# Interpolating Patches Between Cubic Boundaries

### Lucia L. Longhi

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-87-313

December 1985

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/CSD-87-313.pdf

We describe the theoretical frame for a method of creating and describing rounded objects of arbitrary topology in CAD, and its implementation for UNIGRAFIX, a polygon-based modeler developed at UC Berkeley that generates black-and-white, smooth-shaded images on several output devices. The mathematical foundation for building triangular patches interpolating cubic edges and blending with geometric continuity is given, and various approaches are discussed. To represent curvature information, we extended the UNIGRAFIX language to UniCubix, and we implemented uci, an interactive shell that interprets a UniCubix description and converts it into UNIGRAFIX wireframes or polyhedral nets that approximate curved patches. Uci also provides a prototype of a global smoothing operation, that takes a polyhedral object of arbitrary topology and creates the UniCubix representation of a smooth object interpolating the input vertices.

BibTeX citation:

@techreport{Longhi:CSD-87-313, Author = {Longhi, Lucia L.}, Title = {Interpolating Patches Between Cubic Boundaries}, Institution = {EECS Department, University of California, Berkeley}, Year = {1985}, Month = {Dec}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1985/6007.html}, Number = {UCB/CSD-87-313}, Abstract = {We describe the theoretical frame for a method of creating and describing rounded objects of arbitrary topology in CAD, and its implementation for UNIGRAFIX, a polygon-based modeler developed at UC Berkeley that generates black-and-white, smooth-shaded images on several output devices. The mathematical foundation for building triangular patches interpolating cubic edges and blending with geometric continuity is given, and various approaches are discussed. To represent curvature information, we extended the UNIGRAFIX language to UniCubix, and we implemented uci, an interactive shell that interprets a UniCubix description and converts it into UNIGRAFIX wireframes or polyhedral nets that approximate curved patches. Uci also provides a prototype of a global smoothing operation, that takes a polyhedral object of arbitrary topology and creates the UniCubix representation of a smooth object interpolating the input vertices.} }

EndNote citation:

%0 Report %A Longhi, Lucia L. %T Interpolating Patches Between Cubic Boundaries %I EECS Department, University of California, Berkeley %D 1985 %@ UCB/CSD-87-313 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1985/6007.html %F Longhi:CSD-87-313