/// @brief Compute the motion bound for a triangle along a given direction n
/// according to mu < |v * n| + ||w x n||(max||ci*||) where ||ci*|| = ||R0(ci) x w|| / \|w\|. w is the angular velocity
/// and ci are the triangle vertex coordinates.
/// Notice that the triangle is in the local frame of the object, but n should be in the global frame (the reason is that the motion (t1, t2 and t) is in global frame)
FCL_REAL TriangleMotionBoundVisitor::visit(const InterpMotion& motion) const
{
Transform3f tf;
motion.getCurrentTransform(tf);
const Vec3f& reference_p = motion.getReferencePoint();
const Vec3f& angular_axis = motion.getAngularAxis();
FCL_REAL angular_vel = motion.getAngularVelocity();
const Vec3f& linear_vel = motion.getLinearVelocity();
FCL_REAL proj_max = ((tf.getQuatRotation().transform(a - reference_p)).cross(angular_axis)).sqrLength();
FCL_REAL tmp;
tmp = ((tf.getQuatRotation().transform(b - reference_p)).cross(angular_axis)).sqrLength();
if(tmp > proj_max) proj_max = tmp;
tmp = ((tf.getQuatRotation().transform(c - reference_p)).cross(angular_axis)).sqrLength();
if(tmp > proj_max) proj_max = tmp;
proj_max = std::sqrt(proj_max);
FCL_REAL v_dot_n = linear_vel.dot(n);
FCL_REAL w_cross_n = (angular_axis.cross(n)).length() * angular_vel;
FCL_REAL mu = v_dot_n + w_cross_n * proj_max;
return mu;
}
void relativeTransform2(const Transform3f& tf1, const Transform3f& tf2,
Transform3f& tf)
{
const Quaternion3f& q1inv = fcl::conj(tf1.getQuatRotation());
const Quaternion3f& q2_q1inv = tf2.getQuatRotation() * q1inv;
tf = Transform3f(q2_q1inv, tf2.getTranslation() - q2_q1inv.transform(tf1.getTranslation()));
}
FCL_REAL TBVMotionBoundVisitor<RSS>::visit(const InterpMotion& motion) const
{
Transform3f tf;
motion.getCurrentTransform(tf);
const Vec3f& reference_p = motion.getReferencePoint();
const Vec3f& angular_axis = motion.getAngularAxis();
FCL_REAL angular_vel = motion.getAngularVelocity();
const Vec3f& linear_vel = motion.getLinearVelocity();
FCL_REAL c_proj_max = ((tf.getQuatRotation().transform(bv.Tr - reference_p)).cross(angular_axis)).sqrLength();
FCL_REAL tmp;
tmp = ((tf.getQuatRotation().transform(bv.Tr + bv.axis[0] * bv.l[0] - reference_p)).cross(angular_axis)).sqrLength();
if(tmp > c_proj_max) c_proj_max = tmp;
tmp = ((tf.getQuatRotation().transform(bv.Tr + bv.axis[1] * bv.l[1] - reference_p)).cross(angular_axis)).sqrLength();
if(tmp > c_proj_max) c_proj_max = tmp;
tmp = ((tf.getQuatRotation().transform(bv.Tr + bv.axis[0] * bv.l[0] + bv.axis[1] * bv.l[1] - reference_p)).cross(angular_axis)).sqrLength();
if(tmp > c_proj_max) c_proj_max = tmp;
c_proj_max = std::sqrt(c_proj_max);
FCL_REAL v_dot_n = linear_vel.dot(n);
FCL_REAL w_cross_n = (angular_axis.cross(n)).length() * angular_vel;
FCL_REAL mu = v_dot_n + w_cross_n * (bv.r + c_proj_max);
return mu;
}
FCL_REAL TriangleMotionBoundVisitor::visit(const ScrewMotion& motion) const
{
Transform3f tf;
motion.getCurrentTransform(tf);
const Vec3f& axis = motion.getAxis();
FCL_REAL linear_vel = motion.getLinearVelocity();
FCL_REAL angular_vel = motion.getAngularVelocity();
const Vec3f& p = motion.getAxisOrigin();
FCL_REAL proj_max = ((tf.getQuatRotation().transform(a) + tf.getTranslation() - p).cross(axis)).sqrLength();
FCL_REAL tmp;
tmp = ((tf.getQuatRotation().transform(b) + tf.getTranslation() - p).cross(axis)).sqrLength();
if(tmp > proj_max) proj_max = tmp;
tmp = ((tf.getQuatRotation().transform(c) + tf.getTranslation() - p).cross(axis)).sqrLength();
if(tmp > proj_max) proj_max = tmp;
proj_max = std::sqrt(proj_max);
FCL_REAL v_dot_n = axis.dot(n) * linear_vel;
FCL_REAL w_cross_n = (axis.cross(n)).length() * angular_vel;
FCL_REAL mu = v_dot_n + w_cross_n * proj_max;
return mu;
}
FCL_REAL TBVMotionBoundVisitor<RSS>::visit(const ScrewMotion& motion) const
{
Transform3f tf;
motion.getCurrentTransform(tf);
const Vec3f& axis = motion.getAxis();
FCL_REAL linear_vel = motion.getLinearVelocity();
FCL_REAL angular_vel = motion.getAngularVelocity();
const Vec3f& p = motion.getAxisOrigin();
FCL_REAL c_proj_max = ((tf.getQuatRotation().transform(bv.Tr)).cross(axis)).sqrLength();
FCL_REAL tmp;
tmp = ((tf.getQuatRotation().transform(bv.Tr + bv.axis[0] * bv.l[0])).cross(axis)).sqrLength();
if(tmp > c_proj_max) c_proj_max = tmp;
tmp = ((tf.getQuatRotation().transform(bv.Tr + bv.axis[1] * bv.l[1])).cross(axis)).sqrLength();
if(tmp > c_proj_max) c_proj_max = tmp;
tmp = ((tf.getQuatRotation().transform(bv.Tr + bv.axis[0] * bv.l[0] + bv.axis[1] * bv.l[1])).cross(axis)).sqrLength();
if(tmp > c_proj_max) c_proj_max = tmp;
c_proj_max = sqrt(c_proj_max);
FCL_REAL v_dot_n = axis.dot(n) * linear_vel;
FCL_REAL w_cross_n = (axis.cross(n)).length() * angular_vel;
FCL_REAL origin_proj = ((tf.getTranslation() - p).cross(axis)).length();
FCL_REAL mu = v_dot_n + w_cross_n * (c_proj_max + bv.r + origin_proj);
return mu;
}
/** Basic shape to ccd shape */
static void shapeToGJK(const ShapeBase& s, const Transform3f& tf, ccd_obj_t* o)
{
const Quaternion3f& q = tf.getQuatRotation();
const Vec3f& T = tf.getTranslation();
ccdVec3Set(&o->pos, T[0], T[1], T[2]);
ccdQuatSet(&o->rot, q.getX(), q.getY(), q.getZ(), q.getW());
ccdQuatInvert2(&o->rot_inv, &o->rot);
}
void relativeTransform(const Transform3f& tf1, const Transform3f& tf2,
Transform3f& tf)
{
const Quaternion3f& q1_inv = fcl::conj(tf1.getQuatRotation());
tf = Transform3f(q1_inv * tf2.getQuatRotation(), q1_inv.transform(tf2.getTranslation() - tf1.getTranslation()));
}