot (const double TR[], const double R[], double TRresult[])
	TRresult <-- TR * R.
static void	Utils::Algebra3D::TransRotMultTransRotAsTransRot (const double TRa[], const double TRb[], double TR[])
	TRresult <-- TRa * TRb.
Validity of transformation
static bool	Utils::Algebra3D::RotIsValid (const double R[])
	Determine if R represent a valid rotation.
Variables
const double	Utils::Constants::EPSILON = ldexp(1.0, -36)
	Defines epsilon constant.

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Detailed Description

Utility functions for 3D vector operations and affine transformations.

Author:

Erion Plaku

Definition in file Algebra3D.hpp.