Lecture 1 - Projections and Transformations (slides)

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

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

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