Abstract
A new data-parallel algorithm for reconstructing smooth surfaces defined by arbitrary 3D triangular meshes is presented. The obtained surfaces are composed of triangular patches that join with first order geometric continuity. Every patch is generated by a parametric function that approximates the vertices of each control triangle of the mesh. A coarse granularity implementation of those functions, in which each triangular patch is generated on a separate processor, yields the best performances when no communication among processors occurs. The data distribution to attain such an independent task-farm topology is studied. The algorithm has been implemented on a Connection Machine CM-200 system, achieving linear scaling in the number of processors. The simplicity and inherent parallelism of this technique allow its implementation on a wide variety of other parallel and vector architectures.
The author has been supported by the Government of Spain under an FPI fellowship and the CICYT project TAP93-0415. A complementary grant has been received from the Polytechnic University of Catalonia.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
F. Chen and A. Goshtasby. A parallel B-spline surface fitting algorithm. ACM Transactions on Graphics, vol.8, no.1, 1989, 41–50.
M.A. García. Smooth Approximation of Irregular Triangular Meshes with G1 Parametric Surface Patches. Int. Conf. on Computational Graphics and Visualization Techniques, Alvor, Portugal, 1993, 380–389.
M.A. García. Efficient Surface Reconstruction from Scattered Points through Geometric Data Fusion. IEEE Int. Conf. on Multisensor Fusion and Integration for Intelligent Systems. Las Vegas, USA, 1994, 559–566.
M.A. García. Terrain Modelling with Uncertainty for Geographic Information Systems. Int. Society for Photogrammetry and Remote Sensing Commission III Symposium, Munich, Germany, 1994, 273–280.
M.A. García. Reconstruction of Visual Surfaces from Sparse Data using Parametric Triangular Approximants. IEEE Int. Conf. on Image Processing. Austin, USA, 1994, 750–754.
M.A. García. Fast Generation of Free-Form Surfaces by Massively Parallel Approximation of Triangular Meshes of Arbitrary Topology. Technical Report, Institute of Cybernetics, January 1995, 15 pags.
W. Jiaye, Z. Caiming and W. Wenping. Parallel algorithm for B-spline surface interpolation. Int. Conf. on Computer-Aided Design and Computer Graphics. 1989, 260–262.
B. Pham and H. Schroder. Parallel algorithms and a systolic device for cubic B-spline curve and surface generation. Computers & Graphics (Pergamon), vol.15, no.3, 1991, 349–354.
Thinking Machines Corporation. The Connection Machine System, CM-2 User's Guide, V6.1, October 1991.
A. Valenzano, P. Montuschi and L.Ciminiera. Systolic accelerator for parametric surface modelling. IEE proceedings-E, vol.138, no. 4, july 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
García, M.A. (1995). Massively parallel approximation of irregular triangular meshes with G1 parametric surfaces. In: Ferreira, A., Rolim, J. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1995. Lecture Notes in Computer Science, vol 980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60321-2_18
Download citation
DOI: https://doi.org/10.1007/3-540-60321-2_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60321-4
Online ISBN: 978-3-540-44915-7
eBook Packages: Springer Book Archive