Introduction to Computer Graphics

A Brief History of the Internet - sites.cs.ucsb.edu

This history revolves around four distinct aspects. There is the technological evolution that began with early research on packet switching and the ARPANET (and related technologies), and

Closest Pair Problem

Subhash Suri UC Santa Barbara 1-Dimension Problem † 1D problem can be solved in O(nlogn) via sorting. † Sorting, however, does not generalize to higher dimensions. So, let’s develop a divide-and-conquer for 1D. † Divide the points S into two sets S1;S2 by some x-coordinate so that p < q for all p 2 S1 and q 2 S2. † Recursively compute closest pair (p1;p2) in S1 and (q1;q2) in …

Software development activities

Waterfall Model l The classic: l Step after step, after step, … l Never back up . Alternatives to waterfall model l Okay, we all agree – this extreme doesn’t ... l Specify the way objects will behave and interact l Tie to other systems/tools as necessary – Implement and test l Complete at least 1 more iteration ...

  Waterfall

The Levenberg-Marquardt Algorithm

algorithm is rst shown to be a blend of vanilla gradient descent and Gauss-Newton iteration. Subsequently, another perspective on the algorithm is provided by considering it as a trust-region method. 2 The Problem The problem for which the LM algorithm provides a solution is called Nonlinear Least Squares Minimization. This implies that the ...

  Methods, Newton, Gauss

COORDINATE TRANSFORMATIONS IN SURVEYING

In 2D transformations all points lie in a plane. In these notes it is assumed that 2D transformations are transformations from one rectangular coordinate system (u,v) to another rectangular system (x,y). In addition, unless stated otherwise, a rotation is an angle considered to be positive in an

  Transformation, 2d transformations

Lie Groups for 2D and 3D Transformations - Ethan Eade

May 20, 2017 · Lie Groups for 2D and 3D Transformations Ethan Eade Updated May 20, 2017 * 1 Introduction This document derives useful formulae for working with the Lie groups that represent transformations in 2D and 3D space. A Lie group is a topological group that is also a smooth manifold, with some other nice properties.

  Transformation, Group, Lie group

Affine Transformations - Clemson University

C.2 AFFINE TRANSFORMATIONS Let us first examine the affine transforms in 2D space, where it is easy to illustrate them with diagrams, then later we will look at the affines in 3D. Consider a point x = (x;y). Affine transformations of x are all transforms that can be written x0= " ax+ by+ c dx+ ey+ f #; where a through f are scalars. x c f x´

  Transformation, Affine, Affine transformations

7 - Linear Transformations

Linear transformations are defined as functions between vector spaces which preserve addition and multiplication. This is sufficient to insure that th ey preserve additional aspects of the spaces as well as the result below shows. Theorem Suppose that T: V 6 W is a linear transformation and denote the zeros of V and W by 0v and 0w, respectively.

  Transformation

Geometric Transformations: Warping, Registration, …

T(N+1,1:N).T has both forward and inverse transformations. N=2 for 2D image transformation2D image transformation 0 In MATLABnotation b 1 0 1 0 0 0 2 2 1 1 T T a b a b a T b A Geometric TransformationGeometric Transformation EL512 Image ProcessingEL512 Image Processing 15 15

  Registration, Transformation, Geometric, Warping, Geometric transformations

2D Transformations

2D Transformation Given a 2D object, transformation is to change the object’s Position (translation) Size (scaling) Orientation (rotation) Shapes (shear) Apply a sequence of matrix multiplication to the object vertices

  Transformation, 2d transformations

11.1 Camera matrix - Carnegie Mellon University

2D image point What do you think the dimensions are? A camera is a mapping between the 3D world and a 2D image. x = PX 2 4 X Y Z 3 5 = 2 4 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 p 12 3 5 2 6 ... so you need the know the transformations between them. P = 2 4 f 0 px 0 fpy 00 1 3 5 2 4 1000 0100 0010 3 5 P = K[I|0] Can be decomposed into ...

  Transformation