NURBS Curves and Surfaces

NURBS is Non-Uniform Rational B-Spline

Any NURBS object is a four-sided patch. It can be shaped to take on various forms, but it always remains four-sided. NURBS objects can be defined by up to four contour or any number of profile curves.

NURBS surfaces are parameterized, because it is easy to assign a coordinate space to a four-sided patch. Their UV space is also parameterized. NURBS are used for

1. Models with many simple precisely shaped elements: a bird cage, a baby crib, a ship.(See NURBScage.mb in Resources/models)
2. In product design NURBS patches are used for making high-precision models based on blueprints.
3. Procedural models.(http://www.theverymany.net/)
4. Large continuous surfaces, such as fields and terrains, fabric (curtains, simple fabric shape (not true cloth simulation), etc)
5. Organic-looking smooth complex surfaces, made out of multiple patches. (NURBShead.mb)

NURBS Curve
- starts and ends on a control point
- has direction
- is parameterized
- must have at least four control vertices

Anatomy of a NURBS Curve:

Control Vertex (Vertices) –points that lie outside the curve, allow for manipulation with continuity/smoothness
Edit Point(s) – knots (little crosses) that lie on the curve, allow for manipulation with precision
Control Points - points placed on the curve by the user, in order to specify location on the curve (for the purpose of inserting knots, cutting or detaching the curve, etc)
Hull(s) - a line that connects Control Vertices, effect the entire range of the curve

NURBS Curve Tools:

1. CV curve tool – place Control Vertices , Edit Points will be created accordingly.
2. EP curves – create Edit Points, Control Vertices will be created automatically.
3. Pencil Tool- Edit Points are created automatically as you draw the curve.
4. Arc Tools.
5. Create NURBS/ Circle and Square.

Editing Curves:

- Creating sharp angles in a cubic curve by overlapping consecutive CVs or creating a 1degree curve and a 3 degree curve and attaching them
- Attaching and Detaching Curve
- Aligning Curve
- Reversing Curve Direction
- Opening and Closing Curves
- Inserting Knots
- Rebuilding Curve
- Duplicating Surface Curve

Drawing Curves on 3d surfaces:

Modify/Make Live
Project Curve on Surface

Curves are used in animation as motion paths

NURBS Surfaces

Anatomy of a NURBS Surface:

Control Vertices – can move, rotate and scale (Additional selecting by pressing arrow keys on the keyboard)
Hulls – can move, rotate and scale, effect a row of CVs at a time
Surface Point- cannot transform, used for inserting isoparms
Surface Patch- cannot transform, can duplicate via Edit NURBS/Duplicate NURBS Patches
Isoparm – cannot transform, used for detaching surfaces, stiching edges, etc.

NURBS models smoothness display keyboard buttons:
1 – linear mode
3 – cubic mode
these display modes effect only the way NURBS are displayed in viewports, NOT in renders

Creating simple NURBS models/patches:

1. Primitives
2. Revolve(editing curve vs editing model, getting rid of a "pin cushion effect by inserting isoparms)
3. Extrude
4. Loft – for best results use cross sections (curves), with same direction and same number and approximate location of EPs (knots)). Achieve that by either copying and modifying the same curve, or Rebuilding Curve with Match Knots option.
- cross section selection order;
- curves direction;
- open vs closed loft;

5. Planar Surface
6. Extrude and Birail.
7. Boundary and Square.
8. Bevel and Bevel Plus.
9. Trimmed surfaces.

Continuity: positional and tangent. Breaking tangent continuity.

Tutorials and Readings:

-NURBS theory PDF in Resources folder

1. Help/Tutorials/Modeling/NURBS
2. Start/Programs/Maya Learning Tools/NURBS Modeling

NurbsToPoly.pdf in Resources/NURBS