lecture03-1

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

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 551/651 Advanced Graphics Technical Background
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
FLTK Hopefully you downloaded and compiled successfully Questions Assignment 1 – Warmup Interactive B-Spline Editor Due two weeks from today
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Affine Transformations A transformation that preserves Angles Lengths Parallel lines Ex Translation Rotation Scaling Reflection Shear
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 6
Rotations Give me four rotation representations 3x3 matrix Euler Angles Axis-angle Quaternion - Interpolation - Gimbal Lock - Compiling Rot Seqs and their shortcomings…
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 8
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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 33

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

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online