Lecture_Chapter4_a

Defines how local coordinates are expressed in world

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Unformatted text preview: is an object defined? •  Vectors define object in a local coordinate system ECS 175 Chapter 4: Object Transformation 19 How is an object transformed? •  Our “world” uses one coordinate system to describe all objects – the world coordinate system (world frame). •  To translate, rotate, scale (etc.) an object, we perform a coordinate transformation on the local coordinate system. Defines how local coordinates are expressed in world coordinates. ECS 175 Chapter 4: Object Transformation 20 Simple Example: Isotropic scaling •  Example: Scale the object by x2 in all directions world frame local frame object in world frame (note that there appears to be a translation as well) vworld = 2 · vlocal ECS 175 Chapter 4: Object Transformation 21 A Brief Review of Linear Algebra •  Matrix: Linear transformation of vectors ￿ ￿￿ ￿ ￿ ￿ 10 a a = 01 b b identity 2 0 isotropic (uniform) scaling ￿ ￿￿ ￿ ￿ ￿ 0 a 2a = 2 b 2b Linearity M (u + v ) = M u + M v M (sv ) = sM v Not commutative M Av ￿= AM v ECS 175 Chapter 4: Objec...
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This document was uploaded on 03/12/2014 for the course ECS 175 at UC Davis.

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