9-Transformations

9-Transformations - Modeling Transformations Jason Lawrence...

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Unformatted text preview: Modeling Transformations Jason Lawrence CS 4810: Graphics Acknowledgment: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David Dobkin Overview 2D Transformations Basic 2D transformations Matrix representation Matrix composition 3D Transformations Basic 3D transformations Same as 2D Simple 2D Transformations Translation x y P P Simple 2D Transformations Translation x y Simple 2D Transformations Scale x z y Simple 2D Transformation Rotation x z y 2D Modeling Transformations Scale Rotate Translate Scale Translate x y World Coordinates Modeling Coordinates 2D Modeling Transformations x y World Coordinates Modeling Coordinates Let s look at this in detail 2D Modeling Transformations x y Modeling Coordinates 2D Modeling Transformations x y Modeling Coordinates Scale .3, .3 Rotate -90 Translate 5, 3 2D Modeling Transformations x y Modeling Coordinates Scale .3, .3 Rotate -90 Translate 5, 3 2D Modeling Transformations x y Modeling Coordinates Scale .3, .3 Rotate -90 Translate 3, 5 World Coordinates Basic 2D Transformations Translation: x = x + tx y = y + ty Scale: x = x * sx y = y * sy Rotation: x = x*cos - y*sin y = x*sin + y*cos Transformations can be combined (with simple algebra) Basic 2D Transformations Translation: x = x + tx y = y + ty Scale: x = x * sx y = y * sy Rotation: x = x*cos - y*sin y = x*sin + y*cos Basic 2D Transformations Translation: x = x + tx y = y + ty Scale: x = x * sx y = y * sy Rotation: x = x*cos - y*sin y = x*sin + y*cos x = x *sx y = y *sy (x,y) (x ,y ) Basic 2D Transformations Translation: x = x + tx y = y + ty Scale: x = x * sx y = y * sy Rotation: x = x *cos - y *sin y = x *sin + y *cos (x ,y ) x = (x*sx) *cos (y*sy) *sin y = (x*sx) *sin + (y*sy) *cos Basic 2D Transformations Translation: x = x + tx y = y + ty Scale: x...
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9-Transformations - Modeling Transformations Jason Lawrence...

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