Lecture_Chapter3_b

Lecture_Chapter3_b - Review of Tuesday We have learnt how...

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Review of Tuesday We have learnt how to rasterize lines and fill polygons Colors (and other attributes) are specified at vertices Interpolation required to fill polygon with attributes 26 ECS 175 Chapter 3: Object Representation
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Review of Tuesday Mathematical formulation: Given (“positions” and “values”) Find function defined on such that We required our solutions to be linear functions 27 ECS 175 Chapter 3: Object Representation ( x i ,f i ) f f ( x i )= f i [ x 0 ,x n ]
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Interpolation: Linear Linear interpolation 28 ECS 175 Chapter 3: Object Representation Parametric function takes the form Values between u 0 and u 1 are “ mixtures ” of f 0 and f 1 f ( u )=(1 u ) f 0 + uf 1 u =0 . 2 80% f 0 + 20% f 1 Control points are weighted/blended together
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Interpolation: Linear Basis functions/Blending functions/Weights 29 ECS 175 Chapter 3: Object Representation control point contributions are blended together partition of unity (1 u )+ u =1 f ( u )= i b i ( u ) · f i f ( u )=(1 u ) f 0 + uf 1 f ( u b 0 ( u ) · f 0 + b 1 ( u ) · f 1 weights sum up to one
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What about colors? Linear interpolation (component-wise) 30 ECS 175 Chapter 3: Object Representation f RGB ( t )=( f R ( t ) ,f G ( t ) B ( t ))
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What about colors? Linear interpolation across triangle Can we construct function as mixture of corner vertices? 31 ECS 175 Chapter 3: Object Representation f ( α 0 1 2 )= α 0 · f 0 + α 1 · f 1 + α 2 · f 2
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What about colors? Barycentric interpolation across triangle 32 ECS 175 Chapter 3: Object Representation convex combination f ( p )= α 0 f 0 + α 1 f 1 + α 2 f 2 α 0 + α 1 + α 2 =1 0 α 0 1 2 1 Compute weights (barycentric coordinates ) Interpolate values p = α 0 p 0 + α 1 p 1 + α 2 p 2
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What about colors?
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Lecture_Chapter3_b - Review of Tuesday We have learnt how...

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