lecture21

lecture21 - Advanced Computer Graphics Computer Animation...

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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 Deep-water 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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lecture21 - Advanced Computer Graphics Computer Animation...

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