lecture03-1

lecture03-1 - CS 551/651 Advanced Graphics Technical...

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CS 551/651 Advanced Graphics Technical Background

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FLTK Hopefully you downloaded and compiled successfully Questions Assignment 1 – Warmup Interactive B-Spline Editor Due two weeks from today
Topics you should know Object, world, camera coord spaces Lookat point, up vector, angle of view, near/far clipping planes, view frustum Homogeneous coords Transformation matrices Rendering pipeline

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Affine Transformations A transformation that preserves Angles Lengths Parallel lines Ex Translation Rotation Scaling Reflection Shear
Round-off Errors Consider rotating a polygonal model about y-axis x z • Moon = Rot y (5) Moon • Moon = Rot y (5) Rot y (5) Moon • Moon = Rot y (n) Moon

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Orthonormalization All rows of transformation matrix must: Have unit length Be orthogonal to one another • Row 1 dot Row 2 = 0 One technique to orthonormalize Normalize row 1 (excluding last column) • Row 1 x Row 2 = Row 3 (normalize) • Row 3 x Row 1 = Row 2 (normalize) Errors were shifted in matrix
Rotations Give me four rotation representations 3x3 matrix Euler Angles Axis-angle Quaternion - Interpolation - Gimbal Lock - Compiling Rot Seqs and their shortcomings…

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Representing 3 Rotational DOFs 3x3 Matrix (9 DOFs) Rows of matrix define orthogonal axes Euler Angles (3 DOFs) Rot x + Rot y + Rot z Axis-angle (4 DOFs) Axis of rotation + Rotation amount Quaternion (4 DOFs) 4 dimensional complex numbers
Rotation Matrix 9 DOFs must reduce to 3 Rows must be unit length (-3 DOFs) Rows must be orthogonal (-3 DOFs) Drifting matrices is very bad Numerical errors results when trying to gradually

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This note was uploaded on 01/23/2012 for the course CS 551 taught by Professor Staff during the Fall '10 term at Syracuse.

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lecture03-1 - CS 551/651 Advanced Graphics Technical...

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