PPT-Medial axis computation of exact curves and surfaces

M Ramanathan Department of Engineering Design IIT Madras http ediitmacin raman Medial object workshop Cambridge 0 Various skeletons Curve skeletons Midsurface Chordal axis transform CAT. The general approach is that the user enters a sequence of points and a curve is constructed whose shape closely follows this sequence The points are called control points A curve that actually passes through each control point is called an interpo Mike Stannett, University of Sheffield (m.stannett@dcs.shef.ac.uk). New Worlds of Computation, LIFO, . Orléans. , 23 May 2011. Outline of talk. Cosmological computation (what is it?). First-order relativity theories (Andréka et al.). Area. Region . R. . is bounded by the curves . y = 2 – x. 2. and . y = -x. .. Sketch region . R. .. R. What is the area of region . R. ?. Process. To find the area between curves:. Sketch the region defined in the problem.. Module 1. Session Topics. Surfaces and Solids of Revolution. Degree of Revolution. Hollow Objects. Visualizing Revolution. Surfaces and Solids of Revolution. Surfaces and Solids of Revolution are formed when a 2-D shape is revolved about an axis. M. . Ramanathan. Problems in curves and surfaces. Simple problems. Given a point . p. and a parametric curve . C(t), . find the minimum distance between . p . and. C(t). Problems in curves and surfaces. Grassfire . Transform on Medial Axes of 2D Shapes. Tao . Ju. , Lu Liu. Washington University in St. Louis. Erin Chambers, David . Letscher. St. Louis University. Medial axis. The set of interior points with two or more closest points on the boundary. Axis. Wenping. Wang. The University of Hong Kong. Properties of Medial Axis Transform. Medial representation of a shape. First proposed by Blum (1967) – the set of centers and radii of inscribed maximal circles. Moira Chas from Stony Brook University. King Abdul- Aziz University. Spring 2012. Example of surface without boundary. 2. 3. Example of surface without boundary. Example of surface . with . boundary. Definitions MAS. Properties MAS. CAD models TJC. The challenges for computing TJC. CAD models and B-reps. Industrial models are held as a. boundary representation. Edges are bounded by vertices. Faces are bounded by edges. RhinoCAM - MILL. RhinoCAM - MILL . is a 3D solid/surface/STL milling . module of RhinoCAM that . includes 2-1/2 Axis, 3 Axis, full rotary 4 axis and 5 axis milling, drilling & free post processors.. UNIT V. Introduction. Objects in the real world may not always be made up of regular geometric shapes.. Surfaces are made up of curved surfaces & curved edges.. Curves are quite complicated to represent them in exact mathematical equations.. Yufeng Wu. University of Connecticut. DIMACS Workshop on Algorithmics in Human Population-Genomics, 2009. 1. Coalescent Likelihood. D: . a set of binary sequences.. Coalescent genealogy: history with . Tao . Ju. , Lu Liu. Washington University in St. Louis. Erin Chambers, David . Letscher. St. Louis University. Medial axis. The set of interior points with two or more closest points on the boundary. Vor. (S) is the locus of centers of maximum empty disks.. Vor. (S) is the set of “meeting points” if the plane is burned uniformly and simultaneously from every site of S.. Consider the boundary of a convex polygon P as the source of fire. The meeting points inside P realize the medial axis..