Deforming NURBS Surfaces to Target Curves for Immersive VR Sketching

Designing NURBS surfaces by manipulating control points directly requires too much trial and error for immersive VR applications. A more natural interface is provided by deforming a NURBS surface so that it passes through a given target point; and by repeating such deformations we can make the surface follow one or more target curves. These deformations can be achieved by modifying the pseudo-inverse matrix of the basis functions, but this matrix is often ill-conditioned. However, the application of a modified FE approach to the weights and control points provides controllable deformations, which are demonstrated across a range of example shapes.

[1]  John F. Hughes,et al.  Direct manipulation of free-form deformations , 1992, SIGGRAPH.

[2]  Raffaele de Amicis,et al.  Spacedesign: a mixed reality workspace for aesthetic industrial design , 2002, Proceedings. International Symposium on Mixed and Augmented Reality.

[3]  Vincent Cheutet,et al.  3D sketching for aesthetic design using fully free-form deformation features , 2005, Comput. Graph..

[4]  Ari Rappoport,et al.  Simple constrained deformations for geometric modeling and interactive design , 1994, TOGS.

[5]  Michael F. Deering,et al.  HoloSketch: a virtual reality sketching/animation tool , 1995, TCHI.

[6]  Kenneth I. Joy,et al.  Free-form deformations with lattices of arbitrary topology , 1996, SIGGRAPH.

[7]  Oliver Bimber,et al.  A multi-layered architecture for sketch-based interaction within virtual environments , 2000, Comput. Graph..

[8]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[9]  Thomas Ertl,et al.  Deformation of finite element meshes using directly manipulated free-form deformation , 2002, SMA '02.

[10]  I. Gibson,et al.  Surface feature constraint deformation for free-form and interactive design , 1999, SMA '99.

[11]  Jia Lu,et al.  NURBS-based Galerkin method and application to skeletal muscle modeling , 2005, SPM '05.

[12]  Hans-Peter Seidel,et al.  FreeDrawer: a free-form sketching system on the responsive workbench , 2001, VRST '01.

[13]  Andrew Roberts,et al.  3-Draw: a tool for designing 3D shapes , 1991, IEEE Computer Graphics and Applications.

[14]  Pierre Leclercq,et al.  A freehand-sketch environment for architectural design supported by a multi-agent system , 2005, Comput. Graph..

[15]  Hong Qin,et al.  Free-form deformations via sketching and manipulating scalar fields , 2003, SM '03.

[16]  James Christopher Edwards,et al.  Interactive synthetic environments with force feedback , 1998 .

[17]  W. Poeschl.  B-spline finite elements and their efficiency in solving relativistic mean field equations , 1998 .

[18]  Rynson W. H. Lau,et al.  VSculpt : a distributed virtual sculpting environment for collaborative design , 2003, IEEE Trans. Multim..

[19]  Mark Meyer,et al.  Discrete Differential-Geometry Operators for Triangulated 2-Manifolds , 2002, VisMath.

[20]  D. Logan.  A First Course in the Finite Element Method , 2001 .

[21]  Sabine Coquillart,et al.  Extended free-form deformation: a sculpturing tool for 3D geometric modeling , 1990, SIGGRAPH.

[22]  Hong Qin,et al.  Dynamic NURBS with geometric constraints for interactive sculpting , 1994, TOGS.

[23]  Dae-Hyun Kim,et al.  Sketch- and constraint-based design of B-spline surfaces , 2002, SMA '02.

[24]  Michael Garland,et al.  Mesh Modelling with Curve Analogies , 2004, PG.

[25]  K. Höllig.  Finite element methods with B-splines , 1987 .

[26]  Manuel Contero,et al.  A survey on geometrical reconstruction as a core technology to sketch-based modeling , 2005, Comput. Graph..

[27]  Peter Schröder,et al.  Surface drawing: creating organic 3D shapes with the hand and tangible tools , 2001, CHI.

[28]  Gershon Elber,et al.  Inferring 3D models from freehand sketches and constraints , 1997, Comput. Aided Des..

[29]  Daehyun Kim,et al.  A new modeling interface for the pen-input displays , 2006, Comput. Aided Des..