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This article explores the use of implicit surfaces and subdivision surfaces in computer animation. It discusses methods for defining object surfaces using equations, as well as techniques for deforming and animating plant-like structures. The article also introduces various approaches for refining object geometry and describes the properties of limit surfaces.
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Computer AnimationAlgorithms and Techniques Special Models
Implicit Surfaces Defines object surface by all points satisfying equation f(x,y,z) = 0 e.g., x2+y2+z2 - r2 = 0 Often, distance functions using threshold, T e.g., sqrt((x-cx)2+ (y-cy)2+ (z-cz)2) = T Complex surfaces by summation f1(x,y,z) + f2(x,y,z) + ... + fn(x,y,z) = T
Implicit as distance from polyhedra Convex easier to compute than concave
Plant and plant-like structures Botany L-systems geometric interpretation turtle graphics Animating plant growth
Botany stems roots buds leaves flowers http://visual.merriam-webster.com/plants-gardening/plants/plant/structure-plant.php
Subdivision surfaces Refine object geometry Various strategies Keep original vertices? Properties of limit surface? Type of input object? triangles only? See: http://www.holmes3d.net/graphics/subdivision/
Catmull-Clark subdivision Corner-cutting method http://en.wikipedia.org/wiki/Subdivision_surface
Loop subdivision displaces old vertices, mid-points of edges & faces http://en.wikipedia.org/wiki/Loop_subdivision_surface
