BilateralInteractionConstraint

This component belongs to the category of Constraint Laws used for the Lagrange constraint resolution and inherits from the PairInteractionConstraint. The BilateralInteractionConstraint defines an holonomic constraint law between a pair of simulated body, i.e. the constraint defined between the pair of objects must have an equality form:

$Holonomic constraint law$

Such a constraint is suited for attachment cases or sliding joints. For an attachment case, if the vertex i of object 1 and the vertex j of object 2 are attached, the holonomic constraint law can be written as $Attachment law$ .

For a BilateralInteractionConstraint, the constraint matrix $Constraint matrix$ (derivative of the constraint law) corresponds to:

$\begin{equation*} &\mathbf{H}_1 = \begin{bmatrix} \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & \hdots & \begin{bmatrix} 1 & 0 & 0\\\end{bmatrix}_i & \hdots & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_1}\\ \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & \hdots & \begin{bmatrix} 0 & 1 & 0\\\end{bmatrix}_i & \hdots & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_1}\\ \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & \hdots & \begin{bmatrix} 0 & 0 & 1\\\end{bmatrix}_i & \hdots & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_1}\\ \end{bmatrix} \end{equation*}$ for object 1
$\begin{equation*} &\mathbf{H}_2 = \begin{bmatrix} \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & \hdots & \begin{bmatrix} -1 & 0 & 0\\\end{bmatrix}_j & \hdots & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_2}\\ \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & \hdots & \begin{bmatrix} 0 & -1 & 0\\\end{bmatrix}_j & \hdots & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_2}\\ \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_0 & \hdots & \begin{bmatrix} 0 & 0 & -1\\\end{bmatrix}_j & \hdots & \begin{bmatrix} 0 & 0 & 0\\\end{bmatrix}_{N_2}\\ \end{bmatrix} \end{equation*}$ for object 2

As all constraint laws, the BilateralInteractionConstraint will be called in the following functions and for the following steps:

getConstraintViolation(): project the free velocity in the constraint space and compute the free interpenetration $\begin{equation} &\dot{\delta}_1^{free}=\mathbf{H}_1v_1^{free} \end{equation}$
buildConstraintMatrix(): build the compliance made up of $Compliance of object 1$ and $Compliance of object 2$

Data

As a PairInteractionConstraint, the BilateralInteractionConstraint requires the following Data:

object1: link towards the object 1 to constraint
object2: link towards the object 2 to constraint
first_point: index of the constraint on the first model (object 1)
second_point: index of the constraint on the second model (object 2)

Usage

The BilateralInteractionConstraint can only be used in the context of Lagrange constraint resolution. The scene must therefore contain:

a FreeMotionAnimationLoop
a ConstraintSolver

Moreover, each constrained object must define in its node a ConstraintCorrection so that the corrective motion can be applied.

Example

This component is used as follows in XML format:

<BilateralInteractionConstraint template="Vec3d" object1="@CUBE_2/Constraints/points" object2="@CUBE_4/Constraints/points" first_point="1" second_point="0" />

or using SofaPython3:

node.addObject('BilateralInteractionConstraint', template='Vec3d' object1='@CUBE_2/Constraints/points' object2='@CUBE_4/Constraints/points' first_point='1' second_point='0')

An example scene involving a BilateralInteractionConstraint is available in examples/Components/constraint/BilateralInteractionConstraint.scn

Last modified: 15 May 2023

BilateralInteractionConstraint

Data

Usage

Example

Getting Started

Build

Video Tutorials

Using SOFA

Performances

Simulation Principles

System Resolution

Multi-Model Representation

Constraint

Components

AnimationLoops

Collisions

Pipelines

BroadPhases

NarrowPhases

IntersectionDetections

CollisionGroupManagers

Constraints Projective

Constraints Lagrange

Engines

ForceFields

IntegrationSchemes

LinearSolvers

Loaders

Mappings

Masses

Misc

Rendering

Visual

UI

Plugins

Usual plugins

Programming with SOFA

API overview

Contributing to SOFA