G. Farin and D. Hansford. Agnostic G1 Gregory Surfaces. Graphical Models. To appear.
Abstract: A new class of Gregory surfaces, including both rectanular and triangular ones.
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.
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.
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
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.
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.
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.
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.
Abstract: We discuss 2D and 3D Bezier curves with monotone curvature and torsion, generalizing a characterization given by Y. Mineur et al.
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.
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.
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.
Z. Xie, G. Farin: Image Registration Using Hierarchical B-Splines. IEEE Transactions on Visualization and Computer Graphics 10(1): 85-94. 2004
download
G. Farin. History of Curves and Surfaces in CAGD. In: G. Farin, J. Hoschek, and MS Kim, editors. Handbook of CAGD. Elsevier, 2002. , pp. 1-22.
Abstract: We present the most important developments in the field of CAGD.
G. Farin. Shape. In B. Engquist and W. Schmid, editors, Mathematics Unlimited - 2001 and Beyond, pp. 463-477, Springer-Verlag, 2001 .
Abstract: A survey of shape related methods in CAGD.
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.
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.
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.