Non-Uniform Rational B-SplinesNURBS

NURBS Surfaces

NURBS surfaces are based on curves. The main advantage of using NURBS surfaces over polygons, is that NURBS surfaces can create smoother surfaces with less control points. NURBS Surfaces are especially suited for creating organic smoothed surfaces. Besides using primitives, NURBS models are generally constructed by creating curves that will define the profile or shape of an object.

NURBS Curves

Control Vertices or CV’s control the shape a curve by pulling the curve out from a straight line. They are the most basic means of controlling NURBS surfaces. In Maya, the first CV or endpoint of a curve is drawn as a box and the second CV is drawn as a “U”. Each additional CV is a dot.

Control Vertices – control points that edit the shape of a curve

Edit Points – reside on a curve, they are defined by the shape of the curve

NURBS Primitives

NURBS primitives available in Maya.

NURBS

•Control Vertex – the control points for NURBS surfaces. They define the shapes of the curves that make up a surface.

•Isoparm – Curves that run across NURBS surfaces, they are constructed by control vertices.

•Hull – A ring or row of control vertices, they are useful when manipulating multiple control vertices

NURBS

Hulls are made up of “rings” of consecutive control vertices that are connected with straight lines. Hulls allow modelers to move entire rings of cv’s by just selecting the corresponding hull. Hulls run in both directions.

NURBS

Isoparms are the lines that run across a NURBS surface. A surface patch is the area created by intersecting isoparms.

NURBS

•Lofted Surface

•Revolved Surface

•Extruded Surface

•Planar Surface

•Boundary Surface

Surface deformation on a NURBS surface is based on the the interpolation of curves. NURBS surfaces are able to create smooth curved surfaces with less control points than polygon modeling. NURBS surfaces are often created by connecting curves in different methods.

NURBS – Lofted Surface

A lofted surface is created by spanning two or more curves . More detailed lofted surfaces are created by spanning multiple curves to create more complex surfaces.

NURBS – Revolved Surface

A revolved surface is created by revolving a profile curve around an axis or point to create a surface. The profile curve is drawn to create a profile of the desired object.

NURBS – Extruded Surface

An extruded surface is created by “sweeping” a profile curve along a path curve.

NURBS – Planar Surface

A planar surface is created by forming a 2D plane with a boundary defined by a curve. A planar surface can also be formed with multiple curves to form planar surfaces with holes.

NURBS – Boundary Surface

A boundary surface is defined by three or four curves that serve as edges.

Subdivision Surfaces

Subdivision surfaces are based on refined polygon meshes. Subdivision surfaces are created by smoothing polygon meshes using a refinement algorithm such as the Catmull Clark Subdivision scheme.

Catmull-Clark Subdivision Scheme

The smooth operation in Maya applies the Catmull-Clark Subdivision scheme to polygon models. When the Catmull-Clark subdivision scheme is applied to a polygon mesh a face point is created in the center of all faces, and an edge point is placed at the center of all edges. The Catmull-Clark subdivision scheme produces only quadrilaterals which is extremely useful when texturing..

Doo-Sabin Subdivision Scheme

The Doo-Sabin subdivision scheme produces only valence 4 vertices.

Subdivision Surfaces Primitives

Sub-D primitives available in Maya.

Subdivision Surfaces

• Subdivision surfaces can have arbitrary topology (non-quad faces) like polygon objects. NURBS surfaces are always constructed with four sided patches.

• Subdivision surfaces provide shape control similar to NURBS surfaces.

• Subdivision surfaces are “heavier” that NURBS surfaces and polygon objects. This

Hierarchical Subdivision Surfaces

Hierarchical subdivision surfaces contain levels of detail that allow modelers to add more detail to areas of increased surface variation(like creases) and allow the modeler to reduce detail is other regions (like flat areas). In Maya all subdivision surface objects are hierarchical subdivision surfaces.