9

NURBS and Animation 1091
Note:
NSurf Sel doesn’t suppor t copy and paste
of selections as Mesh Select does. Copying and
pastingmeshselectionsisbasedonvertexindexes.
NURBS selections are based on object IDs, w hich
areuniquetoeachmodel.
NUR B S a nd A nimati on
In general, you animate NURBS curves and
NURBS sur faces by turning on the Auto Key
button and transforming sub-object attributes
such as CV or point positions, by animating
the parameters that control dependent NURBS
objects, and so on. You can’t animate N URBS
object creation or creation parameters, or
fundamental changes to NURBS geometry such
as adding or deleting CVs or points, attaching
objects, and so on.
Tip: Toimproveperformancewhileyouanimate
your scene, make the sur faces in your NU R BS
model nonrelational surfaces (page 1–1116).
Modifierstreatnonrelationalsurfacesasifthey
were independent CV sur faces: you can animate
the scene more efficiently, and then turn relational
modeling back on before you render.
Some NURBS editing operations remove
animation controllers.
Operations that R emove Animation
The following operations remove anima tion from
a NURBS object or sub-object:
•MakeIndependent
This operation removes the animation of
anything directly dependent on the object.
• Break,Extend,JoinandZip,Refine,Delete,
Rebuild, Reparameterize, Close, Make Loft,
Convert Curve, and Convert Surface
Any operation that changes the number of
points or CVs in a curve or surface remov es the
animation of all points or CVs that are lost.
•Fuse
The animation of the point or CV being fused
to the other point or CV ( the s econd one
chosen) is lost. The first point or CV acquires
the animation of the second.
NUR B S Concepts
NURBS curves and surfaces did not exist in the
traditional drafting world. They were created
specifically for 3D modeling using computers.
Curves and surfaces represent contours or shapes
within a 3D modeling space. They are constructed
mathematically. NURBS mathematics is complex,
and this section is simply an introduction to some
NURBS concepts that might help you understand
what you are creating, and why NURBS objects
behave as they do. For a comprehensive
description of the mathematics and algorithms
involved in NURBS modeling, see The NURBS
Book by Les Piegl and Wayne Tiller (New York:
Springer, second edition 1997).
Definition and Parameter Space
The term NURBS stands for Non-Uniform
Rational B-Splines. Specifically:
• Non-Uniform means that the extent of a control
vertex’s influence can vary. This is useful when
modeling irregu lar surfaces.
• Rational means that the equation used to
represent the curve or surface is expressed as a
ratio of two polynomials, rather than a single
summed polynomial. The rational equation
provides a better model of some important
cur ves and surfaces, especially conic sect ions,
cones, spheres, and so on.
•AB-spline (for basis spline) is a way to construct
a curve that is interpolated between three or
more points.