Geometric Transformations. 2D and 3D. Tuesday 10/4/2011. How do we use Geometric Transformations? (1/2). Objects in a scene are a collection of points… These objects have location, orientation, size Corresponds to transformations, Translation ( ), Rotation ( ), and Scaling ( ) .
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2D and 3D
You will need to understand these concepts!
Linear Algebra Help SessionNotes: http://cs.brown.edu/courses/cs123/resources/Linear_Algebra.pdf
= a + b
, where = , =
Side effect: House shifts position relative to origin
Some uses we’ll be seeing later
Uniform Scale 3x
Both around object’s center,
not the origin
Note: This is an arbitrary unit vector in space
armTransformations and the scene graph (1/4)
Step 1: Various transformations are applied to each of the leaves (object primitives—head, base, etc.)
Step 2: Transformations are then applied to groups of these objects as a whole (upper body, lower body)
Together this hierarchy of transformations forms the “robot” scene as a whole
object nodes (geometry)