Research

Brush handle design
An application of surface skinning with candidate knots

Number of cross sections = 81
Points per cross section >= 10 and <= 48
Number of control points after merging = (81 x 48)
Number of control points in regular skinning = (81 x 1455)
Savings as compared to regular skinning = 96.7%

Dr. Piegl's research centers around the general area of geometric and numerical computing. It includes such specific fields as geometric modeling, compute graphics, computational geometry, computer-aided design and manufacturing, algorithms and data structures, and software engineering with particular emphasis on commercial-grade and large-scale software design. His research projects include:

Representation of curves and surfaces for CAD
Research and development in NURBS-based design
Raster algorithms for plotting free-form curves
Geometry processing with emphasis on surface-surface intersection
Triangulations in 2-D and 3-D
Scattered data interpolation and digital terrain modeling
Trimmed surface tessellations
Visual perception and a new paradigm in viewing 3-D images
Applications of genetic algorithms in design
Design issues in reverse engineering

His representative journal publications are listed below:

A fast algorithm for parametric curve plotting, Computers and Graphics, Vol. 7, Nos. 3-4, 1983, pp 361-367.
Defining C^1 curves containing conic segments, Computers and Graphics, Vol. 8, No. 2, 1984, pp 177-182.
A generalization of the Bernstein-Bezier method, Computer-Aided Design, Vol. 16, No. 4, 1984, pp 209-215.
Recursive algorithms for the representation of parametric curves and surfaces, Computer-Aided Design, Vol. 17, No. 5, 1985, pp 225-229.
Representation of quadric primitives by rational polynomials, Computer Aided Geometric Design, Vol. 2, Nos. 1-3, 1985, pp 151-155.
Curve fitting for rough cutting, Computer-Aided Design, Vol. 18, No. 2, 1986, pp 79-82.
Representation of rational Bezier curves and surfaces by recursive algorithms, Computer - Aided Design, Vol. 18, No. 7, 1986, pp 361-366.
A geometric investigation of the rational Bezier scheme of Computer-Aided Design, Computers in Industry, Vol. 7, No. 5, 1986, pp 401-410.
The sphere as a rational Bezier surface, Computer Aided Geometric Design, Vol. 3, No. 1, 1986, pp 45-52.
A locally controllable spline with tension for interactive curve design, Computer Aided Geometric Design, Vol. 3, No. 1, 1986, pp 79-81.
Infinite control points - a method for representing surfaces of revolution using boundary data, IEEE Computer Graphics and Applications, Vol. 7, March, 1987, 45-55.
Interactive data interpolation by rational Bezier curves, IEEE Computer Graphics and Applications, Vol. 7, April 1987, pp 45-57.
On the use of infinite control points in CAGD, Computer Aided Geometric Design, Vol. 4, Nos. 1-2, 1987, pp 155-166.
Curve and surface constructions using rational B-splines, Computer-Aided Design, Vol. 19, No. 9, 1987, 485-498.
Less data for shapes, IEEE Computer Graphics and Applications, Vol. 7, August, 1987, pp 48-50.
A technique for smoothing scattered data with conic sections, Computers in Industry, Vol. 9, No. 3, 1987, pp 223-237.
A CAGD theme: geometric continuity and shape parameters, Computer-Aided Design, Vol. 19, No. 10, 1987, pp 566-567.
Hermite- and Coons-like interpolants using rational Bezier approximation form with infinite control points, Computer-Aided Design, Vol. 20, No. 1, 1988, pp 2-10.
Coons-type patches, Computers and Graphics, Vol. 12, No. 2, 1988, pp 221-228.
A negative experiment with univariate blending functions, Computers and Graphics, Vol. 13, No. 2, 1989, pp 217-222.
A menagerie of rational B-spline circles, IEEE Computer Graphics and Applications, Vol. 9, September, 1989, pp 48-56.
Geometric method for intersecting natural quadrics represented in trimmed surface form, Computer-Aided Design, Vol. 21, No. 4, 1989, pp 201-212.
Key developments in computer-aided geometric design, Computer-Aided Design, Vol. 21, No. 5, 1989, pp 262-274.
Modifying the shape of rational B-splines. Part 1: curves, Computer-Aided Design, Vol. 21, No. 8, 1989, pp 509-518.
Modifying the shape of rational B-splines. Part 2: surfaces, Computer-Aided Design, Vol. 21, No. 9, 1989, pp 538-546.
Algorithms for computing conic splines, ASCE Journal of Computing in Civil Engineering, Vol. 4, No. 3, 1990, pp 180-198.
On NURBS: a survey, IEEE Computer Graphics and Applications, Vol. 11, pp 55-71, January 1991.
A program development for a university course in Geometric Modeling, Computers and Graphics, Vol. 14, No. 2, 1990, pp 501-504.
Integer subdivision algorithm for rendering NURBS curves, The Visual Computer, Vol. 8, No. 3, 1992, pp 149-161.
Data reduction using cubic rational B-splines, IEEE Computer Graphics and Applications, May, pp 60-68, 1992.
Algorithm for Delaunay triangulation and convex hull computation using a sparse matrix, Computer-Aided Design, Vol. 24, No. 8, pp 425-436, 1992.
Integer De Casteljau algorithm for rasterizing NURBS curves, Computer Graphics Forum, Vol. 11, No. 2, 1992, pp 151-162.
Delaunay triangulation using a uniform grid, IEEE Computer Graphics and Applications, May, 1993, pp 36-47.
Algorithm and data structure for triangulating multiply connected polygonal domains, Computers and Graphics, Vol. 17, No. 5, pp 563-574, 1993
Algorithm for constrained Delaunay triangulation, The Visual Computer, Vol. 10, No. 5, 1994, pp 255-265.
Software engineering approach to degree elevation of B-spline curves, Computer-Aided Design, Vol. 26, No. 1, pp 17-28 , 1994.
Tessellating trimmed NURBS surfaces, Computer-Aided Design, Vol. 27, No. 1, pp 16-26, 1995.
Algorithm for degree reduction of B-spline curves, Computer-Aided Design, Vol. 27, No. 2, pp 101-110, 1995.
Delaunay triangulation in three dimensions, IEEE Computer Graphics and Applications, Vol. 15, No. 5, pp 62-69, 1995.
Procedural method for terrain surface interpolation, Computers and Graphics, Vol. 20, No. 4, pp 541-566, 1996.
Algorithm for approximate NURBS skinning, Computer-Aided Design, Vol. 28, No. 9, pp 699-706, 1996.
Symbolic operators for NURBS, Computer-Aided Design, Vol. 29, No. 5, pp 361-368, 1997
Perception of images using cylindrical mapping, The Visual Computer, Vol. 13, No. 4, pp 155-167, 1997.
Geometry-based triangulation of trimmed NURBS surfaces, Computer-Aided Design, Vol. 30, No 1, pp 11-18, 1998.
Computing the derivatives of NURBS with respect to a knot, Computer Aided Geometric Design, Vol. 15, No. 9, pp 925-934, 1998.
Curve-curve intersection via genetic algorithms, Mathematical Engineering in Industry, Vol. 7, No. 2, pp 269-282, 1998.
Approximation of offsets of NURBS curves and surfaces, Computer-Aided Design, Vol. 31, No. 2, pp 147-156, 1999.
Cross-sectional design with boundary constraints, Engineering with Computers, Vol. 15, 1999, pp 171-180.
Filling n-sided regions with NURBS patches, The Visual Computer, Vol. 15, No. 2, pp 77-89, 1999.
Reducing the number of control points in surface interpolation, IEEE Computer Graphics and Applications, Vol. 20, No. 5, 2000, pp 70-74.
Surface approximation to scanned data, The Visual Computer, Vol. 16, No. 7, 2000, pp 386-395.
Curve interpolation with arbitrary end derivatives, Engineering with computers, Vol. 16, 2000, pp 73-79.
Least-squares NURBS curve approximation with arbitrary end derivatives, Engineering with computers, Vol. 16, 2000, pp 109-116.
Algorithm for finding all k nearest neighbors, Computer Aided Design, Vol. 34, No. 2, 2002, pp 167-172.
Parametrization for surface fitting in reverse engineering, Computer-Aided Design, Vol. 33, No. 8, 2001, pp 593-603.
Surface skinning revisited, The Visual Computer, to be published.
Biarc approximation of NURBS curves, Computer-Aided Design, to be published.
Circle approximation using integral B-spline curves, Computer-Aided Design, to be published.
Fitting circular arcs to measured data, International Journal of Shape Modeling, to be published.

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