Parallel Transport Frames - TEST

ptf.cpp

//--------------------------------------------------------------
void testApp::setup(){
	ofSetFrameRate(60);
	ofSetVerticalSync(true);
	ofBackground(33);
	
	donnie.create(125);
	donnie.si.drawUsingQuads();
	//renderer.addSceneItem(donnie.si);
	
	renderer.translate(0,0,10);
	
        // just creating some particles and springs.
	Particle* a = ps.createParticle(Vec3(-5,9,0));
	Particle* b = ps.createParticle(Vec3(-5,8.8,0));
	Particle* c = ps.createParticle(Vec3(-5,8.6,0));
	Particle* d = ps.createParticle(Vec3(-5,8.4,0));
	a->disable();
	ps.createSpring(a,b);
	ps.createSpring(b,c);
	ps.createSpring(c,d);
	Particle* prev_particle = d;
	int n = 15;
	for(int i = 0; i < n; ++i) {
		Particle* p = ps.createParticle(Vec3(-5+i*0.4, 7.5,0));
		ps.createSpring(prev_particle, p);
		p->setMass(0.5+(1.0-(float)i/n) * 4.0);
		prev_particle = p;
		
	}
	
	wind = false;
	invert = false;
	paused = false;
}

//--------------------------------------------------------------
void testApp::update(){
	static int counter = 0;
	ofSetWindowTitle(ofToString(ofGetFrameRate()));
	float t = ofGetElapsedTimeMillis() * noise_z;
	donnie.noise(noise_x, noise_y, t, radius);

        // apply some forces to the ParticleSystem (variable ps) so the springs move along.
	if(!paused) {
		++counter;
		float x = 0.0f;
		if(wind) {
			x = sin(counter * 0.04) * 0.03;
		}
		float inv = (invert) ? -1 : 1;
		ps.addForce(Vec3(x,-0.01 * inv,0));
		ps.update();
	}
}

//--------------------------------------------------------------
void testApp::draw(){
	renderer.debugDraw();
	ps.debugDraw();
	
	// calculate orientation frames.
	Vec3 V = ps.springs[0]->a->position - ps.springs[0]->b->position ; // these are the first points
	Vec3 T(0,1,0);
	Vec3 D(0,0,1);
	Vec3 U(0,1,0);
	Vec3 U_prev = U;
	Vec3 D_prev = D;
	Vec3 V_prev = V;
	vector<Spring*>& springs = ps.springs;
	int num = springs.size();
	for(int i = 0; i < num-1; ++i) {
		Spring* sa = springs[i];
		Spring* sb = springs[i+1];
		Particle* a = sa->a;
		Particle* b = sa->b;
		Particle* c = sb->b;

		Vec3 t0 = (b->position - a->position).getNormalized();
		Vec3 t1 = (c->position - b->position).getNormalized();

		Vec3 B = cross(t0, t1);
		if(B.length() <= 0.01) {
			V = V_prev;
			D = D_prev;
		}
		else {
			B.normalize();
			float theta = acos(dot(t0, t1));
			V.rotate(theta, B);
			D.rotate(theta, B);
			U.rotate(theta, B);
		}
		
		float angle = acos(dot(t0, t1));
		
		glBegin(GL_LINES);
			// rotated up
			glColor3f(0,1,0);
			glVertex3fv(a->position.getPtr());
			glVertex3fv((a->position + V).getPtr());
		
			glColor3f(1,1,0);
			glVertex3fv(a->position.getPtr());
			glVertex3fv((a->position + D).getPtr());

			glColor3f(0,1,1);
			glVertex3fv(a->position.getPtr());
			glVertex3fv((a->position + U).getPtr());
			
			// corrected right
			glColor3f(1,0,0);
			glVertex3fv(a->position.getPtr());
			glVertex3fv((a->position + B).getPtr());
		glEnd();
		
		// create circle around "U" axis.
		int num_segments = 10;
		Vec3 to_rotate = D;
		float angle_to_rotate = TWO_PI/(float)num_segments;
		V.normalize();
		D.normalize();
		glColor3f(1,1,1);
		glBegin(GL_LINE_LOOP);
		for(int i = 0; i < num_segments; ++i) {
			to_rotate.rotate(angle_to_rotate, V);
			glVertex3fv((a->position + to_rotate).getPtr());
		}
		glEnd();
		
		V_prev = V;
		D_prev = D;
	}
}

Test render of this PTF code (not sure if this works... seems to be too trivial when comparing with the math described in this paper

Yes! I been trying this myself but didn't get it to behave that way. congrats. (no gimbal lock in there? ;) )

Nice. I think this is a build in feature of the cinder library

Yes, it is...

I can't spot something wrong with it. But also cannot believe it's so trivial :) please correct me if I'm wrong :)

Vec3, Spring !? are these your custom classes? or are they part of the new OF 0071? Thanks for the code by the way I was just about to take a stab at it

I've got the same question as nardove. And how have you defined the 3 properties/Particles (a,b,c) for a spring? Do you have the rest of the source code?

Hi Trent and Nardove. The Vec3 is a typical vector3 class; you can use any, but if you're using openFrameworks that will be ofVec3f. The spring implements hooks law (http://en.wikipedia.org/wiki/Hooke's_law) It has two member "a" and "b" which are the particles. When a spring is create the distance between the particle (a and b) is used as the rest length.