Documentation

animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real > Class Template Reference

#include <odeImplicitSolver.h>

Inheritance diagram for animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >:

animal::OdeSolver< t_Positions, t_Vector, t_Real > animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex > animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings > animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 > animal::MassSpringEngine< X3DTK::MFFloat, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFInt32, X3DTK::MFVec3f, float > animal::MassSpringEngine< Inv_Masses, Velocities, SpringStiffness, IndexedSprings, Points, Real > X3DTK::X3D::AnimalEngineNode< AMassSpringEngine > X3DTK::X3D::MassSpringNode List of all members.

Detailed Description

template<class t_Positions, class t_Vector, class t_Real>
class animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >

Abstract class for implicit ODE solver.

Solves an ODE over a time step. Several explicit integration schemes inherited from parent class OdeSolver are available, along with implicit Euler (method number 4).

This class models a simplified system where damping forces are proportional with elastic forces, applying a uniform factor defined by the damping ratio.

To derive your own ode solver from this class, you must overload the following pure virtual methods:

In this class, it is assumed that matrix df/dx is updated by method computeForce( Vector&, const Positions&, const Vector&).

The solution of the equation system uses a simplified version of damping: the damping matrix is considered strictly proportional with the stiffness matrix. The factor is set using method setDampingRatio( Real ).

Author:
François Faure, Oct. 2003

Definition at line 33 of file odeImplicitSolver.h.

Public Types

typedef t_Positions Positions
 Vector of positions.

typedef t_Vector Vector
 velocities, forces, accelerations

typedef t_Real Real
 time and other scalar values

typedef container_traits<
Vector >::value_type 		Vec

Public Member Functions

 OdeImplicitSolver ()
 Constructor.

virtual void solveODE (Positions &pos, Vector &vel, Real dt)
 Update positions and velocities by solving an ODE over time step dt.

void setDampingRatio (Real d)
 Set the damping ratio used in the equation system.

Real dampingRatio () const
 damping ratio used in the equation system

void setMaxCGiterations (int n)
 Set the maximum number of CG iterations.

int maxCGiterations () const
 Maximum number of CG iterations.

void setSmallDenominatorThreshold (Real s)
 Set the other CG stop criterion.

Real smallDenominatorThreshold () const
 CG stop criterion.

virtual void applyForces (Vector &a, const Vector &f)=0
 Compute the acceleration of the particles when given forces are applied.

virtual void computeAccelerations (Vector &a, const Positions &p, const Vector &v)=0
 Compute the acceleration of the particles for given positions and velocities.

virtual void computeAccelerationsAndStiffness (Vector &a, const Positions &p, const Vector &v)=0
 Compute the acceleration of the particles for given positions and velocities, and updates the gradient matrix.

virtual void v_eq_h_dfdx_x (Vector &v, Real h, const Vector &x)=0
 Compute $ v = h [df/dx] x $.

virtual void v_peq_h_dfdx_x (Vector &v, Real h, const Vector &x)=0
 Compute $ v += h [df/dx] x $.

void compute_implicit_euler_step (Positions &dpos, Vector &dvel, const Positions &pos, const Vector &vel, Real dt)
 Compute position and velocity updates using implicit Euler time integration.

void implicit_euler (Positions &pos, Vector &vel, Real dt)
 Update positions and velocities using implicit Euler time integration.

void multImplicitMatrix (Vector &y, const Vector &x, Real h)
 Compute $ y = (I-h(h+r)M^{-1}G) x $.


Public Attributes

Real _dampingRatio
 damping ratio used in the equation system

int _maxIter
 Maximum number of CG iterations.

Real _smallDenominatorThreshold
 the other CG stop criterion


Static Public Attributes

const int IMPLICIT_EULER = 5
 Symbol of implicit Euler integration.

Member Typedef Documentation

template<class t_Positions, class t_Vector, class t_Real>
typedef t_Positions animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::Positions
 

Vector of positions.

Reimplemented from animal::OdeSolver< t_Positions, t_Vector, t_Real >.

Reimplemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Definition at line 37 of file odeImplicitSolver.h.

template<class t_Positions, class t_Vector, class t_Real>
typedef t_Real animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::Real
 

time and other scalar values

Reimplemented from animal::OdeSolver< t_Positions, t_Vector, t_Real >.

Reimplemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Definition at line 39 of file odeImplicitSolver.h.

template<class t_Positions, class t_Vector, class t_Real>
typedef container_traits<Vector>::value_type animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::Vec
 

Reimplemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Definition at line 84 of file odeImplicitSolver.h.

template<class t_Positions, class t_Vector, class t_Real>
typedef t_Vector animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::Vector
 

velocities, forces, accelerations

Reimplemented from animal::OdeSolver< t_Positions, t_Vector, t_Real >.

Reimplemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Definition at line 38 of file odeImplicitSolver.h.

Constructor & Destructor Documentation

template<class P, class V, class R>
animal::OdeImplicitSolver< P, V, R >::OdeImplicitSolver (   ) 
 

Constructor.

Definition at line 16 of file odeImplicitSolver.inl.

References animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::IMPLICIT_EULER.

Member Function Documentation

template<class t_Positions, class t_Vector, class t_Real>
virtual void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::applyForces (  Vector &  a,
const Vector &  f
)  [pure virtual]
 

Compute the acceleration of the particles when given forces are applied.

Parameters:
a acceleration
f force

Implemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::compute_implicit_euler_step(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::multImplicitMatrix().

template<class P, class V, class R>
void animal::OdeImplicitSolver< P, V, R >::compute_implicit_euler_step (  Positions &  dpos,
Vector &  dvel,
const Positions &  pos,
const Vector &  vel,
Real  dt
) 
 

Compute position and velocity updates using implicit Euler time integration.

Parameters:
dpos position updates
dvel velocity updates
pos current positions
vel current velocities
dt time step

Definition at line 126 of file odeImplicitSolver.inl.

References animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_maxIter, animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_smallDenominatorThreshold, animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::applyForces(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::computeAccelerationsAndStiffness(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::multImplicitMatrix(), animal::v_assign(), animal::v_dot(), animal::v_eq(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::v_eq_h_dfdx_x(), animal::v_peq(), and animal::v_teq().

template<class t_Positions, class t_Vector, class t_Real>
virtual void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::computeAccelerations (  Vector &  a,
const Positions &  p,
const Vector &  v
)  [pure virtual]
 

Compute the acceleration of the particles for given positions and velocities.

Parameters:
a acceleration
p positions
v velocities

Implements animal::OdeSolver< t_Positions, t_Vector, t_Real >.

Implemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

template<class t_Positions, class t_Vector, class t_Real>
virtual void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::computeAccelerationsAndStiffness (  Vector &  a,
const Positions &  p,
const Vector &  v
)  [pure virtual]
 

Compute the acceleration of the particles for given positions and velocities, and updates the gradient matrix.

Parameters:
a acceleration
p positions
v velocities

Implemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::compute_implicit_euler_step(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler().

template<class t_Positions, class t_Vector, class t_Real>
Real animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::dampingRatio (   )  const [inline]
 

damping ratio used in the equation system

Definition at line 58 of file odeImplicitSolver.h.

Referenced by X3DTK::Qt::MassSpringEngineQt::MassSpringEngineQt().

template<class P, class V, class R>
void animal::OdeImplicitSolver< P, V, R >::implicit_euler (  Positions &  pos,
Vector &  vel,
Real  dt
) 
 

Update positions and velocities using implicit Euler time integration.

Parameters:
pos positions (current and updated)
vel velocities (current and updated)
dt time step

Definition at line 46 of file odeImplicitSolver.inl.

References animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_maxIter, animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_smallDenominatorThreshold, animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::applyForces(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::computeAccelerationsAndStiffness(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::multImplicitMatrix(), animal::v_assign(), animal::v_dot(), animal::v_eq(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::v_eq_h_dfdx_x(), animal::v_peq(), and animal::v_teq().

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::solveODE().

template<class t_Positions, class t_Vector, class t_Real>
int animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::maxCGiterations (   )  const [inline]
 

Maximum number of CG iterations.

Definition at line 66 of file odeImplicitSolver.h.

Referenced by X3DTK::Qt::MassSpringEngineQt::MassSpringEngineQt().

template<class P, class V, class R>
void animal::OdeImplicitSolver< P, V, R >::multImplicitMatrix (  Vector &  y,
const Vector &  x,
Real  h
) 
 

Compute $ y = (I-h(h+r)M^{-1}G) x $.

Used internally by the CG solution.

Parameters:
y the result vector
x a given vector
h a given scalar

Definition at line 202 of file odeImplicitSolver.inl.

References animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_dampingRatio, animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::applyForces(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::v_eq_h_dfdx_x(), and animal::v_peq().

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::compute_implicit_euler_step(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler().

template<class t_Positions, class t_Vector, class t_Real>
void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::setDampingRatio (  Real  d  )  [inline]
 

Set the damping ratio used in the equation system.

The damping factor is the product of the stiffness with the damping ratio.

Parameters:
d damping ratio

Definition at line 55 of file odeImplicitSolver.h.

Referenced by X3DTK::Qt::MassSpringEngineQt::setImplicitEulerDampingRatio().

template<class t_Positions, class t_Vector, class t_Real>
void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::setMaxCGiterations (  int  n  )  [inline]
 

Set the maximum number of CG iterations.

Parameters:
n maximum number of iterations

Definition at line 63 of file odeImplicitSolver.h.

Referenced by X3DTK::Qt::MassSpringEngineQt::setMaxCGiterations().

template<class t_Positions, class t_Vector, class t_Real>
void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::setSmallDenominatorThreshold (  Real  s  )  [inline]
 

Set the other CG stop criterion.

Parameters:
s threshold

Definition at line 71 of file odeImplicitSolver.h.

Referenced by X3DTK::Qt::MassSpringEngineQt::setImplicitEulerDividerThreshold().

template<class t_Positions, class t_Vector, class t_Real>
Real animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::smallDenominatorThreshold (   )  const [inline]
 

CG stop criterion.

Definition at line 74 of file odeImplicitSolver.h.

Referenced by X3DTK::Qt::MassSpringEngineQt::MassSpringEngineQt().

template<class P, class V, class R>
void animal::OdeImplicitSolver< P, V, R >::solveODE (  Positions &  pos,
Vector &  vel,
Real  dt
)  [virtual]
 

Update positions and velocities by solving an ODE over time step dt.

Parameters:
pos positions (current and updated
vel velocities (current and updated)
dt time step

Reimplemented from animal::OdeSolver< t_Positions, t_Vector, t_Real >.

Reimplemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Definition at line 31 of file odeImplicitSolver.inl.

References animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::IMPLICIT_EULER.

template<class t_Positions, class t_Vector, class t_Real>
virtual void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::v_eq_h_dfdx_x (  Vector &  v,
Real  h,
const Vector &  x
)  [pure virtual]
 

Compute $ v = h [df/dx] x $.

Parameters:
v the result vector
h a scalar
x a given vector

Implemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::compute_implicit_euler_step(), animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::multImplicitMatrix().

template<class t_Positions, class t_Vector, class t_Real>
virtual void animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::v_peq_h_dfdx_x (  Vector &  v,
Real  h,
const Vector &  x
)  [pure virtual]
 

Compute $ v += h [df/dx] x $.

Parameters:
v the result vector
h a scalar
x a given vector

Implemented in animal::MassSpringSolver< t_Positions, t_Vector, t_InvMasses, t_VecReal, t_VecIndex >, animal::MassSpringSolver< Points, Velocities, Inv_Masses, SpringStiffness, IndexedSprings >, and animal::MassSpringSolver< X3DTK::MFVec3f, X3DTK::MFVec3f, X3DTK::MFFloat, X3DTK::MFFloat, X3DTK::MFInt32 >.

Member Data Documentation

template<class t_Positions, class t_Vector, class t_Real>
Real animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_dampingRatio
 

damping ratio used in the equation system

Definition at line 80 of file odeImplicitSolver.h.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::multImplicitMatrix().

template<class t_Positions, class t_Vector, class t_Real>
int animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_maxIter
 

Maximum number of CG iterations.

Definition at line 81 of file odeImplicitSolver.h.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::compute_implicit_euler_step(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler().

template<class t_Positions, class t_Vector, class t_Real>
Real animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::_smallDenominatorThreshold
 

the other CG stop criterion

Definition at line 82 of file odeImplicitSolver.h.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::compute_implicit_euler_step(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::implicit_euler().

template<class t_Positions, class t_Vector, class t_Real>
const int animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::IMPLICIT_EULER = 5 [static]
 

Symbol of implicit Euler integration.

Definition at line 40 of file odeImplicitSolver.h.

Referenced by animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::OdeImplicitSolver(), and animal::OdeImplicitSolver< t_Positions, t_Vector, t_Real >::solveODE().

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