FiberMesh: designing freeform surfaces with 3D curves

ABSTRACT

This paper presents a system for designing freeform surfaces with a collection of 3D curves. The user first creates a rough 3D model by using a sketching interface. Unlike previous sketching systems, the user-drawn strokes stay on the model surface and serve as handles for controlling the geometry. The user can add, remove, and deform these control curves easily, as if working with a 2D line drawing. The curves can have arbitrary topology; they need not be connected to each other. For a given set of curves, the system automatically constructs a smooth surface embedding by applying functional optimization. Our system provides real-time algorithms for both control curve deformation and the subsequent surface optimization. We show that one can create sophisticated models using this system, which have not yet been seen in previous sketching or functional optimization systems.

REFERENCES

• 1: 3ds MAX, 2007. Autodesk, http://www.autodesk.com/3dsmax.
• 2: Brett Allen , Brian Curless , Zoran Popović, The space of human body shapes: reconstruction and parameterization from range scans, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 3: Alexis Angelidis , Marie-Paule Cani , Geoff Wyvill , Scott King, Swirling-sweepers: constant-volume modeling, Graphical Models, v.68 n.4, p.324-332, July 2006 [doi>10.1016/j.gmod.2005.11.001]
• 4: Alexander I. Bobenko , Peter Schröder, Discrete Willmore flow, Proceedings of the third Eurographics symposium on Geometry processing, July 04-06, 2005, Vienna, Austria
• 5: Mario Botsch , Leif Kobbelt, An intuitive framework for real-time freeform modeling, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 6: Mario Botsch , Olga Sorkine, On Linear Variational Surface Deformation Methods, IEEE Transactions on Visualization and Computer Graphics, v.14 n.1, p.213-230, January 2008 [doi>10.1109/TVCG.2007.1054]
• 7: Mario Botsch , Mark Pauly , Markus Gross , Leif Kobbelt, PriMo: coupled prisms for intuitive surface modeling, Proceedings of the fourth Eurographics symposium on Geometry processing, June 26-28, 2006, Cagliari, Sardinia, Italy
• 8: Timothy A. Davis, Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method, ACM Transactions on Mathematical Software (TOMS), v.30 n.2, p.196-199, June 2004 [doi>10.1145/992200.992206]
• 9: Felippa, C., 2007. Nonlinear finite element methods. www.colorado.edu/engineering/CAS/courses.d/NFEM.d/.
• 10: Fu, H., Au, O. K.-C., and Tai, C.-L. 2007. Effective derivation of similarity transformations for implicit Laplacian mesh editing. Computer Graphics Forum 21, 1, 34--45.
• 11: Gingold, C., 2007. SPORE's magic crayons. Game Developers Conference.
• 12: Jin Huang , Xiaohan Shi , Xinguo Liu , Kun Zhou , Li-Yi Wei , Shang-Hua Teng , Hujun Bao , Baining Guo , Heung-Yeung Shum, Subspace gradient domain mesh deformation, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006
• 13: Takeo Igarashi , John F. Hughes, Smooth meshes for sketch-based freeform modeling, Proceedings of the 2003 symposium on Interactive 3D graphics, April 27-30, 2003, Monterey, California [doi>10.1145/641480.641507]
• 14: Takeo Igarashi , Satoshi Matsuoka , Hidehiko Tanaka, Teddy: a sketching interface for 3D freeform design, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.409-416, July 1999 [doi>10.1145/311535.311602]
• 15: Takeo Igarashi , Tomer Moscovich , John F. Hughes, As-rigid-as-possible shape manipulation, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 16: Levent Burak Kara , Kenji Shimada, Sketch-Based 3D-Shape Creation for Industrial Styling Design, IEEE Computer Graphics and Applications, v.27 n.1, p.60-71, January 2007 [doi>10.1109/MCG.2007.18]
• 17: Olga A. Karpenko , John F. Hughes, SmoothSketch: 3D free-form shapes from complex sketches, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006
• 18: Karpenko, O., Hughes, J. F., and Raskar, R. 2002. Free-form sketching with variational implicit surfaces. Computer Graphics Forum 21, 3, 585--594.
• 19: Leif Kobbelt , Swen Campagna , Jens Vorsatz , Hans-Peter Seidel, Interactive multi-resolution modeling on arbitrary meshes, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.105-114, July 1998 [doi>10.1145/280814.280831]
• 20: Yaron Lipman , Olga Sorkine , David Levin , Daniel Cohen-Or, Linear rotation-invariant coordinates for meshes, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 21: Lee Markosian , Jonathan M. Cohen , Thomas Crulli , John Hughes, Skin: a constructive approach to modeling free-form shapes, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.393-400, July 1999 [doi>10.1145/311535.311595]
• 22: Maxis, 2007. SPORE#8482;. Electronic Arts, www.spore.com.
• 23: Maya, 2007. Autodesk, http://www.autodesk.com/maya.
• 24: Henry P. Moreton , Carlo H. Séquin, Functional optimization for fair surface design, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.167-176, July 1992
• 25: Nealen, A., and Sorkine, O., 2007. A note on boundary constraints for linear variational surface design. Technical Report, TU Berlin.
• 26: Andrew Nealen , Olga Sorkine , Marc Alexa , Daniel Cohen-Or, A sketch-based interface for detail-preserving mesh editing, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 27: Andrew Nealen , Takeo Igarashi , Olga Sorkine , Marc Alexa, Laplacian mesh optimization, Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia, November 29-December 02, 2006, Kuala Lumpur, Malaysia [doi>10.1145/1174429.1174494]
• 28: Ronald N. Perry , Sarah F. Frisken, Kizamu: a system for sculpting digital characters, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.47-56, August 2001 [doi>10.1145/383259.383264]
• 29: S. Schaefer , J. Warren , D. Zorin, Lofting curve networks using subdivision surfaces, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, July 08-10, 2004, Nice, France [doi>10.1145/1057432.1057447]
• 30: Schmidt, R., Wyvill, B., Sousa, M., and Jorge, J. 2005. ShapeShop: Sketch-based solid modeling with blobtrees. In Eurographics Workshop on Sketch-Based Interfaces and Modeling, 53--62.
• 31: Schneider, R., and Kobbelt, L. 2001. Geometric fairing of irregular meshes for free-form surface design. Computer Aided Geometric Design 18, 4, 359--379.
• 32: Thomas W. Sederberg , Jianmin Zheng , Almaz Bakenov , Ahmad Nasri, T-splines and T-NURCCs, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 33: Karan Singh , Eugene Fiume, Wires: a geometric deformation technique, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.405-414, July 1998 [doi>10.1145/280814.280946]
• 34: Least-Squares Meshes, Proceedings of the Shape Modeling International 2004, p.191-199, June 07-09, 2004 [doi>10.1109/SMI.2004.38]
• 35: O. Sorkine , D. Cohen-Or , Y. Lipman , M. Alexa , C. Rössl , H.-P. Seidel, Laplacian surface editing, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, July 08-10, 2004, Nice, France [doi>10.1145/1057432.1057456]
• 36: Sorkine, O. 2006. Differential representations for mesh processing. Computer Graphics Forum 25, 4, 789--807.
• 37: Robert W. Sumner , Jovan Popović, Deformation transfer for triangle meshes, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 38: Vitaly Surazhsky , Craig Gotsman, Explicit surface remeshing, Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, June 23-25, 2003, Aachen, Germany
• 39: Toledo, S. 2003. Taucs: A Library of Sparse Linear Solvers. Tel Aviv University.
• 40: Greg Turk , James F. O'brien, Modelling with implicit surfaces that interpolate, ACM Transactions on Graphics (TOG), v.21 n.4, p.855-873, October 2002 [doi>10.1145/571647.571650]
• 41: Wolfram von Funck , Holger Theisel , Hans-Peter Seidel, Vector field based shape deformations, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006
• 42: Max Wardetzky , Miklós Bergou , David Harmon , Denis Zorin , Eitan Grinspun, Discrete quadratic curvature energies, Computer Aided Geometric Design, v.24 n.8-9, p.499-518, November, 2007 [doi>10.1016/j.cagd.2007.07.006]
• 43: William Welch , Andrew Witkin, Free-form shape design using triangulated surfaces, Proceedings of the 21st annual conference on Computer graphics and interactive techniques, p.247-256, July 1994 [doi>10.1145/192161.192216]
• 44: Yizhou Yu , Kun Zhou , Dong Xu , Xiaohan Shi , Hujun Bao , Baining Guo , Heung-Yeung Shum, Mesh editing with poisson-based gradient field manipulation, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 45: Zayer, R., Rössl, C., Karni, Z., and Seidel, H.-P. 2005. Harmonic guidance for surface deformation. Computer Graphics Forum 24, 3, 601--609.
• 46: Kun Zhou , Jin Huang , John Snyder , Xinguo Liu , Hujun Bao , Baining Guo , Heung-Yeung Shum, Large mesh deformation using the volumetric graph Laplacian, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 47: Denis Zorin , Peter Schröder , Wim Sweldens, Interactive multiresolution mesh editing, Proceedings of the 24th annual conference on Computer graphics and interactive techniques, p.259-268, August 1997 [doi>10.1145/258734.258863]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Geometric algorithms, languages, and systems
      I.3.6 Methodology and Techniques
          Subjects: Interaction techniques

General Terms:
Algorithms, Design

Keywords:
deformations, differential representations, fair surface design, sketch based interfaces and modeling, sketching