PPT-Concave and Convex

MIRRORS Concave Mirrors A con cave mirror has a surface that curves inward like a cave or a bowl It follows the law of reflection however when parallel light rays approach a curved surface and strike at different points on the curve each ray will reflect at a slightly different direction . Problems in Ramsey theory typically ask a question of the form: "how many elements of some structure must there be to guarantee that a particular property will hold?“. Here we consider geometric Ramsey-type results about finite point sets in the plane.. Given a set of points (x. 1. ,y. 1. ),(x. 2. ,y. 2. ),…,(x. n. ,y. n. ), the . convex hull. is the smallest convex polygon containing all the points.. Convex Hulls. Given a set of points (x. 1. ,y. relaxations. via statistical query complexity. Based on:. V. F.. , Will Perkins, Santosh . Vempala. . . On the Complexity of Random Satisfiability Problems with Planted . Solutions.. STOC 2015. V. F.. Lenses. A . convex lens. (or a . converging lens. ) converges parallel light rays passing through it.. Various shapes of convex lenses. Terms for describing lenses. Optical centre. is the centre of a lens.. Origami World. David . Fouhey. , . Abhinav. Gupta, Martial Hebert. 1. 2. 3. Local Evidence. 4. Hoiem. et al. 2005, . Saxena. et al. 2005, . Fouhey. et al. 2013, etc.. Constraints. 5. Constraints for Single Image 3D. Section 6.2. Learning Goal. We will use our knowledge of the characteristics. of solids so that we can match a convex. polyhedron to its net. We’ll know we’ve got it. when we’re able to create a net for a given solid.. for Sequential Game Solving. Overview. Sequence-form transformation. Bilinear saddle-point problems. EGT/Mirror . prox. Smoothing techniques for sequential games. Sampling techniques. Some experimental results. S4P1 Students will investigate the nature of light using tools such as mirrors, lenses, and prisms. ..  . c. . Identify the physical attributes of a convex lens, a concave lens, and a prism and where each is used. . Properties & Attributes. A . few polygons. Triangle. Quadrilateral (much more on these later). Pentagon. Hexagon. Heptagon. Octagon. Regular. . polygons . are . both . equilateral. and . equiangular. http://. www.robots.ox.ac.uk. /~oval/. Slides available online http://. mpawankumar.info. Convex Sets. Convex Functions. Convex Program. Outline. Convex Set. x. 1. x. 2. λ. . x. 1. (1 - . λ. ) . Majorization. ANNA . SHTENGEL, Weizmann Institute of Science. ROI PORANNE and OLGA SORKINE-HORNUNG, ETH Zurich. SHAHAR Z. KOVALSKY, Duke University. YARON LIPMAN, Weizmann Institute of . Science. ACM Transactions on Graphics . Converging Lens = Convex. A . ray of light. is an extremely narrow beam of light.. All visible objects emit or reflect . light rays. in all directions.. . Our eyes detect . light rays. .. . We see images when . A planar region . . is called . convex. if and only if for any pair . of points . , . in . , the line segment . lies . completely. in . . .  . Otherwise, it is called . concave. . . Convex.  . Nicholas . Ruozzi. University of Texas at Dallas. Where We’re Going. Multivariable calculus tells us where to look for global optima, but our goal is to design algorithms that can actually find one!.