Parallel Transport Frames - from graph

test.cpp

// Generate spiral
	int prev_vertex = gr.addVertex(Vec3(0,0,0));
	int prev_node = gr.addNode(new Node(prev_vertex));
	int num_edges = 30;
	float angle = 0;
	float radius = 2.0f;
	float y = 0;
	for(int i = 0; i < num_edges; ++i) {
		angle += ((float)TWO_PI/(num_edges*0.25));
		float x = cos(angle) * radius;
		float z = sin(angle) * radius;
		int new_vertex = gr.addVertex(Vec3(x,y,z));
		int new_node = gr.addNode(new Node(new_vertex));
		gr.addEdge(new Edge(prev_node, new_node));
		prev_node = new_node;
		prev_vertex = new_vertex;
		y += 0.2;
	}

// -------------------------------




// Generate transporting frames
void Tubes::computeEdgeCoordinateSystems() {
	vector<vector<Edge*> > paths;
	if(!graph.findPaths(paths)) {
		return;
	}
	vector<Edge*> edges;
	for(int i = 0; i < paths.size(); ++i) {
		edges = paths[i];
		if(edges.size() < 2) {
			printf("path is too tiny..\n");
			continue;
		}
		Vec3 start = graph.getEdgeStartVertex(edges[0]);
		Vec3 end = graph.getEdgeStartVertex(edges[1]);
		Vec3 V = (end - start).normalize();
		Vec3 D(0,0,1);
		Vec3 U(0,1,0);
		Vec3 D_prev = D;
		Vec3 U_prev = U;
		Vec3 V_prev = V;
		for(int j = 0; j < edges.size()-1; ++j) {
			Edge* edge_a = edges[j];
			Edge* edge_b = edges[j+1];
			
			Vec3 va = graph.getEdgeStartVertex(edge_a);
			Vec3 vb = graph.getEdgeEndVertex(edge_a);
			Vec3 vc = graph.getEdgeEndVertex(edge_b);
			Vec3 t0 = (vb - va).getNormalized();
			Vec3 t1 = (vc - vb).getNormalized();
			Vec3 B = cross(t0,t1);
			
			// vectors are parallel, so just copy
			if(B.length() <= 0.01) {
				V = V_prev;
				D = D_prev;
			}
			else {
				B.normalize();
				float theta = acosf(dot(t0, t1));
				V.rotate(theta, B);
				D.rotate(theta, B);
				U.rotate(theta, B);
			}
			
			edge_a->setAxis(U, D, V);
			V_prev = V.getNormalized();
			D_prev = D.getNormalized();
			U_prev = U.getNormalized();
		}
	}
}

Small step size

big step size (fails?)