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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 Wyvill’s 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( α ) • y=r sin( α ) – 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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