lect04_PointsVectors - Points and Vectors Same...

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1 CSE452 Lecture 4: Points, Vectors and shapes Slide 1 CSE452 Computer Graphics Lecture 4: Points, Vectors and Shapes CSE452 Lecture 4: Points, Vectors and shapes Slide 2 Points and Vectors Points and Vectors Same representation Different meaning: Point: a fixed location (relative to {0,0}) Vector: a direction and length can be translated to anywhere 8 x, y <H or 8 x, y, z <L x Y p = 8 1, 2 < 1 2 v = 8 1, 2 < p = 8 2, 2 < 2 CSE452 Lecture 4: Points, Vectors and shapes Slide 3 Point Operations Point Operations Subtraction Result is a vector Addition with a vector Result is a point Can two points add? Not yet… p 1 p 2 v p1 + v = p2 = 9 p1 x + vx,p1 y + vy = p2 p1 = v = 9 p2 x p1 x ,p2 y p1 y = CSE452 Lecture 4: Points, Vectors and shapes Slide 4 Vector Operations Vector Operations Addition/Subtraction Result is a vector Scaling Result is a vector Magnitude A unit vector : v1 ± v2 = 9 v1 x ± v2 x ,v1 y ± v2 y = s v = 8 s vx,s vy < v1 v2 1 + 2 v1 v2 » v » = " vx 2 + vy 2 v s v » v » = 1 CSE452 Lecture 4: Points, Vectors and shapes Slide 5 Vector Operations Vector Operations Dot product Result is a scalar In coordinates v 1 v 2 = » v 1 »» v 2 » Cos @ α D v1 v2 = v1 x v2 x + v1 y v2 y v 1 v 2 α CSE452 Lecture 4: Points, Vectors and shapes Slide 6 Vector Operations Vector Operations Uses of dot products Computing angle between vectors Parallel : Orthogonal
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This note was uploaded on 03/03/2010 for the course CSE 451 taught by Professor Xu during the Spring '10 term at Washington University in St. Louis.

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lect04_PointsVectors - Points and Vectors Same...

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