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Lecture10-Viewing-I

# Lecture10-Viewing-I - CS 455 Computer Graphics Viewing...

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CS 455 – Computer Graphics Viewing Transformations I

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Motivation Want to see our “virtual” 3-D world on a 2-D screen

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Graphics Pipeline Model Space World Space Eye/Camera Space Screen Space Model Transformations Viewing Transformation Projection & Window Transformation
Viewing Transformations Projection: take a point from m dimensions to n dimensions where n < m There are essentially two types of viewing transforms: Orthographic: parallel projection - Points project directly onto the view plane - In eye/camera space (after viewing tranformation) : drop z Perspective: convergent projection - Points project through the origin onto the view plane - In eye/camera space (after viewing tranformation) : divide by z

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Parallel Projections We will deal only with Orthographic Projection direction is parallel to projection plane normal Center of projection (COP) is at infinity Projectors from COP are parallel Parallel lines remain parallel All angles are preserved for faces parallel to the projection plane Center of projection at infinity p 1 p 2 p 1 p 2 Projectors
Points project orthogonally onto (i.e., normal to) the view plane: Projection lines are parallel Orthographic Projection x y z

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Projection Environment x y z The view plane is in the xy plane and passes through the origin The view direction is parallel to the z axis The eyepoint or camera position is on the +z axis, a distance d from the origin We will use a right-handed view system d
Parallel Projection x y z What is (x’, y’, z’)? A point in 3-space projects onto the viewplane via a projector which is parallel to the z axis (x, y, z) (x’, y’, z’)

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Parallel Projection x z (x, y, z) So z’ = 0, x’ = x Looking down the y axis: (x’, y’, z’)
Parallel Projection y z (x, y, z) So y’ = y Looking down the x axis: (x’, y’, z’)

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Parallel Projection Thus, for parallel, orthographic projections, x’ = x, y’ = y, z’ = 0
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Lecture10-Viewing-I - CS 455 Computer Graphics Viewing...

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