SimTK::Geodesic Class Reference

This class stores a geodesic curve after it has been determined. More...

Public Member Functions
	Geodesic ()
	Construct an empty geodesic. More...
int	getNumPoints () const
const Array_< Transform > &	getFrenetFrames () const
	Frenet frame of geodesic at arc length s: More...
Array_< Transform > &	updFrenetFrames ()
void	addFrenetFrame (const Transform &Kf)
Array_< Real > &	updArcLengths ()
const Array_< Real > &	getArcLengths () const
void	addArcLength (Real s)
Array_< Real > &	updCurvatures ()
const Array_< Real > &	getCurvatures () const
void	addCurvature (Real kappa)
Array_< Vec2 > &	updDirectionalSensitivityPtoQ ()
const Array_< Vec2 > &	getDirectionalSensitivityPtoQ () const
void	addDirectionalSensitivityPtoQ (const Vec2 &jP)
Array_< Vec2 > &	updDirectionalSensitivityQtoP ()
const Array_< Vec2 > &	getDirectionalSensitivityQtoP () const
void	addDirectionalSensitivityQtoP (const Vec2 &jQ)
Array_< Vec2 > &	updPositionalSensitivityPtoQ ()
const Array_< Vec2 > &	getPositionalSensitivityPtoQ () const
void	addPositionalSensitivityPtoQ (const Vec2 &jtP)
Array_< Vec2 > &	updPositionalSensitivityQtoP ()
const Array_< Vec2 > &	getPositionalSensitivityQtoP () const
void	addPositionalSensitivityQtoP (const Vec2 &jtQ)
void	setTorsionAtP (Real tauP)
void	setTorsionAtQ (Real tauQ)
void	setBinormalCurvatureAtP (Real muP)
void	setBinormalCurvatureAtQ (Real muQ)
Real	getLength () const
	Return the total arc length of this geodesic curve. More...
Real	calcLengthDot (const Vec3 &xdotP, const Vec3 &xdotQ) const
	Given the time derivatives of the surface coordinates of P and Q, calculate the rate of change of length of this geodesic. More...
const Vec3 &	getPointP () const
	Return the location on the surface of the geodesic's starting point P, measured and expressed in the surface frame S. More...
const Vec3 &	getPointQ () const
	Return the location on the surface of the geodesic's ending point Q, measured and expressed in the surface frame S. More...
const UnitVec3 &	getNormalP () const
	Return the surface outward unit normal at P, which is aligned with the curve normal there but will have opposite sign if the geodesic curvature is positive at P. More...
const UnitVec3 &	getNormalQ () const
	Return the surface outward unit normal at Q, which is aligned with the curve normal there but will have opposite sign if the geodesic curvature is positive at Q. More...
const UnitVec3 &	getTangentP () const
	Return the unit tangent to the geodesic at P, pointing in the direction of increasing arc length parameters (i.e., towards Q). More...
const UnitVec3 &	getTangentQ () const
	Return the unit tangent to the geodesic at Q, pointing in the direction of increasing arc length parameters (i.e., away from P). More...
const UnitVec3 &	getBinormalP () const
	Return the unit binormal vector to the curve at P, defined as bP = tP X nP. More...
const UnitVec3 &	getBinormalQ () const
	Return the unit binormal vector to the curve at Q, defined as bQ = tQ X nQ. More...
Real	getCurvatureP () const
	Return the geodesic normal curvature at P, defined to be positive when the surface is convex in the curve tangent direction at P, negative if the surface is concave in that direction. More...
Real	getCurvatureQ () const
	Return the geodesic normal curvature at Q, defined to be positive when the surface is convex in the curve tangent direction at Q, negative if the surface is concave in that direction. More...
Real	getTorsionP () const
	Return the geodesic torsion at P, that is, the twisting of the Frenet frame as you move along the tangent towards Q. More...
Real	getTorsionQ () const
	Return the geodesic torsion at Q, that is, the twisting of the Frenet frame as you move along the tangent away from P, that is, off the end of the geodesic. More...
Real	getBinormalCurvatureP () const
	Return the surface curvature in the binormal direction at P; don't confuse this with the geodesic torsion at P. More...
Real	getBinormalCurvatureQ () const
	Return the surface curvature in the binormal direction at Q; don't confuse this with the geodesic torsion at Q. More...
Real	getJacobiP () const
	Return jP, the Jacobi field term giving the sensitivity of the P end of the geodesic to changes in tangent direction at the Q end, assuming the geodesic length is fixed. More...
Real	getJacobiQ () const
	Return jQ, the Jacobi field term giving the sensitivity of the Q end of the geodesic to changes in tangent direction at the P end, assuming the geodesic length is fixed. More...
Real	getJacobiPDot () const
	Return the derivative of jP with respect to s, the arc length of the geodesic (which always runs from P to Q). More...
Real	getJacobiQDot () const
	Return the derivative of jQ with respect to s, the arc length of the geodesic. More...
Real	getJacobiTransP () const
Real	getJacobiTransQ () const
Real	getJacobiTransPDot () const
Real	getJacobiTransQDot () const
void	clear ()
	Clear the data in this geodesic, returning it to its default-constructed state, although memory remains allocated. More...
void	setIsConvex (bool isConvex)
void	setIsShortest (bool isShortest)
void	setInitialStepSizeHint (Real sz)
void	setAchievedAccuracy (Real acc)
bool	isConvex () const
bool	isShortest () const
Real	getInitialStepSizeHint () const
Real	getAchievedAccuracy () const
void	dump (std::ostream &o) const

Detailed Description

This class stores a geodesic curve after it has been determined.

The curve is represented by a discrete set of Frenet frames along its arc length, with each frame providing a point on the curve, the tangent along the curve there, surface normal, and binormal. The number of points is determined by the accuracy to which the geodesic was calculated and the complexity of the surface. For analytical geodesics, we'll sample the curve to generate enough points for visualization but the accuracy will be machine precision. The first point is at arclength s=0, the last is at the actual length of the geodesic. We call the first point P and the last point Q, and the geodesic arc length increases from P to Q, with the tangent always pointing in the direction of increasing arc length.

Constructor & Destructor Documentation

Geodesic()

SimTK::Geodesic::Geodesic ( )

inline

Construct an empty geodesic.

Member Function Documentation

getNumPoints()

int SimTK::Geodesic::getNumPoints ( ) const

inline

getFrenetFrames()

const Array_<Transform>& SimTK::Geodesic::getFrenetFrames ( ) const

inline

Frenet frame of geodesic at arc length s:

• origin: point on geodesic at s
• z axis: outward surface (unit) normal n at s
• y axis: unit tangent t at s in direction of increasing arc length
• x axis: unit binormal at s: b=t X n (x=y X z)

Note that this convention is different from that of a curve, because our normal vector always points outwards from the surface.

updFrenetFrames()

Array_<Transform>& SimTK::Geodesic::updFrenetFrames ( )

inline

addFrenetFrame()

void SimTK::Geodesic::addFrenetFrame ( const Transform &  Kf )

inline

updArcLengths()

Array_<Real>& SimTK::Geodesic::updArcLengths ( )

inline

getArcLengths()

const Array_<Real>& SimTK::Geodesic::getArcLengths ( ) const

inline

addArcLength()

void SimTK::Geodesic::addArcLength ( Real  s )

inline

updCurvatures()

Array_<Real>& SimTK::Geodesic::updCurvatures ( )

inline

getCurvatures()

const Array_<Real>& SimTK::Geodesic::getCurvatures ( ) const

inline

addCurvature()

void SimTK::Geodesic::addCurvature ( Real  kappa )

inline

updDirectionalSensitivityPtoQ()

Array_<Vec2>& SimTK::Geodesic::updDirectionalSensitivityPtoQ ( )

inline

getDirectionalSensitivityPtoQ()

const Array_<Vec2>& SimTK::Geodesic::getDirectionalSensitivityPtoQ ( ) const

inline

addDirectionalSensitivityPtoQ()

void SimTK::Geodesic::addDirectionalSensitivityPtoQ ( const Vec2 &  jP )

inline

updDirectionalSensitivityQtoP()

Array_<Vec2>& SimTK::Geodesic::updDirectionalSensitivityQtoP ( )

inline

getDirectionalSensitivityQtoP()

const Array_<Vec2>& SimTK::Geodesic::getDirectionalSensitivityQtoP ( ) const

inline

addDirectionalSensitivityQtoP()

void SimTK::Geodesic::addDirectionalSensitivityQtoP ( const Vec2 &  jQ )

inline

updPositionalSensitivityPtoQ()

Array_<Vec2>& SimTK::Geodesic::updPositionalSensitivityPtoQ ( )

inline

getPositionalSensitivityPtoQ()

const Array_<Vec2>& SimTK::Geodesic::getPositionalSensitivityPtoQ ( ) const

inline

addPositionalSensitivityPtoQ()

void SimTK::Geodesic::addPositionalSensitivityPtoQ ( const Vec2 &  jtP )

inline

updPositionalSensitivityQtoP()

Array_<Vec2>& SimTK::Geodesic::updPositionalSensitivityQtoP ( )

inline

getPositionalSensitivityQtoP()

const Array_<Vec2>& SimTK::Geodesic::getPositionalSensitivityQtoP ( ) const

inline

addPositionalSensitivityQtoP()

void SimTK::Geodesic::addPositionalSensitivityQtoP ( const Vec2 &  jtQ )

inline

setTorsionAtP()

void SimTK::Geodesic::setTorsionAtP ( Real  tauP )

inline

setTorsionAtQ()

void SimTK::Geodesic::setTorsionAtQ ( Real  tauQ )

inline

setBinormalCurvatureAtP()

void SimTK::Geodesic::setBinormalCurvatureAtP ( Real  muP )

inline

setBinormalCurvatureAtQ()

void SimTK::Geodesic::setBinormalCurvatureAtQ ( Real  muQ )

inline

getLength()

Real SimTK::Geodesic::getLength ( ) const

inline

Return the total arc length of this geodesic curve.

Will return zero if no curve has been calculated.

calcLengthDot()

Real SimTK::Geodesic::calcLengthDot ( const Vec3 &  xdotP, const Vec3 &  xdotQ  ) const

inline

Given the time derivatives of the surface coordinates of P and Q, calculate the rate of change of length of this geodesic.

Only the components of xdotP and xdotQ along the curve tangent directions can affect its length; moves in the normal or binormal direction leave the length unchanged.

getPointP()

const Vec3& SimTK::Geodesic::getPointP ( ) const

inline

Return the location on the surface of the geodesic's starting point P, measured and expressed in the surface frame S.

getPointQ()

const Vec3& SimTK::Geodesic::getPointQ ( ) const

inline

Return the location on the surface of the geodesic's ending point Q, measured and expressed in the surface frame S.

getNormalP()

const UnitVec3& SimTK::Geodesic::getNormalP ( ) const

inline

Return the surface outward unit normal at P, which is aligned with the curve normal there but will have opposite sign if the geodesic curvature is positive at P.

getNormalQ()

const UnitVec3& SimTK::Geodesic::getNormalQ ( ) const

inline

Return the surface outward unit normal at Q, which is aligned with the curve normal there but will have opposite sign if the geodesic curvature is positive at Q.

getTangentP()

const UnitVec3& SimTK::Geodesic::getTangentP ( ) const

inline

Return the unit tangent to the geodesic at P, pointing in the direction of increasing arc length parameters (i.e., towards Q).

getTangentQ()

const UnitVec3& SimTK::Geodesic::getTangentQ ( ) const

inline

Return the unit tangent to the geodesic at Q, pointing in the direction of increasing arc length parameters (i.e., away from P).

getBinormalP()

const UnitVec3& SimTK::Geodesic::getBinormalP ( ) const

inline

Return the unit binormal vector to the curve at P, defined as bP = tP X nP.

getBinormalQ()

const UnitVec3& SimTK::Geodesic::getBinormalQ ( ) const

inline

Return the unit binormal vector to the curve at Q, defined as bQ = tQ X nQ.

getCurvatureP()

Real SimTK::Geodesic::getCurvatureP ( ) const

inline

Return the geodesic normal curvature at P, defined to be positive when the surface is convex in the curve tangent direction at P, negative if the surface is concave in that direction.

This is a scalar kappaP=-dot(DtP/ds,nP). Note that the geodesic curvature is the same as the surface curvature in the curve tangent direction.

getCurvatureQ()

Real SimTK::Geodesic::getCurvatureQ ( ) const

inline

Return the geodesic normal curvature at Q, defined to be positive when the surface is convex in the curve tangent direction at Q, negative if the surface is concave in that direction.

This is a scalar kappaQ=-dot(DtQ/ds,nQ). Note that the geodesic curvature is the same as the surface curvature in the curve tangent direction, and remember that the curve tangent at Q points away from P, that is, off the end of the geodesic.

getTorsionP()

Real SimTK::Geodesic::getTorsionP ( ) const

inline

Return the geodesic torsion at P, that is, the twisting of the Frenet frame as you move along the tangent towards Q.

The sign follows the right hand rule with your thumb directed along the tangent. This is a scalar tauP=-dot(DbP/Ds,nP).

getTorsionQ()

Real SimTK::Geodesic::getTorsionQ ( ) const

inline

Return the geodesic torsion at Q, that is, the twisting of the Frenet frame as you move along the tangent away from P, that is, off the end of the geodesic.

The sign follows the right hand rule with your thumb directed along the tangent. This is a scalar tauQ=-dot(DbQ/Ds,nQ).

getBinormalCurvatureP()

Real SimTK::Geodesic::getBinormalCurvatureP ( ) const

inline

Return the surface curvature in the binormal direction at P; don't confuse this with the geodesic torsion at P.

Surface curvature in a direction is a property of the surface independent of any curve.

getBinormalCurvatureQ()

Real SimTK::Geodesic::getBinormalCurvatureQ ( ) const

inline

Return the surface curvature in the binormal direction at Q; don't confuse this with the geodesic torsion at Q.

Surface curvature in a direction is a property of the surface independent of any curve.

getJacobiP()

Real SimTK::Geodesic::getJacobiP ( ) const

inline

Return jP, the Jacobi field term giving the sensitivity of the P end of the geodesic to changes in tangent direction at the Q end, assuming the geodesic length is fixed.

This is a scalar jP=dot(DP/DthetaQ,bP) where thetaQ is a right-hand-rule rotation about the normal nQ at Q. Caution: jP and jQ have opposite signs.

getJacobiQ()

Real SimTK::Geodesic::getJacobiQ ( ) const

inline

Return jQ, the Jacobi field term giving the sensitivity of the Q end of the geodesic to changes in tangent direction at the P end, assuming the geodesic length is fixed.

This is a scalar jQ=-dot(DQ/DthetaP,bQ) where thetaP is a right-hand-rule rotation about the normal nP at P. Note that jQ has the opposite sign from jP.

getJacobiPDot()

Real SimTK::Geodesic::getJacobiPDot ( ) const

inline

Return the derivative of jP with respect to s, the arc length of the geodesic (which always runs from P to Q).

That is jPDot = d/ds jP.

getJacobiQDot()

Real SimTK::Geodesic::getJacobiQDot ( ) const

inline

Return the derivative of jQ with respect to s, the arc length of the geodesic.

That is, jQDot = d/ds jQ.

getJacobiTransP()

Real SimTK::Geodesic::getJacobiTransP ( ) const

inline

getJacobiTransQ()

Real SimTK::Geodesic::getJacobiTransQ ( ) const

inline

getJacobiTransPDot()

Real SimTK::Geodesic::getJacobiTransPDot ( ) const

inline

getJacobiTransQDot()

Real SimTK::Geodesic::getJacobiTransQDot ( ) const

inline

clear()

void SimTK::Geodesic::clear ( )

inline

Clear the data in this geodesic, returning it to its default-constructed state, although memory remains allocated.

setIsConvex()

void SimTK::Geodesic::setIsConvex ( bool  isConvex )

inline

setIsShortest()

void SimTK::Geodesic::setIsShortest ( bool  isShortest )

inline

setInitialStepSizeHint()

void SimTK::Geodesic::setInitialStepSizeHint ( Real  sz )

inline

setAchievedAccuracy()

void SimTK::Geodesic::setAchievedAccuracy ( Real  acc )

inline

isConvex()

bool SimTK::Geodesic::isConvex ( ) const

inline

isShortest()

bool SimTK::Geodesic::isShortest ( ) const

inline

getInitialStepSizeHint()

Real SimTK::Geodesic::getInitialStepSizeHint ( ) const

inline

getAchievedAccuracy()

Real SimTK::Geodesic::getAchievedAccuracy ( ) const

inline

dump()

void SimTK::Geodesic::dump

(

std::ostream &

o

)

const

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

• Geodesic.h