Homogeneous coordinates in computer graphics ppt

Data: 3.09.2017 / Rating: 4.7 / Views: 594

---

Gallery of Video:

---

Gallery of Images:

---

Homogeneous coordinates in computer graphics ppt

Graphics Systems, Video Display Devices, Refresh Cathode Ray Tubes, Raster Scan Displays, Color CRT Monitors, Direct View Storage Devices, Flat Panel Displays, Plasma. UnitIII PPT Slides Text Books: 1. Computer Computer Graphics Principles point in 2D gives this coordinate system its name homogeneous coordinates. Projective geometry view volume 2D device coordinates Clipped world Computer graphics treats all projections the from homogeneous coordinates. Homogeneous Coordinates and Computer Graphics Tom Davis November 20, 2001 The relationship between. Homogeneous Coordinates In order to represent a translation as a matrix multiplication operation we use 3 x 3 matrices and pad our points to become 3 x 1 matrices. This coordinate system (using three values to represent a 2D point) is called homogeneous coordinates. CS348a: Computer Graphics Handout# 15 1 Why homogeneous coordinates? # 2: Geometry Homogeneous Coordinates. CSE167: Computer Graphics Instructor: Ronen Barzel UCSD, Winter 2006. Homography 3D TRANSFORMATIONS 1. Homogeneous coordinates in 3 dimensions A point in homogeneous coordinates Microsoft PowerPoint L63dtrans. ppt Outline Twodimensional computer graphics Translation necessary but nonlinear Homogeneous coordinates Affine geometry and spaces Frames Computer Graphics Shmuel Wimer Bar Ilan April 2010 Homogeneous Coordinates April 2010 2D Scaling Homogeneous Coordinates PowerPoint Presentation. Transformations Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts University of New Mexico Angel: Interactive Computer. 3D projection Transformations in 2 Dimensions Van Dam, Feiner, and Hughes, Computer Graphics Homogeneous Coordinates in 2 Dimensions. Lecture 3: Coordinate Systems and Transformations rich enough for use in computer graphics. homogeneous representations of the same point or vector with. transformation does not depend on the choice of homogeneous coordinates for a given point. A transformation of the projective space is a mapping M. Projective space Not using homogeneous coordinates may make it hard to use strongly optimized hardware to its fullest. Whatever program recognizes that optimized instructions of the hardware can be used (typically a compiler but things are more complicated sometimes) for homogeneous coordinates will have a hard time with optimizing for other representations. Viewpoint Projections and Specifications Feiner, and Hughes, Computer Graphics Extend 3D coordinates to homogeneous coordinates Homogeneous Coordinates. One of the many purposes of using homogeneous coordinates is to capture the concept of infinity. In the Euclidean coordinate system, infinity is something that does not exist. Mathematicians have discovered that many geometric concepts and computations can be greatly simplified if the concept of infinity is used. Transformations Translation, Rotation, Scale Composite transformations 2 Homogeneous Coordinates Homogeneous coordinates are key to all computer graphics systems Homogeneous coordinates are very useful and fundamental concept in computer graphics. If the homogeneous coordinates of a point are multiplied by a nonzero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infinity, the number of coordinates required to allow this extension is one more than the dimension of the projective space being considered.

---

Related Images:

---