Illustrating smooth surfaces

We present a new set of algorithms for line-art rendering of smooth surfaces. We introduce an efficient, deterministic algorithm for finding silhouettes based on geometric duality, and an algorithm for segmenting the silhouette curves into smooth parts with constant visibility. These methods can be used to find all silhouettes in real time in software. We present an automatic method for generating hatch marks in order to convey surface shape. We demonstrate these algorithms with a drawing style inspired by A Topological Picturebook by G. Francis.

[1]  ElberGershon.  Line Art Illustrations of Parametric and Implicit Forms , 1998 .

[2]  Thomas F. Banchoff,et al.  The normal Euler class and singularities of projections for polyhedral surfaces in 4-space , 1998 .

[3]  Cassidy J. Curtis.  Loose and sketchy animation , 1998, International Conference on Computer Graphics and Interactive Techniques.

[4]  David Banks,et al.  Image-guided streamline placement , 1996, SIGGRAPH.

[5]  Oliver Deussen,et al.  An illustration technique using hardware-based intersections and skeletons , 1999 .

[6]  W. Boothby.  An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[7]  Aaron Hertzmann,et al.  Introduction to 3D Non-Photorealistic Rendering: Silhouettes and Outlines , 1999 .

[8]  Lee Markosian,et al.  Real-time nonphotorealistic rendering , 1997, SIGGRAPH.

[9]  Pascal Mamassian,et al.  Observer biases in the 3D interpretation of line drawings , 1998, Vision Research.

[10]  H. Whitney.  On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane , 1955 .

[11]  Theodor Brocker,et al.  Mappings of the plane into the plane , 1975 .

[12]  U. Reif.  A degree estimate for subdivision surfaces of higher regularity , 1996 .

[13]  George K. Francis.  A Topological Picturebook , 1988 .

[14]  Gershon Elber.  Line Art Rendering via a Coverage of Isoparametric Curves , 1995, IEEE Trans. Vis. Comput. Graph..

[15]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[16]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[17]  Victoria Interrante,et al.  Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution , 1997, SIGGRAPH.

[18]  Hans Køhling Pedersen.  A framework for interactive texturing on curved surfaces , 1996, SIGGRAPH.

[19]  Gershon Elber,et al.  Hidden curve removal for free form surfaces , 1990, SIGGRAPH.

[20]  Ramesh Raskar,et al.  Image precision silhouette edges , 1999, SI3D.

[21]  David Salesin,et al.  Rendering parametric surfaces in pen and ink , 1996, SIGGRAPH.

[22]  Lambertus Hesselink,et al.  The topology of symmetric, second-order tensor fields , 1994, Proceedings Visualization '94.

[23]  Hassler Whitney,et al.  Singularities of Mappings of Euclidean Spaces , 1992 .

[24]  Amy A. Gooch,et al.  Interactive Non-Photorealistic Technical Illustration , 1998 .

[25]  Raymond Baxter Dowden,et al.  The Natural Way To Draw , 1941 .

[26]  Wilfrid Lefer,et al.  Creating Evenly-Spaced Streamlines of Arbitrary Density , 1997, Visualization in Scientific Computing.

[27]  Peter-Pike J. Sloan,et al.  Interactive technical illustration , 1999, SI3D.

[28]  E. Welzl,et al.  Contour Edge Analysis for Polyhedron Projections , 1997 .

[29]  Gershon Elber,et al.  Interactive Line Art Rendering of Freeform Surfaces , 1999, Comput. Graph. Forum.

[30]  Gershon Elber,et al.  Line Art Illustrations of Parametric and Implicit Forms , 1998, IEEE Trans. Vis. Comput. Graph..

[31]  Lambertus Hesselink,et al.  The topology of symmetric, second-order tensor fields , 1994, VIS '94.

[32]  David Salesin,et al.  Orientable textures for image-based pen-and-ink illustration , 1997, SIGGRAPH.

[33]  Takafumi Saito,et al.  Comprehensible rendering of 3-D shapes , 1990, SIGGRAPH.

[34]  George K. Francis.  The Etruscan Venus , 1991 .

[35]  Gershon Elber,et al.  Output sensitive extraction of silhouettes from polygonal geometry , 1999, Proceedings. Seventh Pacific Conference on Computer Graphics and Applications (Cat. No.PR00293).

[36]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[37]  Adam Finkelstein,et al.  Texture mapping for cel animation , 1998, SIGGRAPH.