Cloth Simulation Integrators in C++ and OpenGL

Technical Animation Assignment 2

Language: C++ , opengl

Algorithms: Spring - Mass Damper, Vertlet , Euler Implicit

Constraints: Two points are not movable, Shear, Structural and Spring constraints.

Force: Gravity, Damping.

Code for Euler Step

void Particle::eulerStep(float timeStep)
{	timeStep = 1;
	damping = 0.0025;
	if (!isMovable) return;	
	//get the acceleration for this timestep //newtonian force
	
	glm::vec3 temp = position;
	
	//euler integration
	position = position + velocity * (timeStep);
	velocity = velocity * damping + (total_force/mass) *(timeStep);
	lastPos = temp;	
	//clear out the forces
	total_force = glm::vec3(0,0,0);	
}

Code for Symplectic Euler

//Symplectic Euler integrator
 void Particle::symplecticEuler(float timeStep)
 {
	 timeStep = 1;
	 if (!isMovable) return;
	 //get the acceleration for this timestep //newtonian force
	 velocity = velocity * damping; //derivative of position is velocity
	 glm::vec3 temp = position;

	 //euler integration
	 velocity = velocity + (total_force / mass) * (timeStep);
	 position = position + velocity * (timeStep);

	 lastPos = temp;
	 //clear out the forces
	 total_force = glm::vec3(0, 0, 0);	
 	
 }

Code for Vertlet Integration:

void Particle::Vertletstep(float timeStep) {
	
if (isMovable) {
	//apply force
	glm::vec3 temp = position;
	position += (position-lastPos) * damping + (total_force/mass)*(timeStep/100);
	lastPos = temp;
//	move(position-lastPos);
	total_force = glm::vec3(0,0,0);
}

Damping factor : 0.5

Timestep: 1000/60

Results:

Euler Forward Integrator : TimeStep 2, damping 0.05 : Unstable

Vertlet Integrator :TimeStep : 1000 fps, damping: 0.01, constraint size :20

Vertlet Integrator: Increased the constraint size from 20 to 50

Conclusion:

•Euler Forward Integrator becomes unstable if time step is too large.

•Vertlet Integration is not dependent on velocity.

Resources:

https://viscomp.alexandra.dk/?p=147

Code Resource which I used for testing my code:

https://github.com/bailus/Cloth