PPT-Curves and Surfaces from 3-D Matrices

Dan Dreibelbis University of North Florida Richard Goals What is a 3D matrix Vector multiplication with a tensor Geometric objects from tensors Motivation Pretty pictures Richards work. Positive de64257nite matrices ar e even bet ter Symmetric matrices A symmetric matrix is one for which A T If a matrix has some special pr operty eg its a Markov matrix its eigenvalues and eigenvectors ar e likely to have special pr operties as we 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 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. M. Ramanathan. Department of Engineering Design,. IIT Madras. http://. ed.iitm.ac.in. /~. raman. Medial object workshop, Cambridge. 0. Various skeletons. Curve skeletons. Mid-surface. Chordal. axis transform (CAT). 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. Honors Advanced Algebra II/Trigonometry. Ms. . lee. Essential. Stuff. Essential Question: What is a matrix, and how do we perform mathematical operations on matrices?. Essential Vocabulary:. Matrix. Overview. 3D Shape Primitives:. Points. Vertices.. Curves. Lines, polylines, curves.. Surfaces. Triangle meshes, splines, subdivision surfaces, implicit surfaces, particles.. Solids. Basic Shapes. Fundamental Shapes. 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.. Matrix Multiplication. Matrix multiplication is defined differently than matrix addition. The matrices need not be of the same dimension. Multiplication of the elements will involve both multiplication and addition. Objectives: to represent translations and dilations w/ matrices. : to represent reflections and rotations with matrices. Objectives. Translations & Dilations w/ Matrices. Reflections & Rotations w/ Matrices. RASWG 12/02/2019. Jan Uythoven, Andrea Apollonio, . Miriam Blumenschein . Risk Matrices. Used in RIRE method. Reliability Requirements and Initial Risk . Estimation (RIRE). Developed by Miriam Blumenschein (TE-MPE-MI). MATRICES. Una matriz es todo arreglo rectangular de números reales . . definidos en filas y/o columnas entre paréntesis o corchetes. Así tenemos:. NOTACION MATRICIAL. . Las matrices se denotan por letras mayúsculas y los elemento se designan con . Rotation of coordinates -the rotation matrixStokes Parameters and unpolarizedlight1916 -20041819 -1903Hans Mueller1900 -1965yyxyEEEElinear arbitrary anglepolarization right or left circularpolarizati This Slideshow was developed to accompany the textbook. Precalculus. By Richard Wright. https://www.andrews.edu/~rwright/Precalculus-RLW/Text/TOC.html. Some examples and diagrams are taken from the textbook..