G. Farin and D. Hansford
Agnostic G1 Gregory Surfaces
Graphical Models, vol 74, pp. 346-350, 2012

Abstract: A new class of Gregory surfaces, including both rectanular and triangular ones.

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G. Farin
The Shape of Triangles
IEEE Transactions on Visualization and Computer Graphics 16(1), pp. 43-47, 2012

Abstract: Shape measures, including one using singular values of a linear map associated with a triangle.

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K. Müller, Ch. Fünfzig, L. Reusche, D. Hansford, G.E. Farin, H. Hagen
Double insertion, nonuniform, stationary subdivision surfaces
ACM Transactions of Graphics 29(3), 2010

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A. Constantiniu, P. Steinmann, T. Bobach, G. Farin, H. Hagen
The Adaptive Delaunay Tessellation: a neighborhood covering meshing technique
Computational Mechanics 42(5), pp. 655-669. 2008

Abstract: A generalization of Delaunay triangulations which also contains general polygons

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G. Farin
Geometric Hermite Interpolation with Circular Precision
Computer Aided Design 40(4): 476-479, 2008

Abstract: A description of rational cubic interpolants capable of reproducing circular arcs.

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G. Farin
Rational Quadratic Circles are Chord Length Parametrized
Computer Aided Geometric Design 23(9): 722-724. 2006

Abstract: A short note showing that circular arcs in rational quadratic form have chord length as their paprameter.

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G. Farin
Dimensions of Spline Spaces over Unconstricted Triangulations
J. Computational and Applied Mathematics 192(2): 320-327. 2006

Abstract: The dimension of general piecewise polynomial function spaces over arbitrary triangulations is not known. If we restrict the type of triangulation, a specialized result may be found.

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A. Huang, G. Nielson, A. Razdan, G. Farin, P. Baluch, and D. Capco
Thin Structure Segmentation and Visualization in Three-Dimensional Biomedical Images: A Shape-Based Approach
IEEE Transactions Visualization and Comp. Graphics (12)1: 93-102. 2006

Abstract: We present a method for extracting thin structures from 3D data sets.

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G. Farin
Class A Bezier Curves
Computer Aided Geometric Design 23(7): 573-571. 2006

Abstract: We discuss 2D and 3D Bezier curves with monotone curvature and torsion, generalizing a characterization given by Y. Mineur et al.

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G. Farin
Rational Quadratic Circles are Chord Length Parametrized
Computer Aided Geometric Design 23(9): 722-724. 2006

Abstract: We show that circular arcs which are represented as rational Bezier curves have chord length as their parameter.

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L. Zhang, A. Razdan, G. Farin, J. Femiani, M. Bae, C. Lockwood
3D face authentication and recognition based on bilateral symmetry analysis
The Visual Computer 22(1): 43-55. 2006

Abstract: We present a method for 3D face recognition and authentication. Its most salient feature is the extraction of the face symmetry line.

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G. Stylianou and G. Farin
Crest Lines for Surface Segmentation and Flattening
IEEE Transactions on Visualization and Computer Graphics 10(5): 536-544, 2004

Abstract: We show how crest lines may be utilized for geometry extraction.

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Z. Xie, G. Farin
Image Registration Using Hierarchical B-Splines
IEEE Transactions on Visualization and Computer Graphics 10(1): 85-94, 2004

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G. Farin
History of Curves and Surfaces in CAGD
In Handbook of CAGD,
G. Farin, J. Hoschek, and MS Kim, editors, pp. 1-22, Elsevier, 2002

Abstract: We present the most important developments in the field of CAGD.

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G. Farin
Shape
In Mathematics Unlimited - 2001 and Beyond,
B. Engquist and W. Schmid, editors, pp. 463-477, Springer-Verlag, 2001

Abstract: A survey of shape related methods in CAGD.

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G. Fain and D. Holliday
A geometric interpretation of the diagonal of a tensor-product Bézier volume
Computer Aided Geometric Design, 16:837-840, 1999

Abstract: A geometric interpretation of the diagonal of a tensor-product trivariate Bézier volume is given.

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G. Farin and D. Hansford
Discrete Coons patches
Computer Aided Geometric Design, 16(7):671-689, 1999

Abstract: We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles.

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L. Gross and G. Farin
A transfinite form of Sibson's interpolant
Discrete Applied Mathematics, 93:33-50, 1999

Abstract: We present a version of Sibson's scattered data interpolant where the data are continuous functions instead of just discrete data.

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