Efficient Collision Detection for Animation and Robotics Part 2 pptx

[...]... head and tail The edge points from tail to head It has two adjacent faces cobounding it as well Looking from the the tail end toward the head, the adjacent face lying to the right hand side is what we called the right face" and similarly for the left face" please see Fig .2. 1 Each polyhedron data structure has a eld for its features faces, edges, vertices and Voronoi cells described below in Sec 2. 1.4... planar boundaries This leads to the de nition of Voronoi regions which will be described next in Sec 2. 1.4 2 2 2 17 2. 1.4 Voronoi Region A Voronoi region associated with a feature is a set of points exterior to the polyhedron which are closer to that feature than any other The Voronoi regions form a partition of space outside the polyhedron according to the closest feature The collection of Voronoi... includes a list of its boundary, coboundary, and Voronoi regions de ned later in Sec 2. 1.4 15 HE Left Face Right Face E TE Figure 2. 1: A winged edge representation In addition, we will use the word above" and beneath" to describe the relationship between a point and a face In the homogeneous representation where a point P is presented as a vector Px ; Py ; Pz ; 1 and F 's normalized unit outward normal... proximity problem in R is to partition the plane into regions, each of these is the set of the points which are closer to a point pi 2 S than any other If we know this partitioning, then we can solve the problem of proximity directly by a simple query The partition is based on the set of closest points, e.g bisectors which have 2 or 3 closest points Given two points pi and pj , the set of points closer... v where f, e, v stands for the total number of faces, edges, vertices respectively Each feature except vertex is an open subset of an a ne plane and does not contain its boundary This implies the following relationships: fi = A; i = 1; : : :; n fi fj = ;; i 6= j 1 De nition: B is in the boundary of F and F is in coboundary of B , if and only if B is in the closure of F , i.e B F and B has one fewer... earlier animation and simulation systems are restricted to polyhedral models However, modeling with surfaces bounded by linear boundaries poses a serious restriction in these systems Our contact determination algorithms for curved objects are applicable on objects described using spline representations B zier and e B-spline patches and algebraic surfaces These representations can be used as primitives for. .. rotation as well as translational components of the motion with respect to the origin The collision detection algorithm is based only on local features of the polyhedra or control polytope of spline patches and does not require the position of the other features to be updated for the purpose of collision detection at every instant ... HE , TE = Hx , Tx; Hy , Ty ; Hz , TZ ; 0 where HE and TE e are the head and tail of the edge E respectively An edge E points into a face F , ~
NF 0 e An edge E is parallel to a face F , ~
NF = 0 e An edge E points out of a face F , ~
NF 0 e 16 2. 1.3 Voronoi Diagram The proximity problem, i.e given a set S of N points in R , for each point pi 2 S what is the set of points x; y in the plane that... The class of parametric and implicit surfaces described in terms of piecewise polynomial equations is currently considered the state of the art for modeling applications 35, 46 These include free-form surfaces described using spline patches, primitive objects like polyhedra, quadrics surfaces like cones, ellipsoids, 18 torus and their combinations obtained using CSG operations For arbitrary curved... Sec.3 .2 are established based upon the Voronoi regions If a point P on object A lies inside the Voronoi region of fB on object B , then fB is a closest feature to the point P More details will be presented in Chapter 3. In Chapter 3, we will describe our incremental distance computation algorithm which utilizes the concept of Voronoi regions and the properties of convex polyhedra to perform collision . x0 y0 w2 h1" alt=""