B.Sc. Multimedia Computing3D Modelling and Animation

Nurbs Modelling

NURBS

NURBS in an acronym for Non-Uniform Rational B-Splines

Non-Uniform refers to the parameterization of the curve. Non-Uniform curves allow the presence of multi-knots, which are needed to represent Bezier curves.

Rational refers to the underlying mathematical representation. This property allows NURBS to represent conics (parabolas, circles, and ellipses) in addition to free-form curves.

B-splines are sectional polynomial curves that have a parametric representation.

The Historical Origins of NURBS

Splines are types of curves, originally developed for ship building where naval architects needed a way to produce a smooth curve through a set of points.

The solution was to place metal weights (knots) at the control points, and bend a thin metal or wooden beam (spline) through the weights.

Spline Knots

Anatomy of a NURBS Curve

First VertexSpan

Knots and Edit Points

Control Vertices

HullsCurve Point

Nurbs Sphere: Object Mode

Isoparms

Nurbs Sphere: CVs

Nurbs Sphere: Hulls

Nurbs Sphere: Add Isoparm

Line follows mouse cursor New Isoparm added

Nurbs Scooter

Using NURBS Geometry

NURBS geometry is ideally for representing smooth-flowingsurfaces and provide an organic quality to the surface contours.There are many NURBS primitives shapes available in MAYA.These can be combined with each other to form more sophisticatedgeometry and may also be combined with other geometry such aspolygons to form composite geometry for modeling tasks.

e.g NURBS aircraft fuselage and polygon wing structures