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Unformatted text preview: Advanced Computer Graphics Computer Animation Implicit Surfaces Professor Brogan Many slides from Brian Wyvills online materials at U. Calgary Papers for Tuesday Spacetime Constraints, Witkin and Kass Siggraph Deepwater Animation and Rendering Gamasutra.com, Sept 26, 2001 Implicit Surfaces Surfaces defined by points that satisfy f(P) = 0 Implicit Function Example, a circle Parametric x=r cos( ) y=r sin( ) Implicit x 2 + y 2 + r 2 = 0 Implicit Surface Modeling Useful for modeling natural and smooth/organic synthetic phenomena Living forms, liquids, clouds Each primitive is represented by a skeletal element which contributes in defining a scalar field Every point in space is assigned a scalar value equal to shortest distance to a skeletal element Implicit Surface Modeling Simplest skeletal element is a point A (distance) contour of that point defines the (surface of the) model Ex: two points approach and their contours blend Combining Skeletal Primitives Blending Skeletal Elements Define a simple surface as: A central point, C A radius of influence, R A density function, f() A threshold value, T All points, P, for which dist (P, C) < R Implicit surface = f (dist(P, C)) T = 0 Blending Skeletal Elements Example: metaballs f(dist) = Surface drawn where f(dist) T = 0 Surface drawn at this radius Value of T Blending Skeletal Elements Example: two metaballs Surface drawn where: f(dist 1 ) + f(dist 2 ) T = 0 Do we draw surface here?...
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 Fall '10
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 Computer Graphics

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