Review of numerical methods for ODEs Numerical Methods for PDEs Spring 2007. Jim E. Jones. References: Numerical Analysis, Burden & Faires Scientific Computing: An Introductory Survey, Heath. Ordinary Differential Equation: Initial Value Problem (IVP).By shadow
ACM Solid and Physical Modeling Conference, 2006. Generalized Penetration Depth Computation. http://gamma.cs.unc.edu/pdg. Liang-Jun Zhang Gokul Varadhan Dinesh Manocha Dept of Computer Sci. University of North Carolina Chapel Hill, USA. Young J. Kim Dept of Computer Sci.By mary-gilmore
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4. 5. 3. 6. 2. 1. 0. Convex Hull. Given a set of pins on a pinboard And a rubber band around them How does the rubber band look when it snaps tight? We represent the convex hull as the sequence of points on the convex hull polygon, in counter-clockwise order. A. B.
Convex Lenses. Thicker in the center than edges. Lens that converges (brings together) light rays. Forms real images and virtual images depending on position of the object. The Magnifier. Concave Lenses. Lenses that are thicker at the edges and thinner in the center.
CONVEX POLYTOPES. Gleb Kodinets. GALE TRANSFORM. GALE TRANSFORM. בדומה לטרנספורם דואלי טרנספורם גאיל מעביר קונפיגורציה גאומטרית אחד לקונפיגורציה גאומטרית אחרת. המציאו אותו כדי ללמוד יותר את פאונים הקמורים ממימד גבוה יותר טוב.
Convex Combinations. Suppose we have data n observations for t variables ( x 1 , x 2 , …, x t ). Observation j ’s data are represented by ( x 1j , x 2j , …, x tj ). A convex combination of the data points is given by:. Notes. The γ cannot be negative. The sum of the γ must equal 1.
Convex Programming. Brookes Vision Reading Group. Huh?. What is convex ??? What is programming ??? What is convex programming ???. Huh?. What is convex ??? What is programming ??? What is convex programming ???. Convex Function. f(t x + (1-t) y) <= t f(x) + (1-t) f(y). Convex Function.
Convex Relaxations. May 2, 2004. Ben Recht. Outline. Lagrangian Duality Linear Programming and Combinatorics Non-convex quadratic programming Positivstellensatz and Polynomial Programming. Lagrangian Duality. General Problem. Lagrangian Duality. General Problem Lagrangian:.
smallest convex set containing all the points. Convex hull. smallest convex set containing all the points. Convex hull. smallest convex set containing all the points. Convex hull. 3. 2. start = 1. 1.next = 2 = 3.prev 2.next = 3 = 4.prev 3.next = 4 = 1.prev 4.next = 1 = 2.prev.
Example : An object 3 cm high is placed 20 cm from (a) a convex and (b) a concave spherical mirror, each of 10 cm focal length. Determine the position and nature of the image in each case. a) Convex. S = 20 cm h o = 3 cm f = -10 cm. behind mirror (virtual image). (image is upright).
Convex Mirrors. Convex Mirrors. Convex Mirror. F and C are behind mirror. 2. Principle Rays – Same as in Concave Mirrors. Always remember that when locating an image – ALL RAYS ORIGINATE FROM THE OBJECT!. Convex Mirrors Focal Point. For convex mirrors: