Sketch- and constraint-based design of B-spline surfaces

This paper describes a sketch- and constraint-based approach to editing of free-form curves and surfaces. We present a simple touch-and-replace technique to edit 2D and 3D curves. We introduce auxiliary surfaces that allow for a reliable interpretation of users' pen-strokes in 3D and we present a new method for sketch-and constraint-based surface sculpting.

[1]  Günther Greiner,et al.  Variational Design and Fairing of Spline Surfaces , 1994, Comput. Graph. Forum.

[2]  J. A. Gregory.  Geometric continuity , 1989 .

[3]  Hans-Peter Seidel,et al.  Fair Surface Reconstruction Using Quadratic Functionals , 1995, Comput. Graph. Forum.

[4]  Hans-Peter Seidel,et al.  Automatic Modeling of Smooth Spline Surfaces , 1997 .

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  Beat D. Brüderlin,et al.  Computing Curve-Surface Incidence Constraints Efficiently , 1998 .

[7]  Larry L. Schumaker,et al.  On Generalized Cross Validation for Tensor Smoothing Splines , 1990, SIAM J. Sci. Comput..

[8]  Richard H. Bartels,et al.  Constraint-based curve manipulation , 1993, IEEE Computer Graphics and Applications.

[9]  Hans-Peter Seidel,et al.  Knot insertion from a blossoming point of view , 1988, Comput. Aided Geom. Des..

[10]  Cindy Grimm,et al.  A Framework for Synchronized Editing of Multiple Curve Representations , 1998, Comput. Graph. Forum.

[11]  Beat D. Brüderlin,et al.  A Constraint-Based Shape Modeling System , 1998 .

[12]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[13]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[14]  Beat D. Brüderlin,et al.  A Constraint-Based Method for Sculpting Free-Form Surfaces , 1999, Geometric Modelling.

[15]  Andrew P. Witkin,et al.  Variational surface modeling , 1992, SIGGRAPH.

[16]  Beat D. Brüderlin,et al.  Declarative Geometric Modeling with Constraints , 2000, CAD.

[17]  Gerald Farin,et al.  Curves and surfaces for cagd , 1992 .

[18]  George Celniker,et al.  Linear constraints for deformable non-uniform B-spline surfaces , 1992, I3D '92.

[19]  I. Gibson,et al.  A New Approach for Direct Manipulation of Free‐Form Curve , 1998, Comput. Graph. Forum.

[20]  Ron Goldman,et al.  Functional composition algorithms via blossoming , 1993, TOGS.

[21]  Shigeo Takahashi,et al.  Variational design of curves and surfaces using multiresolution constraints , 1998, The Visual Computer.

[22]  Philip J. Schneider,et al.  An algorithm for automatically fitting digitized curves , 1990 .

[23]  Thomas Baudel,et al.  A mark-based interaction paradigm for free-hand drawing , 1994, UIST '94.

[24]  Elaine Cohen,et al.  Chapter 7: An Envelope Approach to a Sketching Editor for Hierarchical Free-form Curve Design and Modification , 1992, Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces.

[25]  Thesis,et al.  Filleting and Rounding using Trimmed Tensor Product Surfaces , 1987 .

[26]  Hans Hagen,et al.  Variational Surface Design and Surface Interrogation , 1993, Comput. Graph. Forum.

[27]  Hans-Peter Seidel,et al.  Computing B-spline control points , 1989 .