# Procedural Spline Interpolation in UNICUBIX

### Carlo H. Séquin

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-87-321

January 1987

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/CSD-87-321.pdf

UNICUBIX is an extension to the Berkeley UNIGRAFIX modeling and rendering system. The original system, restricted to polyhedral object, is extended by permitting cubic curves in place of the previous linear edges between pairs or vertices, and triangular or quadrilateral patches between such curved borders. Where desired, the patches are joined together with
*G*-continuity using procedures that guarantee locality of control.

A sequence of procedural steps determines first the vertex normals, then the Bezier control points for the curved edges, and finally the internal control points for all patches. These steps use an intuitive geometric approach to fitting spline curves and surfaces through the given set of vertices. A variety of rules and procedures makes it possible to provide pleasing default values for even difficult situations. There are no restrictions on the topology of the original polyhedral net defining the shape of the object.

BibTeX citation:

@techreport{Séquin:CSD-87-321, Author = {Séquin, Carlo H.}, Title = {Procedural Spline Interpolation in UNICUBIX}, Institution = {EECS Department, University of California, Berkeley}, Year = {1987}, Month = {Jan}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/6004.html}, Number = {UCB/CSD-87-321}, Abstract = {UNICUBIX is an extension to the Berkeley UNIGRAFIX modeling and rendering system. The original system, restricted to polyhedral object, is extended by permitting cubic curves in place of the previous linear edges between pairs or vertices, and triangular or quadrilateral patches between such curved borders. Where desired, the patches are joined together with <i>G</i>-continuity using procedures that guarantee locality of control. <p> A sequence of procedural steps determines first the vertex normals, then the Bezier control points for the curved edges, and finally the internal control points for all patches. These steps use an intuitive geometric approach to fitting spline curves and surfaces through the given set of vertices. A variety of rules and procedures makes it possible to provide pleasing default values for even difficult situations. There are no restrictions on the topology of the original polyhedral net defining the shape of the object.} }

EndNote citation:

%0 Report %A Séquin, Carlo H. %T Procedural Spline Interpolation in UNICUBIX %I EECS Department, University of California, Berkeley %D 1987 %@ UCB/CSD-87-321 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/6004.html %F Séquin:CSD-87-321