# Symmetric Interpolation of Triangular and Quadrilateral Patches Between Cubic Boundaries

### Leon A. Shirman

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-87-319

December 1986

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/CSD-87-319.pdf

In her Master's Project, Lucia Longhi [Longhi '85] has implemented an exploratory program, called uci, for interpolating triangular Gregory patches between cubic boundaries. This work is a continuation of the research in the area of smooth surface interpolation.

First, a symmetric version of the polygon tessellating program, ugtese [Gigus '85], has been developed. It splits faces of a polygon into bilaterally symmetric convex parts. Second, uci has been extended to include quadrilateral Gregory patches; this reduces the occurrence of asymmetric creases in the interpolating surfaces. Third, several new approaches are discussed to represent the surface with Bezier and Gregory patches and to determine the corresponding control vertices. Fourth, a method for subdivision of triangular Gregory patches into Bezier patches is described.

BibTeX citation:

@techreport{Shirman:CSD-87-319, Author = {Shirman, Leon A.}, Title = {Symmetric Interpolation of Triangular and Quadrilateral Patches Between Cubic Boundaries}, Institution = {EECS Department, University of California, Berkeley}, Year = {1986}, Month = {Dec}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/6005.html}, Number = {UCB/CSD-87-319}, Abstract = {In her Master's Project, Lucia Longhi [Longhi '85] has implemented an exploratory program, called uci, for interpolating triangular Gregory patches between cubic boundaries. This work is a continuation of the research in the area of smooth surface interpolation. <p> First, a symmetric version of the polygon tessellating program, ugtese [Gigus '85], has been developed. It splits faces of a polygon into bilaterally symmetric convex parts. Second, uci has been extended to include quadrilateral Gregory patches; this reduces the occurrence of asymmetric creases in the interpolating surfaces. Third, several new approaches are discussed to represent the surface with Bezier and Gregory patches and to determine the corresponding control vertices. Fourth, a method for subdivision of triangular Gregory patches into Bezier patches is described.} }

EndNote citation:

%0 Report %A Shirman, Leon A. %T Symmetric Interpolation of Triangular and Quadrilateral Patches Between Cubic Boundaries %I EECS Department, University of California, Berkeley %D 1986 %@ UCB/CSD-87-319 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/6005.html %F Shirman:CSD-87-319