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Unformatted text preview: CS 455 – Computer Graphics Viewing Transformations I Motivation Want to see our “virtual” 3D world on a 2D screen 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 Parallel Projections • We will deal only with Orthographic (in this set of slides) § Projection direction is parallel to projection plane normal § Center of projection (COP) is at infinity § Parallel lines remain parallel § All angles are preserved for faces parallel to the projection plane Center of projection at infinity p1 p2 p1’ p2’ Projectors • Points project orthogonally onto (i.e., normal to) the view plane: § Projection lines are parallel Orthographic Projection x y z 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 righthanded view system d Parallel Projection x y z • What is (x’, y’, z’)? • A point in 3space projects onto the viewplane via a projector which is parallel to the z axis (x, y, z) (x’, y’, z’) 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’) Parallel Projection • Thus, for parallel, orthographic projections, x’ = x, y’ = y, z’ = 0 • So, to perform a parallel projection on an object,...
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 Winter '08
 Jones,M
 Cartesian Coordinate System, Euclidean geometry, Center of Projection

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