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Modeling II
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Spline surfaces
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Spline patch (very general form: NURBS patch) (demo in Cinema 4D and in
Maya)
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Trim curves to create non-quadrangular shapes (demo in Maya)
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Used in computer-aided engineering (cars, planes, machines, ...)
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Problem: How to stitch patches together without holes or creases?
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Subdivision surfaces
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Start with a polyhedron and apply a smoothing subdivision method an adjustable
number of times
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There are lots
of different subdivision algorithms, but everbody uses that of Catmull
and Clark, which is one of the two oldest subdivision methods. The standard
subdivision algorithms let the result converge to a smooth "limit surface".
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Advantadges: only polygons for modeling and rendering; no problems with
stitching (actually, only not so obvious problems); number of polygons
adjustable
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Used in character animation and game production
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The terms used for subdivision surfaces in 3D software such as HyperNurbs
or NURMS are misleading. However, one can mathematically prove for many
types of subdivision algorithms that their limit surfaces could precisely
be formed from spline surfaces---however, only with a most complex stiching.
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Implicit surfaces (also known as isosurfaces or as equipotential surfaces)
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Don't define a surface explicitly as a mapping (u,v) |---> x(u,v),
but implicitly as the set of all x such that f(x)
= 0 for a given function f. For instance, f(x) := |x|2-4
will produce a sphere (that is, its surface, not its interior) of radius
2 around the origin.
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Standard use: metaballs (demo with Cinema 4D)
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Voxels
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Build 3D objects as solids using small cubical volume elements ("voxels")
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Very memory-intensive if applied without precautions
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Often used for "volumetric" rendering, for instance semitransparent clouds
or fire balls with inner structure
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Points
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Basic idea: We have several millions of pixels on the screen. Why throw
hundreds
of millions of polygons at them? Store, edit, and render point clouds instead:
"point-based rendering"
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Demo: Pointshop3D