Advanced Computer Graphics CS32310 October 2012 H Holstein.

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Presentation transcript:

Advanced Computer Graphics CS32310 October 2012 H Holstein

Coordinate Systems Mapping of points in space to tuple numbers Existence of inverse mapping René Descartes D space 3 mutually perpendicular axes: x,y,z Right handed convention User defined position of origin and axis orientation

Distance from the origin O A B

Vectors (3D) The displacement of a point P ( a x, a y, a z ) from the origin O defines a vector a = [ a x, a y, a z ] Ordered 3-tuple. Magnitude and direction, but location unspecified. A B a

Laws of Algebra (for the field of real numbers R)

Laws of Vector Algebra

L E A R N !!

x y z rule!