NURBS Extension for VRML97

Discussion & Node proposal
12 March 1999

updated 15 Nov 1999

Background	Clauses	Annexes
Introduction	1 Concepts	References
	2 Proposed Nodes	API's and Libraries
	3 Conclusion	Tools
		Examples

Introduction

This paper describes new nodes proposed for VRML97, based on Non Uniform Rational B-Splines (NURBS). In general, use of NURBS in VRML would have the following immediate benefits:

reduced download size of VRML files because of the compact NURBS description
smoother, richer shapes
easier authoring, because most 3D modeling programs are already NURBS-based
better animation, since changing a few parameters has a great impact on shapes and animations
automatic scalability of the display (LOD) depending on CPU and graphics card performance and world complexity.

NURBS curves and surfaces have been used in industrial design of car bodies, ship hulls and airplanes for a long time since their mathematical qualities are especially suited for modeling fluid shapes. Designing with NURBS is intuitive and easy to understand. Hence, numerous tools beyond CAD/CAM offer NURBS support. The success of NURBS throughout CAD/CAM/CAE and CGI in general is due to the following:

Any desired shape can be described using NURBS without loss of mathematical exactness. While shapes like cylinders or conics can only be approximated by polygons, NURBS give an exact mathematical description.
Intuitive methods to design and manipulate any desired shape are provided by various tools.
NURBS algorithms are fast and stable.

Therefore adopting NURBS support in a VRML environment seems to be a self-evident step that would yield a number of benefits:

Creating virtual worlds in VRML is always a trade-off between quality (number of defined polygons) and bandwidth (download size of a world). Smooth surfaces are created by exporting huge VRML IndexedFaceSets from modeling programs. Objects defined in the NURBS format overcome these limitations because smoothness is obtained with very little data without loss of quality.
The VRML authoring process is accelerated since NURBS offer intuitive methods for designing objects, especially natural shapes like human bodies.
The smoothness and curvature can be easily controlled and manipulated.
Scalability of the rendering system can be realized through dynamic tessellation. Depending on client CPU and 3D graphics system performance, the level of detail (LOD) of the rendered NURBS model can be adapted so that reasonable frame rates can be achieved on any system.
Morphing, i.e. animation of single points of a surface, is realized with minimal effort by an easy-to-understand method. Animating single control points and altering weight values results in naturally flowing movements.
Using NURBS based splines for interpolation of positions along a curve could reduce VRML file size for many types of animation.

The mathematical background required to work with NURBS is not very complex. There are many toolsthat can assist in the creation and editing of NURBS surfaces. A good introduction to NURBS is given in [1]. A thorough mathematical study on NURBS can be found in [2].

References

[1] http://devworld.apple.com/dev/techsupport/develop/issue25/schneider.html
[2] The NURBS Book, Les Piegl and Wayne Tiller, Springer 1997
[3] Open Inventor C++ Reference Manual: The Official Reference Document for Open Inventor, Release 2, Open Inventor Architecture Group, Addison-Wesley, 1994.

Some Tools supporting NURBS

[1] Kinetix 3D Studio Max
[2] Rhino3D
[3] TGS Amapi
[4] Alias|Wavefront Maya

API's or libraries supporting NURBS

VRML Java Nurbs package from Timothy F. Rohaly http://www.ocnus.com/NURBS/.
This package contains a general set of classes written in Java to represent and manipulate NURBS.
In addition to a NurbsSurface PROTO a NurbsCurve and NurbsRevolve PROTO is implemented.

OpenGL contains in the glu extensions package NURBS Curve & Surface Primitives.
A surface can optionally be trimmed by a NURBS Curve or a piece wise linear curve.

Open Inventor has the SoNurbsSurface node.

Example C Source code for evaluating Points on a NurbsCurve or NurbsSurface based on the NURBS Book.