Lecture 1 - Projections and Transformations (slides)

# Graphics lecture 1 slide 51 x r cos y r sin r

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: trices Byθ bout each of the axes ByBy✓aabout each of the axes ! ✓ about each of the axes Graphics Lecture 1: Slide 50! 0 0 1 0 0 1 0 0 B0 cos ✓ sin ✓ B sin ✓ Rx = B 0 cos ✓ @0 Rx = B sin ✓ cos ✓ @0 sin ✓ cos ✓ 0 0 0 0 0 00 0cos ✓ 0 sin ✓ B cos ✓ 10 sin ✓ 0 B 00 1 0 Ry = B @ Ry = B sin ✓ 0 cos ✓ @ sin ✓ 0 cos ✓ 0 0 0 0 0 0 0 0✓ cos sin ✓ 0 cos ✓ s B sin ✓ cos in ✓ 00 ✓ B B sin ✓ cos ✓ 0 Rz = @ Rz = B 0 0 1 @0 0 1 0 0 0 0 0 0 1 01 0 C 0C 0C C 0A 0A 1 1 1 01 0 C 0C 0C C 0A 0A 1 1 1 01 0 C 0C 0C C 0A 0A 1 1 Example: Derivation of Rz Example: Derivation of Rz z -axis goes into page z-axis goes into page! Graphics Lecture 1: Slide 51! ✓◆ ✓ ◆ x r cos ' = y r sin ' ✓ ◆ r cos(' + ✓) ! r sin(' + ✓) ✓ ◆ r cos ' cos ✓ r sin ' sin ✓ = r cos ' sin ✓ + r sin ' cos ✓ ✓ ◆ x cos ✓ y sin ✓ = x sin ✓ + y cos ✓ ✓ ◆✓ ◆ cos ✓ sin ✓ x = sin ✓ cos ✓ y # # 0 1 cos ✓ sin ✓ 0 0 B sin ✓ cos ✓ 0 0C B C @0 0 1 0A 0 0 01 44 / 47 Rotations have a direction Rota...
View Full Document

## This document was uploaded on 03/26/2014.

Ask a homework question - tutors are online