Graphics Reference
In-Depth Information
Fig. 14.5 The power of NURBS is its ability to interpolate curvature between control points.
If you use more than are needed, the likelihood of a distorted curve is increased
those same curves. Curves allow the construction of extremely complex shapes with
resolution-independent accuracy. The degree of precision and fl exibility afforded by
NURBS curves is not equaled in polygonal models.
14.2.1
Curve Components
14.2.1.1
Control Vertices
Control vertices (CVs) are used to infl uence the shape of a curve. CVs are not
embedded in a curve the way a vertex is part of an edge. Instead, although they may
lie directly over the curve they modify, they can also be located anywhere else.
Their distance and position exerts a magnetic infl uence on the shape of the curve
they belong to based on their weight .
14.2.1.2
Degrees
NURBS curves come in a variety of degrees . A one-degree curve is a perfectly
straight line because it has only two control points. To make it into a two-degree
curve, a third control point is inserted between its start and end points. This allows
the new CV to infl uence the curve shape. For greater control, a fourth control point
may be added (Fig. 14.6 ). This would be a three-degree curve. Three-degree curves
are used for curves that must be made tangent with another curve or surface. This is
because tangency requires one CV on either side of a pair of endpoints. For manu-
facturable objects, fi ve to seven degree curves are used to control the accuracy of the
surfaces at a higher level.
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