IMEXIntegrator::IMEXIntegrator(std::vector<RodEnergy*>& energies, Rod& r) :
Integrator(r, energies) {
// Fill hess base
std::vector<Triplet> triplets;
for (int i=1; i < r.numEdges()-1; i++) {
if (i > 1) {
triplets.push_back(Triplet(i-1, i-2, -2.0*r.getCS()[i].twistCoeff()/r.restVoronoiLength(i)));
}
if (i < r.numEdges()-2) {
triplets.push_back(Triplet(i-1, i, -2.0*r.getCS()[i+1].twistCoeff()/r.restVoronoiLength(i+1)));
}
}
hessBase = Eigen::SparseMatrix<real>(r.numEdges()-2, r.numEdges()-2);
hessBase.setFromTriplets(triplets.begin(), triplets.end());
}
void static calcRotEqs(const Rod& r, const VecXe& rot, const std::vector<Vec3e>& curveBinorm,
VecXe& grad, std::vector<Triplet>& triplets) {
Eigen::Matrix<real, 2, 2> J;
J << 0.0, -1.0, 1.0, 0.0;
for (int i=1; i<r.numEdges()-1; i++) {
Vec3e m1 = cos(rot(i)) * r.next().u[i] + sin(rot(i)) * r.next().v(i);
Vec3e m2 = -sin(rot(i)) * r.next().u[i] + cos(rot(i)) * r.next().v(i);
Vec2e curvePrev(curveBinorm[i-1].dot(m2), -curveBinorm[i-1].dot(m1)); // omega ^i _i
Vec2e curveNext(curveBinorm[i].dot(m2), -curveBinorm[i].dot(m1)); // omega ^i _i+1
real dWprev = 1.0 / r.restVoronoiLength(i) *
curvePrev.dot(J * r.getCS()[i].bendMat() * (curvePrev - r.restCurveNext(i)));
real dWnext = 1.0 / r.restVoronoiLength(i+1) *
curveNext.dot(J * r.getCS()[i+1].bendMat() * (curveNext - r.restCurvePrev(i+1)));
real twistPrev = rot(i) - rot(i-1) + r.next().refTwist(i);
real twistNext = rot(i+1) - rot(i) + r.next().refTwist(i+1);
grad(i-1) = -(dWprev + dWnext + 2.0 * r.getCS()[i].twistCoeff() *
(twistPrev/r.restVoronoiLength(i) - twistNext/r.restVoronoiLength(i+1)));
real hess = 2.0*(r.getCS()[i].twistCoeff()/r.restVoronoiLength(i) +
r.getCS()[i+1].twistCoeff()/r.restVoronoiLength(i+1));
hess += 1.0 / r.restVoronoiLength(i) *
(curvePrev.dot(J.transpose() * r.getCS()[i].bendMat() * J * curvePrev)
- curvePrev.dot(r.getCS()[i].bendMat() * (curvePrev - r.restCurveNext(i))));
hess += 1.0 /r.restVoronoiLength(i+1) *
(curveNext.dot(J.transpose() * r.getCS()[i+1].bendMat() * J * curveNext)
- curveNext.dot(r.getCS()[i+1].bendMat() * (curveNext - r.restCurvePrev(i+1))));
triplets.push_back(Triplet(i-1, i-1, hess));
}
}
void RodSoundApp::draw() {
while (running &&
// app::getElapsedSeconds() - tAtLastDraw < 1.0/app::getFrameRate() &&
fe.nextTimestep(c) > 1.0 / (real) SampleRate) {
update();
}
tAtLastDraw = app::getElapsedSeconds();
PROFILER_START("Draw");
// Clear out the window with grey
gl::clear(Color(0.45, 0.45, 0.5));
// Enable alpha blending and depth testing
gl::enableAlphaBlending();
gl::enableDepthRead(true);
gl::enableDepthWrite(true);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
// Draw framerate counter
gl::setMatricesWindow(getWindowSize());
std::stringstream ss;
ss << getAverageFps();
gl::drawStringRight(ss.str(),
Vec2c(getWindowWidth()-toPixels(10), getWindowHeight()-toPixels(20)),
Color(0.0, 0.0, 0.0),
Font("Arial", toPixels(12)));
// Set projection/modelview matrices
gl::setMatrices(cam);
// Draw the rod and the normal of the bishop frame
for(int i=0; i<r->numEdges(); i++) {
Vec3c p0 = EtoC(r->cur().POS(i));
Vec3c p1 = EtoC(r->cur().POS(i+1));
gl::drawLine(p0, p1);
gl::color(1.0, 1.0, 0.0);
gl::lineWidth(1.0);
Vec3c u = EtoC(r->cur().u[i]);
gl::drawLine((p0+p1)/2.0, (p0+p1)/2.0+u*(p1-p0).length()*2.0);
}
m.apply();
l->setDiffuse(Color::white());
l->setAmbient(Color::white());
l->setPosition(Vec3c(0.0, 50.0, 0.0));
l->enable();
diffuseProg.bind();
for (int i=0; i<r->numCPs(); i++) {
gl::pushModelView();
gl::translate(EtoC(r->cur().POS(i)));
spheredl->draw();
gl::popModelView();
}
diffuseProg.unbind();
rodProg.bind();
floorTex.enableAndBind();
gl::draw(floor);
floorTex.disable();
rodProg.unbind();
// Draw rod edges
rodProg.bind();
rodTex.enableAndBind();
for (int i=0; i<r->numEdges(); i++) {
gl::pushModelView();
Vec3c v = EtoC(r->cur().edge(i).normalized());
gl::translate(EtoC(r->cur().POS(i)));
Quaternion<real> q(Vec3c(0.0, 1.0, 0.0), v);
real angle = acos(std::max((real)-1.0, std::min((real)1.0, (q*Vec3c(-1.0, 0.0, 0.0)).dot(EtoC(r->cur().u[i])))));
if ((q*Vec3c(-1.0, 0.0, 0.0)).dot(EtoC(r->cur().v(i))) > 0.0) angle = -angle;
gl::rotate(Quaternion<real>(v, angle));
gl::rotate(q);
gl::rotate(Vec3c(0.0, r->cur().rot(i)*180.0/constants::pi, 0.0));
gl::scale(1.0, r->cur().edgeLength(i), 1.0);
cylinderdl->draw();
gl::popModelView();
}
rodTex.unbind();
rodProg.unbind();
for (RodEnergy* e : energies) {
e->draw(c.timestep());
}
integrator->draw();
fe.record(c);
PROFILER_STOP("Draw");
}