FiberMesh: designing freeform surfaces with 3D curves

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.

[1]  Peter Schröder,et al.  Discrete Willmore flow , 2005, SIGGRAPH Courses.

[2]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..

[3]  Marc Alexa,et al.  Laplacian mesh optimization , 2006, GRAPHITE '06.

[4]  Takeo Igarashi,et al.  Smooth meshes for sketch-based freeform modeling , 2003, I3D '03.

[5]  Marc Alexa,et al.  A sketch-based interface for detail-preserving mesh editing , 2005, SIGGRAPH 2005.

[6]  James F. O'Brien,et al.  Modelling with implicit surfaces that interpolate , 2002, TOGS.

[7]  Christian Rössl,et al.  Laplacian surface editing , 2004, SGP '04.

[8]  H. Shum,et al.  Subspace gradient domain mesh deformation , 2006, SIGGRAPH 2006.

[9]  Peter Schröder,et al.  Interactive multiresolution mesh editing , 1997, SIGGRAPH.

[10]  Levent Burak Kara,et al.  Sketch-Based 3D-Shape Creation for Industrial Styling Design , 2007, IEEE Computer Graphics and Applications.

[11]  John M. Snyder,et al.  Large mesh deformation using the volumetric graph Laplacian , 2005, SIGGRAPH '05.

[12]  O. Sorkine.  Differential Representations for Mesh Processing , 2006 .

[13]  Brian Wyvill,et al.  ShapeShop: sketch-based solid modeling with BlobTrees , 2006, SBM.

[14]  Jovan Popović,et al.  Deformation transfer for triangle meshes , 2004, SIGGRAPH 2004.

[15]  Christian Rössl,et al.  Harmonic Guidance for Surface Deformation , 2005, Comput. Graph. Forum.

[16]  Andrew P. Witkin,et al.  Free-form shape design using triangulated surfaces , 1994, SIGGRAPH.

[17]  Hans-Peter Seidel,et al.  Interactive multi-resolution modeling on arbitrary meshes , 1998, SIGGRAPH.

[18]  Eugene Fiume,et al.  Wires: a geometric deformation technique , 1998, SIGGRAPH.

[19]  Ronald N. Perry,et al.  Kizamu: a system for sculpting digital characters , 2001, SIGGRAPH.

[20]  J. Hughes,et al.  SmoothSketch: 3D free-form shapes from complex sketches , 2006, ACM Trans. Graph..

[21]  Takeo Igarashi,et al.  As-rigid-as-possible shape manipulation , 2005, ACM Trans. Graph..

[22]  Daniel Cohen-Or,et al.  Least-squares meshes , 2004, Proceedings Shape Modeling Applications, 2004..

[23]  Olga Sorkine-Hornung,et al.  On Linear Variational Surface Deformation Methods , 2008, IEEE Transactions on Visualization and Computer Graphics.

[24]  Hans-Peter Seidel,et al.  Vector field based shape deformations , 2006, SIGGRAPH 2006.

[25]  Leif Kobbelt,et al.  An intuitive framework for real-time freeform modeling , 2004, SIGGRAPH 2004.

[26]  Ramesh Raskar,et al.  Free‐form sketching with variational implicit surfaces , 2002, Comput. Graph. Forum.

[27]  Eitan Grinspun,et al.  Discrete quadratic curvature energies , 2007, Comput. Aided Geom. Des..

[28]  Zoran Popovic,et al.  The space of human body shapes: reconstruction and parameterization from range scans , 2003, ACM Trans. Graph..

[29]  Lee Markosian,et al.  Skin: a constructive approach to modeling free-form shapes , 1999, SIGGRAPH.

[30]  Carlo H. Séquin,et al.  Functional optimization for fair surface design , 1992, SIGGRAPH.

[31]  Craig Gotsman,et al.  Explicit Surface Remeshing , 2003, Symposium on Geometry Processing.

[32]  P. Wriggers.  Nonlinear Finite Element Methods , 2008 .

[33]  D. Levin,et al.  Linear rotation-invariant coordinates for meshes , 2005, SIGGRAPH 2005.

[34]  Leif Kobbelt,et al.  Geometric fairing of irregular meshes for free-form surface design , 2001, Comput. Aided Geom. Des..

[35]  Geoff Wyvill,et al.  Swirling-sweepers: Constant-volume modeling , 2006, Graph. Model..

[36]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[37]  Scott Schaefer,et al.  Lofting curve networks using subdivision surfaces , 2004, SGP '04.

[38]  Markus H. Gross,et al.  PriMo: coupled prisms for intuitive surface modeling , 2006, SGP '06.

[39]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, SIGGRAPH 2004.

[40]  Hongbo Fu,et al.  Effective Derivation of Similarity Transformations for Implicit Laplacian Mesh Editing , 2007, Comput. Graph. Forum.