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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
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
b identity 2
0 isotropic (uniform) scaling
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.
- Spring '08