Graphics Reference
In-Depth Information
Fig. 14.3
Comparison of how the same shape would be built in NURBS and polygons
To make all objects out of four-sided patches requires some effort to analyze surfaces
to determine how many patches are needed and how they should be arranged.
Working with NURBS is always a two-step process. First, you have to make the
curves. Next, you build the surface. In polygons, you just move the polygons or their
vertices. This is one of the reasons why simple objects made from linear segments
are built in polygons. The more complex an object's curve defi nition is, the better
justifi ed NURBS become.
NURBS must satisfy certain conditions that are irrelevant to polygonal modeling
(Fig.
14.3
). Their direction must be correct or surfaces built from them may be
twisted, their knot defi nitions must be correct, or they may have unwanted kinks (or
not enough). It is not enough for the endpoints of two curves to be coincident, they
must be tangent as well or there will be a visible tangent break between surfaces.
14.1.3
Genus
The
genus
of a surface describes its topological complexity based on the number of
enclosed loops in the object (Fig.
14.4
). A periodic sphere is genus 0 because it has
no loops. A torus is genus 1 because it has one loop. A genus 2 surface looks like a
pair of tori that have been welded together to form a double loop. Each successively
higher genus value represents the addition of another loop. High genus models are
more complicated to make with NURBS patches than lower order genus patches
due to the patch layout complexity at branch locations.
14.1.4
Non-editable Values
NURBS objects contain non-editable values that artists familiar with polygon editing
might be surprised by. The principal non-editable values are:
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