Collision prediction for polyhedra under screw motions
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
From curve design algorithms to the design of rigid body motions
The Visual Computer: International Journal of Computer Graphics
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Generalized penetration depth computation
Proceedings of the 2006 ACM symposium on Solid and physical modeling
PriMo: coupled prisms for intuitive surface modeling
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Subdivision schemes for the fair discretization of the spherical motion group
Journal of Computational and Applied Mathematics
PolyDepth: Real-time penetration depth computation using iterative contact-space projection
ACM Transactions on Graphics (TOG)
Haptic display of rigid body contact using generalized penetration depth
ICIRA'11 Proceedings of the 4th international conference on Intelligent Robotics and Applications - Volume Part I
ACM Transactions on Graphics (TOG)
Computer-Aided Design
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The generalized penetration depth PD of two overlapping bodies X and Y is the distance between the given colliding position of X and the closest collision-free Euclidean copy X^@e to X according to a distance metric. We present geometric optimization algorithms for the computation of PD with respect to an object-oriented metric S which takes the mass distribution of the moving body X into consideration. We use a kinematic mapping which maps rigid body displacements to points of a 6-dimensional manifold M^6 in the 12-dimensional space R^1^2 of affine mappings equipped with S. We formulate PD as the solution of the constrained minimization problem of finding the closest point on the boundary of the set of all points of M^6 which correspond to colliding configurations. Based on the theory of gliding motions, the closest point with respect to the metric S (@?PD"S) can be computed with an adapted projected gradient algorithm. We also present an algorithm for the computation of the closest point with respect to the geodesic metric G of M^6 induced by S (@?PD"G). Moreover we introduce two methods for the computation of a collision-free initial guess and give a physical interpretation of PD"S and PD"G.