44 lines
858 B
Markdown
44 lines
858 B
Markdown
---
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layout: math
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title: Environment
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---
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## Affine Transforms & Vector Math
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<!-- ASCIImath -->
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Matrix multiplication
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$
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[[a, b, c], [d, e, f], [g, h, i]] [[x], [y], [z]] = [[ax + by + cz], [dx + ey + fz], [gx + hy + iz]]
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$
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Translation
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$
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[[1, 0, tx], [0, 1, ty], [0, 0, 1]] [[x], [y], [1]] = [[dot x], [dot y], [1]]
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$
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Scaling
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$
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[[sx, 0, 0], [0, sy, 0], [0, 0, 1]] [[x], [y], [1]] = [[dot x], [dot y], [1]]
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$
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Rotation $theta$
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$
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[[cos theta, -sin theta, 0], [sin theta, cos theta, 0], [0, 0, 1]] [[x], [y], [1]] = [[dot x], [dot y], [1]]
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$
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Shearing
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$
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[[1, shx, 0], [shy, 1, 0], [0, 0, 1]] [[x], [y], [1]] = [[dot x], [dot y], [1]]
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$
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Affine Transform (Translation + Scaling + Rotation + Shearing)
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$
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[[sx * cos theta, -sin theta * shx, tx], [sin theta * shy, sy * cos theta, ty], [0, 0, 1]] [[x], [y], [1]] = [[dot x], [dot y], [1]]
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$
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