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Modeling II
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Constructive Solid Geometry (CSG)
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Construct complex 3D objects using Boolean operations on primitives
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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. Important
is to have a subdivion algorithm that lets 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 terminology "HyperNURBS" of Cinema 4D for subdivision surfaces is misleading.
However, one can 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 explicitely as a mapping (u,v) |---> x(u,v),
but implicitely 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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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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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