// Adds the gradient of the penalty potential (-1 * force) for a particle-edge
// pair to the total.
// Read the positions of the particle and edge endpoints from the input
// variable x.
// Inputs:
// x: The positions of the particles in the scene.
// vidx: The index of the particle.
// eidx: The index of the edge, i.e. the indices of the particle making up the
// endpoints of the edge are given by m_scene.getEdge(eidx).first and
// m_scene.getEdges(eidx).second.
// Outputs:
// gradE: The total gradient of penalty force. *ADD* the particle-edge
// gradient to this total gradient.
void PenaltyForce::addParticleEdgeGradEToTotal(const VectorXs &x, int vidx, int eidx, VectorXs &gradE)
{
VectorXs x1 = x.segment<2>(2*vidx);
VectorXs x2 = x.segment<2>(2*m_scene.getEdge(eidx).first);
VectorXs x3 = x.segment<2>(2*m_scene.getEdge(eidx).second);
double r1 = m_scene.getRadius(vidx);
double r2 = m_scene.getEdgeRadii()[eidx];
// your implementation here
int eidx1 = m_scene.getEdge(eidx).first;
int eidx2 = m_scene.getEdge(eidx).second;
scalar alpha = (x1-x2).dot(x3-x2)/(x3-x2).squaredNorm();
if(alpha<0) alpha = 0;
if(alpha>1) alpha = 1;
Vector2s n = alpha*x3+(1-alpha)*x2-x1;
if(n.norm()>r1+r2+m_thickness) return;
Vector2s nhat = n/n.norm();
MatrixXs gradn(2, 6);
Matrix2s I = I.Identity();
gradn<<-I, (1-alpha)*I, alpha*I;
VectorXs gradV = m_k*(n.norm()-r1-r2-m_thickness)*gradn.transpose()*nhat;
gradE(2*vidx) += gradV(0);
gradE(2*vidx+1) += gradV(1);
gradE(2*eidx1) += gradV(2);
gradE(2*eidx1+1) += gradV(3);
gradE(2*eidx2) += gradV(4);
gradE(2*eidx2+1) += gradV(5);
}
scalar HertzianPenaltyForce::computePotential( const VectorXs& q, const SparseMatrixsc& M, const VectorXs& r ) const
{
assert( q.size() % 2 == 0 ); assert( q.size() == M.rows() ); assert( q.size() == M.cols() ); assert( r.size() == q.size() / 2 );
scalar U{ 0.0 };
// For each ball
for( unsigned ball0 = 0; ball0 < r.size(); ++ball0 )
{
// For each subsequent ball
for( unsigned ball1 = ball0 + 1; ball1 < r.size(); ++ball1 )
{
// Compute the total radius
const scalar total_radius{ r(ball0) + r(ball1) };
// Compute a vector pointing from ball0 to ball1
const Vector2s n{ q.segment<2>( 2 * ball1 ) - q.segment<2>( 2 * ball0 ) };
// If the squared distance is greater or equal to the sum of the radii squared, no force
if( n.squaredNorm() > total_radius * total_radius )
{
continue;
}
// Compute the penetration depth
const scalar delta{ n.norm() - total_radius };
assert( delta < 0.0 );
// U = 0.5 * k * pen_depth^(5/2)
U += 0.5 * m_k * std::pow( -delta, scalar( 2.5 ) );
}
}
return U;
}
static PyObject* insertBall( PyObject* self, PyObject* args )
{
Vector2s q;
Vector2s v;
scalar r;
scalar m;
int fixed;
assert( args != nullptr );
using std::is_same;
static_assert( is_same<scalar,double>::value || is_same<scalar,float>::value, "Error, scalar type must be double or float for Python interface." );
if( !PyArg_ParseTuple( args, is_same<scalar,double>::value ? "ddddddi" : "ffffffi", &q.x(), &q.y(), &v.x(), &v.y(), &r, &m, &fixed ) )
{
PyErr_Print();
std::cerr << "Failed to read parameters for insertBall, parameters are: double x, double y, double vx, double vy, double radius, double mass, bool fixed. Exiting." << std::endl;
std::exit( EXIT_FAILURE );
}
if( r <= 0.0 )
{
std::cerr << "Error in insert ball, radius must be positive. Exiting." << std::endl;
std::exit( EXIT_FAILURE );
}
if( m <= 0.0 )
{
std::cerr << "Error in insert ball, mass must be positive. Exiting." << std::endl;
std::exit( EXIT_FAILURE );
}
if( fixed != 0 && fixed != 1 )
{
std::cerr << "Error in insert ball, fixed value must be 0 or 1. Exiting." << std::endl;
std::exit( EXIT_FAILURE );
}
assert( s_ball_state != nullptr );
s_ball_state->pushBallBack( q, v, r, m, fixed );
return Py_BuildValue( "" );
}
void TeleportedCircleCircleConstraint::computeContactBasis( const VectorXs& q, const VectorXs& v, MatrixXXsc& basis ) const
{
assert( fabs( m_n.norm() - 1.0 ) <= 1.0e-6 );
const Vector2s t{ -m_n.y(), m_n.x() };
assert( fabs( t.norm() - 1.0 ) <= 1.0e-6 ); assert( fabs( m_n.dot( t ) ) <= 1.0e-6 );
basis.resize( 2, 2 );
basis.col( 0 ) = m_n;
basis.col( 1 ) = t;
}
bool MathUtilities::isRightHandedOrthoNormal( const Vector2s& a, const Vector2s& b, const scalar& tol )
{
// All basis vectors should be unit
if( fabs( a.norm() - 1.0 ) > tol ) { return false; }
if( fabs( b.norm() - 1.0 ) > tol ) { return false; }
// All basis vectors should be mutually orthogonal
if( fabs( a.dot( b ) ) > tol ) { return false; }
// Coordinate system should be right handed
assert( fabs( cross( a, b ) - 1.0 ) <= 1.0e-6 || fabs( cross( a, b ) + 1.0 ) <= 1.0e-6 );
if( cross( a, b ) <= 0.0 ) { return false; }
return true;
}
void TwoDSceneSVGRenderer::renderSolidCircle( std::fstream& file, const Vector2s& center, const scalar& r, const renderingutils::Color& color ) const
{
file << "<circle fill=\"#";
file << intToHexString(floor(255.0*color.r+0.5)) << intToHexString(floor(255.0*color.g+0.5)) << intToHexString(floor(255.0*color.b+0.5)) << "\"" << " stroke=\"#";
file << intToHexString(floor(255.0*color.r+0.5)) << intToHexString(floor(255.0*color.g+0.5)) << intToHexString(floor(255.0*color.b+0.5)) << "\"" << " stroke-width=\"0\" cx=\"";
file << center.x();
file << "\" cy=\"";
file << center.y();
file << "\" r=\"";
file << r;
file << "\"/>" << std::endl;
}
Vector2s RigidBody::computeCenterOfMass( const VectorXs& vertices, const VectorXs& masses ) const
{
// COMPLETE THIS CODE
assert( vertices.size()%2 == 0 );
assert( 2*masses.size() == vertices.size() );
Vector2s com;
com.setZero();
for(int i=0;i<masses.size();i++) {
com+=masses(i)*vertices.segment<2>(2*i);
}
com /= m_M;
return com;
}
// Adds the gradient of the penalty potential (-1 * force) for a particle-
// half-plane pair to the total.
// Read the positions of the particle from the input variable x.
// Inputs:
// x: The positions of the particles in the scene.
// vidx: The index of the particle.
// pidx: The index of the half-plane, i.e. the position and normal vectors
// for the half-plane can be retrieved by calling
// m_scene.getHalfplane(pidx).
// Outputs:
// gradE: The total gradient of the penalty force. *ADD* the particle-
// half-plane gradient to this total gradient.
void PenaltyForce::addParticleHalfplaneGradEToTotal(const VectorXs &x, int vidx, int pidx, VectorXs &gradE)
{
VectorXs x1 = x.segment<2>(2*vidx);
VectorXs nh = m_scene.getHalfplane(pidx).second;
VectorXs px = m_scene.getHalfplane(pidx).first;
// your implementation here
Vector2s n = (px-x1).dot(nh)/nh.squaredNorm()*nh;
Vector2s nhat = n/n.norm();
scalar r1 = m_scene.getRadius(vidx);
if(n.norm()>r1+m_thickness) return;
Matrix2s gradn = -nh*nh.transpose()/nh.squaredNorm();
Vector2s gradV = m_k*(n.norm()-r1-m_thickness)*gradn.transpose()*nhat;
gradE(2*vidx) += gradV(0);
gradE(2*vidx+1) += gradV(1);
}
Vector2s vavImage::GetWhitePoints()
{
Vector2s out;
for (int j = 0; j < m_Image.cols; ++j)
{
for (int i = 0; i < m_Image.rows; ++i)
{
cv::Vec3b intensity = m_Image.at<cv::Vec3b>(i, j);
if (intensity[0] != 0 || intensity[1] != 0 || intensity[2] != 0)
{
out.push_back(Vector2(i, j));
//std::cout << i << " " << j << std::endl;
}
}
}
return out;
}
// TODO: Don't do the if here, have children do what they need to do
scalar Constraint::computeLambda( const VectorXs& q, const VectorXs& v ) const
{
MatrixXXsc basis;
computeBasis( q, v, basis );
assert( basis.rows() == basis.cols() );
assert( basis.cols() == 2 || basis.cols() == 3 );
const VectorXs rel_vel = computeRelativeVelocity( q, v );
assert( rel_vel.size() == basis.rows() );
if( basis.cols() == 3 )
{
const Vector2s tangent_vel( rel_vel.dot( basis.col( 1 ) ), rel_vel.dot( basis.col( 2 ) ) );
return tangent_vel.norm();
}
else if( basis.cols() == 2 )
{
return fabs( rel_vel.dot( basis.col( 1 ) ) );
}
std::cerr << "Unhandled case in Constraint::computeLambda" << std::endl;
std::exit( EXIT_FAILURE );
}
// Adds the gradient of the penalty potential (-1 * force) for a pair of
// particles to the total.
// Read the positions of the particles from the input variable x. Radii can
// be obtained from the member variable m_scene, the penalty force stiffness
// from member variable m_k, and penalty force thickness from member variable
// m_thickness.
// Inputs:
// x: The positions of the particles in the scene.
// idx1: The index of the first particle, i.e. the position of this particle
// is ( x[2*idx1], x[2*idx1+1] ).
// idx2: The index of the second particle.
// Outputs:
// gradE: The total gradient of penalty force. *ADD* the particle-particle
// gradient to this total gradient.
void PenaltyForce::addParticleParticleGradEToTotal(const VectorXs &x, int idx1, int idx2, VectorXs &gradE)
{
VectorXs x1 = x.segment<2>(2*idx1);
VectorXs x2 = x.segment<2>(2*idx2);
double r1 = m_scene.getRadius(idx1);
double r2 = m_scene.getRadius(idx2);
// your implementation here
Vector2s n = x2-x1;
if(n.norm()>r1+r2+m_thickness) return;
Vector2s nhat = n/n.norm();
MatrixXs gradn(2, 4);
Matrix2s I = I.Identity();
gradn<<-I, I;
VectorXs gradV = m_k*(n.norm()-r1-r2-m_thickness)*gradn.transpose()*nhat;
gradE(2*idx1) += gradV(0);
gradE(2*idx1+1) += gradV(1);
gradE(2*idx2) += gradV(2);
gradE(2*idx2+1) += gradV(3);
}
void VortexForce::addGradEToTotal( const VectorXs& x, const VectorXs& v, const VectorXs& m, VectorXs& gradE )
{
assert( x.size() == v.size() );
assert( x.size() == m.size() );
assert( x.size() == gradE.size() );
assert( x.size()%2 == 0 );
assert( m_particles.first >= 0 ); assert( m_particles.first < x.size()/2 );
assert( m_particles.second >= 0 ); assert( m_particles.second < x.size()/2 );
Vector2s rhat = x.segment<2>(2*m_particles.second)-x.segment<2>(2*m_particles.first);
scalar r = rhat.norm();
assert( r != 0.0 );
rhat /= r;
rhat *= m_kbs;
// Rotate rhat 90 degrees clockwise
scalar temp = rhat.x();
rhat.x() = -rhat.y();
rhat.y() = temp;
rhat -= v.segment<2>(2*m_particles.second)-v.segment<2>(2*m_particles.first);
rhat /= r*r;
rhat *= m_kvc;
gradE.segment<2>(2*m_particles.first) -= -rhat;
gradE.segment<2>(2*m_particles.second) += -rhat;
}
static VectorXs parallelTransport2D( const VectorXs& n0, const VectorXs& n1, const VectorXs& t0 )
{
assert( fabs( n0.norm() - 1.0 ) <= 1.0e-6 ); assert( fabs( n1.norm() - 1.0 ) <= 1.0e-6 );
// x is cos of angle, y is sin of angle
const Vector2s r{ n0.dot( n1 ), MathUtilities::cross( n0, n1 ) };
assert( fabs( r.norm() - 1.0 ) <= 1.0e-6 );
// Rotate t0
VectorXs t1{ 2 };
t1( 0 ) = r.x() * t0.x() - r.y() * t0.y();
t1( 1 ) = r.y() * t0.x() + r.x() * t0.y();
assert( fabs( t0.norm() - t1.norm() ) <= 1.0e-6 );
// TODO: Assert n0,t0 angle is same as n1,t1 angle
return t1;
}
void TwoDSceneSVGRenderer::renderRigidBodyScene( const std::string& name, const RigidBodyScene& rbscene ) const
{
// const VectorXs& x = m_scene.getX();
// assert( x.size()%2 == 0 );
// assert( 2*m_scene.getNumParticles() == x.size() );
// int numparticles = x.size()/2;
// const std::vector<scalar>& radii = m_scene.getRadii();
// assert( numparticles == (int) radii.size() );
std::fstream file(name.c_str(), std::fstream::out);
if(!file)
{
std::cerr << "Failure writing SVG file!" << std::endl;
exit(1);
}
scalar scale, xmin, ymin, xshift, yshift;
computeSimToImageMap( scale, xmin, ymin, xshift, yshift );
file << "<?xml version=\"1.0\" encoding=\"utf-8\"?> <!-- Generator: Adobe Illustrator 13.0.0, SVG Export Plug-In . SVG Version: 6.00 Build 14948) --> <svg version=\"1.2\" baseProfile=\"tiny\" id=\"Layer_1\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" x=\"0px\" y=\"0px\" width=\"";
file << m_w;
file << "px\" height=\"";
file << m_h;
file << "px\" viewBox=\"0 0 ";
file << m_w << " " << m_h;
file << "\" xml:space=\"preserve\">" << std::endl;
// Simulate a background color by rendering a large colored quad
file << "<polygon points=\"" << 0 << "," << 0 << " " << m_w << "," << 0 << " " << m_w << "," << m_h << " " << 0 << "," << m_h;
file << "\" style=\"fill:#" << intToHexString(floor(255.0*m_bgcolor.r+0.5)) << intToHexString(floor(255.0*m_bgcolor.g+0.5)) << intToHexString(floor(255.0*m_bgcolor.b+0.5));
file << "; stroke:#000000;stroke-width:0\"/>" << std::endl;
const std::vector<RigidBody> rbs = rbscene.getRigidBodies();
assert( m_particle_colors.size() == rbs.size() );
// For each rigid body
for( std::vector<RigidBody>::size_type i = 0; i < rbs.size(); ++i )
{
scalar r = rbs[i].getRadius();
renderingutils::Color rbcolor = m_particle_colors[i];
// Render each edge of each rigid body
for( int j = 0; j < rbs[i].getNumVertices(); ++j )
{
const Vector2s& xi = rbs[i].getWorldSpaceVertex(j);
const Vector2s& xj = rbs[i].getWorldSpaceVertex((j+1)%rbs[i].getNumVertices());
Vector2s p0;
p0 << scale*(xi.x()-xmin) + xshift, ((scalar)m_h) - scale*(xi.y()-ymin) - yshift;
Vector2s p1;
p1 << scale*(xj.x()-xmin) + xshift, ((scalar)m_h) - scale*(xj.y()-ymin) - yshift;
renderSweptEdge( file, p0, p1, scale*r, rbcolor );
}
}
// Render each spring force
for( std::vector<RigidBody>::size_type i = 0; i < m_svg_renderers.size(); ++i )
{
renderingutils::Color clr = m_svg_renderers[i]->getColor();
Vector2s xi = m_svg_renderers[i]->getVertexOne(rbs);
Vector2s xj = m_svg_renderers[i]->getVertexTwo(rbs);
Vector2s p0;
p0 << scale*(xi.x()-xmin) + xshift, ((scalar)m_h) - scale*(xi.y()-ymin) - yshift;
Vector2s p1;
p1 << scale*(xj.x()-xmin) + xshift, ((scalar)m_h) - scale*(xj.y()-ymin) - yshift;
renderSweptEdge( file, p0, p1, scale*0.03, clr );
}
file << "</svg>" << std::endl;
file.close();
}
void TwoDSceneSVGRenderer::renderShared( std::fstream& file, const VectorXs& x, const std::vector<std::pair<int,int> >& edges, const std::vector<scalar>& radii, const std::vector<scalar>& edgeradii, const scalar& scale, const scalar& xmin, const scalar& ymin, const scalar& xshift, const scalar& yshift ) const
{
int numparticles = x.size()/2;
for( std::vector<renderingutils::ParticlePath>::size_type i = 0; i < m_particle_paths.size(); ++i )
{
const std::list<Vector2s>& ppath = m_particle_paths[i].getPath();
const renderingutils::Color& pathcolor = m_particle_paths[i].getColor();
file << "<polyline points=\"";
for( std::list<Vector2s>::const_iterator itr = ppath.begin(); itr != ppath.end(); ++itr )
{
Vector2s point;
point << scale*(itr->x()-xmin) + xshift, ((scalar)m_h) - scale*(itr->y()-ymin) - yshift;
file << point.x() << "," << point.y() << " ";
}
file << "\" style=\"fill:none;stroke:#";
file << intToHexString(floor(255.0*pathcolor.r+0.5)) << intToHexString(floor(255.0*pathcolor.g+0.5)) << intToHexString(floor(255.0*pathcolor.b+0.5));
file << ";stroke-width:1\"/>" << std::endl;
}
// Render edges
assert( edgeradii.size() == edges.size() );
for( std::vector<std::pair<int,int> >::size_type i = 0; i < edges.size(); ++i )
{
assert( edges[i].first >= 0 );
assert( edges[i].first < m_scene.getNumParticles() );
assert( edges[i].second >= 0 );
assert( edges[i].second < m_scene.getNumParticles() );
int i0 = edges[i].first;
int i1 = edges[i].second;
Vector2s p0;
p0 << scale*(x(2*i0)-xmin) + xshift, ((scalar)m_h) - scale*(x(2*i0+1)-ymin) - yshift;
Vector2s p1;
p1 << scale*(x(2*i1)-xmin) + xshift, ((scalar)m_h) - scale*(x(2*i1+1)-ymin) - yshift;
renderSweptEdge( file, p0, p1, scale*edgeradii[i], m_edge_colors[i] );
}
// Render halfplanes
for(int i=0; i < m_scene.getNumHalfplanes(); i++)
{
Vector2s p0;
p0 << scale * (m_scene.getHalfplane(i).first[0]-xmin) + xshift, ((scalar)m_h) - scale*(m_scene.getHalfplane(i).first[1]-ymin) - yshift;
Vector2s n0;
n0 << m_scene.getHalfplane(i).second[0], -m_scene.getHalfplane(i).second[1];
n0.normalize();
renderHalfplane(file, p0, n0, m_halfplane_colors[i]);
}
// Render particles
for( int i = 0; i < numparticles; ++i )
{
Vector2s center;
center << scale*(x(2*i)-xmin) + xshift, ((scalar)m_h) - scale*(x(2*i+1)-ymin) - yshift;
renderSolidCircle( file, center, scale*radii[i], m_particle_colors[i] );
}
}
void TwoDSceneSVGRenderer::renderSweptEdge( std::fstream& file, const Vector2s& x0, const Vector2s& x1, const scalar& r, const renderingutils::Color& color ) const
{
scalar theta = atan2(x1.y()-x0.y(),x1.x()-x0.x());
scalar rx = -r*sin(theta);
scalar ry = r*cos(theta);
scalar p0x = x0.x() + rx;
scalar p0y = x0.y() + ry;
scalar p1x = x0.x() - rx;
scalar p1y = x0.y() - ry;
scalar p2x = x1.x() - rx;
scalar p2y = x1.y() - ry;
scalar p3x = x1.x() + rx;
scalar p3y = x1.y() + ry;
file << "<polygon points=\"" << p0x << "," << p0y << " " << p1x << "," << p1y << " " << p2x << "," << p2y << " " << p3x << "," << p3y;
file << "\" style=\"fill:#" << intToHexString(floor(255.0*color.r+0.5)) << intToHexString(floor(255.0*color.g+0.5)) << intToHexString(floor(255.0*color.b+0.5));
file << "; stroke:#000000;stroke-width:0\"/>" << std::endl;
renderSolidCircle( file, x0, r, color );
renderSolidCircle( file, x1, r, color );
}
