void Joint::PreStep(float inv_dt)
{
// Pre-compute anchors, mass matrix, and bias.
Mat22 Rot1(body1->rotation);
Mat22 Rot2(body2->rotation);
r1 = Rot1 * localAnchor1;
r2 = Rot2 * localAnchor2;
// deltaV = deltaV0 + K * impulse
// invM = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)]
// = [1/m1+1/m2 0 ] + invI1 * [r1.y*r1.y -r1.x*r1.y] + invI2 * [r1.y*r1.y -r1.x*r1.y]
// [ 0 1/m1+1/m2] [-r1.x*r1.y r1.x*r1.x] [-r1.x*r1.y r1.x*r1.x]
Mat22 K1;
K1.col1.x = body1->invMass + body2->invMass; K1.col2.x = 0.0f;
K1.col1.y = 0.0f; K1.col2.y = body1->invMass + body2->invMass;
Mat22 K2;
K2.col1.x = body1->invI * r1.y * r1.y; K2.col2.x = -body1->invI * r1.x * r1.y;
K2.col1.y = -body1->invI * r1.x * r1.y; K2.col2.y = body1->invI * r1.x * r1.x;
Mat22 K3;
K3.col1.x = body2->invI * r2.y * r2.y; K3.col2.x = -body2->invI * r2.x * r2.y;
K3.col1.y = -body2->invI * r2.x * r2.y; K3.col2.y = body2->invI * r2.x * r2.x;
Mat22 K = K1 + K2 + K3;
K.col1.x += softness;
K.col2.y += softness;
M = K.Invert();
Vec2 p1 = body1->position + r1;
Vec2 p2 = body2->position + r2;
Vec2 dp = p2 - p1;
if (World::positionCorrection)
{
bias = -biasFactor * inv_dt * dp;
}
else
{
bias.Set(0.0f, 0.0f);
}
if (World::warmStarting)
{
// Apply accumulated impulse.
body1->velocity -= body1->invMass * P;
body1->angularVelocity -= body1->invI * Cross(r1, P);
body2->velocity += body2->invMass * P;
body2->angularVelocity += body2->invI * Cross(r2, P);
}
else
{
P.Set(0.0f, 0.0f);
}
}
// refine the plane given set of inlier points
gtsam::Pose2 PoseEstimator::refine(const Datums& ps, const Mask& mask,
boost::optional<Model> bestModel) {
// filter inlier
std::vector<Point2Pair> putatives;
for (size_t i = 0; i < ps.size(); i++) {
if (!mask[i]) continue;
putatives.push_back(ps[i]);
}
// check inlier size
if (putatives.size() < 2)
throw std::runtime_error("minimal pose solver must have input inlier size >= 2");
// method of 'A Method for Registration of 3D Shapes', by Besl and McKay, 1992
// TODO: not sure this is correct in 2D
// 1. find centroids of each dataset
Vector2 cent1 = zero(2);
Vector2 cent2 = zero(2);
for (size_t i = 0; i < putatives.size(); i++) {
cent1 += putatives[i].first.vector();
cent2 += putatives[i].second.vector();
}
cent1 = cent1 / static_cast<double>(putatives.size());
cent2 = cent2 / static_cast<double>(putatives.size());
// 2. SVD
Matrix H = zeros(2,2);
for (size_t i = 0; i < putatives.size(); i++)
H = H + (putatives[i].first.vector() - cent1) *
(putatives[i].second.vector() - cent1).transpose();
Matrix U,V;
Vector S;
svd(H, U, S, V);
// 3. get rotation matrix
Matrix R = V * U.transpose();
if (R.determinant() < 0) {
V(0,1) = -V(0,1);
V(1,1) = -V(1,1);
R = V * U.transpose();
}
// 4. translation
Vector2 t = -R * cent1 + cent2;
return Pose2(Rot2(atan2(R(1,0), R(0,0))), Point2(t));
}
void Joint::Set(Body* b1, Body* b2, const Vec2& anchor)
{
body1 = b1;
body2 = b2;
Mat22 Rot1(body1->rotation);
Mat22 Rot2(body2->rotation);
Mat22 Rot1T = Rot1.Transpose();
Mat22 Rot2T = Rot2.Transpose();
localAnchor1 = Rot1T * (anchor - body1->position);
localAnchor2 = Rot2T * (anchor - body2->position);
P.Set(0.0f, 0.0f);
softness = 0.0f;
biasFactor = 0.2f;
}
