Iterative Process to Improve Simple Adaptive Subdivision Surfaces Method with Butterfly Scheme

Subdivision surfaces were applied to the entire meshes in order to produce smooth surfaces refinement from coarse mesh. Several schemes had been introduced in this area to provide a set of rules to converge smooth surfaces. However, to compute and render all the vertices are really inconvenient in terms of memory consumption and runtime during the subdivision process. It will lead to a heavy computational load especially at a higher level of subdivision. Adaptive subdivision is a method that subdivides only at certain areas of the meshes while the rest were maintained less polygons. Although adaptive subdivision occurs at the selected areas, the quality of produced surfaces which is their smoothness can be preserved similar as well as regular subdivision. Nevertheless, adaptive subdivision process burdened from two causes; calculations need to be done to define areas that are required to be subdivided and to remove cracks created from the subdivision depth difference between the selected and unselected areas. Unfortunately, the result of adaptive subdivision when it reaches to the higher level of subdivision, it still brings the problem with memory consumption. This research brings to iterative process of adaptive subdivision to improve the previous adaptive method that will reduce memory consumption applied on triangular mesh. The result of this iterative process was acceptable better in memory and appearance in order to produce fewer polygons while it preserves smooth surfaces.

Authors:

• Noor Asma Husain
• Mohd Shafry Mohd Rahim
• Abdullah Bade

Keywords:

• Subdivision surfaces
• adaptive subdivision
• selectioncriteria
• handle cracks
• smooth surface

References:

[1] Isa, S.A.M., et al., Rendering Process of Digital Terrain Model on
Mobile Devices. Advances in Multimedia - An International Journal
(AMIJ), 2010. 1(1).
[2] Zorin, D. and P. Schr¨oder, Subdivision for Modeling and Animation.
2000, ACM SIGGRAPH Course Notes 2000: New York University
Caltech.
[3] DeRose, T., M. Kass, and T. Truong, Subdivision Surfaces in Character
Animation. Proceedings of the 25th Annual Conference on Computer
Graphics and Interactive Techniques, 1998. vol. 32: p. 85-94.
[4] Catmull, E. and J. Clark, Recursively generated b-spline surfaces on
arbitrary topological meshes. Computer-Aided Design, 1978. vol. 10(no.
6): p. 350-355.
[5] Doo, D. and M. Sabin, Behaviour of recursive division surfaces near
extraordinary points. Computer-Aided Design, 1978. vol. 10(no. 6): p.
356-360.
[6] Loop, C., Smooth Subdivision Surfaces Based on Triangles in
Department of Mathematics. 1987, The University Of Utah.
[7] Dyn, N., D. Levin, and J.A. Gregory, A Butterfly Subdivision Scheme
for Surface Interpolation with Tension Control. ACM Transactions on
Graphics, 1990. vol. 9(no. 2): p. 160-169.
[8] Kobbelt, L., 3-Subdivision, in Proceedings of the 27th Annual
Conference on Computer Graphics and Interactive Techniques. 2000,
ACM Press/Addison-Wesley Publishing Co. p. 103-112.
[9] Velho, L. and D. Zorin, 4-8 Subdivision. Computer Aided Geometric
Design, 2001. 18(5): p. 397-427.
[10] Muller, H. and R. Jaeschke, Adaptive Subdivision Curves and Surfaces,
in Proceeding Computer Graphics International. 1998. p. 48-58.
[11] Pakdel, H.-R. and F. Samavati. Incremental Adaptive Loop Subdivision.
in International Conference on Computational Science and Its
Applications 2004: Springer-Verlag Berlin Heidelberg.
[12] Amresh, A., G. Farin, and A. Razdan, Adaptive Subdivision Schemes for
Triangular Meshes, in Hierarchical and Geometrical Methods in
Scientific Visualization, G. Farin, H. Hagen, and B. Hamann, Editors.
2001. p. 319-327.
[13] Meyer, M., et al. Discrete Differential-Geometry Operators for
Triangulated 2-Manifolds. in Visualization and Mathematics III. 2003:
Heidelberg: Springer-Verlag.
[14] Isenberg, T., K. Hartmann, and H. K¨onig, Interest Value Driven
Adaptive Subdivision, in Simulation und Visualisierung, T. Schulze, S.
Schlechtweg, and V. Hinz, Editors. 2003, SCS European Publishing
House. p. 139-149.
[15] Liu, W. and K. Kondo, An Adaptive Scheme for Subdivision Surfaces
based on Triangular Meshes. Journal for Geometry and Graphics, 2004.
vol. 8(No. 1): p. 69-80.
[16] Wu, J., W. Liu, and T. Wang. Adaptive Refinement Scheme for
Subdivision Surfaces based on Triangular Meshes. in Ninth International
Conference on Computer Aided Design and Computer Graphics. 2005:
IEEE.
[17] E.Bank, R., A. H.Sherman, and A. Weiser, Some Refinement Algorithms
and Data Structures for Regular Local Mesh Refinement, in Scientific
Computing, R. Stepleman, et al., Editors. 1983: IMACS/North-Holland.
p. 3-17.
[18] Pakdel, H.-R. and F.F. Samavati, Incremental subdivision for triangle
meshes. Int. J. Computational Science and Engineering, 2007. Vol.
3(No. 1): p. 13.
[19] Gardere, L. and B. Landry, Project 2: Subdivision Surfaces. 2002.
[20] Husain, N.A., et al. Iterative Selection Criteria to Improve Simple
Adaptive Subdivision Surfaces Method in Handling Cracks for
Triangular Meshes. in Proceedings of the 9th ACM SIGGRAPH
Conference on Virtual-Reality Continuum and its Applications in
Industry 2010. Soeul,Korea.