PPT-3D Projection Transformations

3D Projections Perspective and Parallel Projections Parallel Projections Orthographic and Oblique Isometric View Oblique Projections Contents 3D . 1 2D Transformations Given a point cloud polygon or sampled parametric curve w e can use transformations for several purposes 1 Change coordinate frames world window viewport devic e etc 2 Compose objects of simple parts with local scaleposition orie a 12 22 a a mn is an arbitrary matrix Rescaling The simplest types of linear transformations are rescaling maps Consider the map on corresponding to the matrix 2 0 0 3 That is 7 2 0 0 3 00 brPage 2br Shears The next simplest type of linear transfo . November 5, 2012. . Ms. Smith. Mrs. Malone. DO NOW. :. Date. : . November 5, 2012. 6.9C . demonstrate . energy transformations such as how energy in a flashlight battery changes from chemical energy to electrical energy to light energy.. of Object Features. OBJECT FEATURES. Edges. are lines that represent the boundary. between two faces. . Corners. Represent the intersection of two or. more edges.. Edge. Corner. Edge. No edge. No corner. Lecture 3. Jitendra. Malik. Pose and Shape. Rotations and reflections are examples. of orthogonal transformations . Rigid body motions. (Euclidean transformations / . isometries. ). Theorem:. Any rigid body motion can be expressed as an orthogonal transformation followed by a translation.. Camera geometry and image alignment. Josef . Sivic. http://. www.di.ens.fr. /~josef. INRIA, . WILLOW, ENS/INRIA/CNRS UMR 8548. Laboratoire. . d’Informatique. , . Ecole. . Normale. . Supérieure. map. orthographic projection. map. orthographic projection. orthographic projection. 3D Modeling by. Orthographic Projection. Classic Isometric (3/4) View. x. 0. = 0 x. 1. = 2x x. 2. = 4x x. Affine transformations . preserve. affine combinations of points. . . Affine transformations preserve lines and planes.. . Parallelism of lines and planes is preserved. . The columns of the matrix reveal the transformed coordinate frame.. Learning Targets: 8.G.2,8.G.3, 8.G.4. Follow the slides to learn more about transformations. Students should have paper and a pencil for notes at their desk while going through this presentation.. Transformation: a transformation is a change in position, shape or size.. in real life. HW: Maintenance Sheet 3 . (7-8). I can use the properties of translations, rotations, and reflections on line segments, angles, parallel lines or geometric figures. . I can show and explain two figures are congruent using transformations (explaining the series of transformations used) . What is a Parent Function. A parent function is the most basic version of an algebraic function.. Types of Parent Functions. Linear f(x) = mx b. Quadratic f(x) = x. 2. Square Root f(x) = √x. Exponential f(x) = . Stan Birchfield. MTF measures camera sharpness. Optical transfer function (OTF). Fourier transform of impulse response. Modulation transfer function (MTF). Magnitude of OTF. Spatial frequency response (SFR). CSE 455. Ali Farhadi. Many slides from Steve Seitz and Larry . Zitnick. What are geometric transformations?. Translation. Preserves: Orientation. Translation and rotation. Scale. Similarity transformations. CS5670: Computer Vision. Reading. Szeliski. : Chapter 3.6. Announcements. Project 2 out, due Thursday, March 3 by 8pm. Do be done in groups of 2 – if you need help finding a partner, try Ed Discussions or let us know.