25xcos90 025ysin905 y1 025xsin90 025ycos903

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Unformatted text preview: (x’, y’) (x, y) θ φ Trig Identity… x’ = r cos(φ) cos(θ) – r sin(φ) sin(θ) y’ = r sin(φ) sin(θ) + r cos(φ) cos(θ) Substitute… x’ = x cos(θ) - y sin(θ) y’ = x sin(θ) + y cos(θ) 14 2- D Rota:on (x’, y’) (x, y) θ x’ = x cos(θ) - y sin(θ) y’ = x sin(θ) + y cos(θ) 15 Basic 2D Transforma:ons •  Transla:on: –  x’ = x + tx –  y’ = y + ty •  Scale: –  x’ = x * sx –  y’ = y * sy •  Rota:on: –  x’ = x*cosΘ - y*sinΘ –  y’ = x*sinΘ + y*cosΘ 16 Basic 2D Transforma:ons •  Transla:on: –  x’ = x + tx –  y’ = y + ty •  Scale: –  x’ = x * sx –  y’ = y * sy •  Rota:on: –  x’ = x*cosΘ - y*sinΘ –  y’ = x*sinΘ + y*cosΘ X1 = 0.25*x Y1 = 0.25*y 17 Basic 2D Transforma:ons •  Transla:on: –  x’ = x + tx –  y’ = y + ty •  Scale: –  x’ = x * sx –  y’ = y * sy •  Rota:on: –  x’ = x*cosΘ...
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This note was uploaded on 03/19/2013 for the course CSC 101 taught by Professor Merl during the Fall '12 term at Arizona State University at the West Campus.

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