Abstract
Proposed in this paper is a new approach for offset surface construction using three- dimensional (3D) distance volumes. After converting an original compound surface into a triangular mesh, the approach creates a distance volume of the triangular mesh. With this distance volume and a given offset value, it extracts the offset points in each slice to create a sequence of two dimensional (2D) cross-sections. The approach then performs offset surface construction using the serial cross-sections. For more accurate and efficient computation of the distance volume, the concept of space division is combined with the concept one of distance propagation to the whole space of interest. The resulting offset surface is a G1 composite surface consisting of three kinds of surfaces: skinned, capped, andor branched surfaces. The proposed approach provides offset surfaces that are accurate and free of degeneracy. Some experimental results demonstrate its usefulness and quality.
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References
Zeid I (1991) CAD/CAM theory and practice. McGraw-Hill, New York
Lasser D, Hoschek J (1993) Fundamentals of computer aided geometric design. AK Peters, Wellesley, Massachusetts, USA
Qiulin D, Davies BJ (1987) Surface engineering geometry for computer-aided design and manufacture. Ellis Horwood, New York
Borgefors G (1984) Distance transformations in arbitrary dimensions. Comput Vision Image Underst 27(3):321–345
Jones MJ, Satherley R (2001) Shape representation using space filled sub-voxel distance fields. In: Proceedings of the International Conference on Shape Modelling and Applications, pp 316–325
Satherley R, Jones MJ (2001) Vector-city vector distance transform. Comput Vision Image Underst 82:238–254
Marchand-Maillet S, Sharaiha YM (1999) Euclidean ordering via chamfer distance calculations. Comput Vision Image Underst 73(3):404–413
Mullikin J (2001) The vector distance transform in two and three dimensions. Graph Models Image Process 54(6):526–535
Rosenfeld A, Pfaltz JL (1966) Sequential operations in digital picture processing. J ACM 13(4):471–494
Chen M, Kaufman A, Yagel R (2000) Volume graphics. Springer, Berlin Heidelberg New York
Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph 21(4):163–169
Piegl L, Tiller W (1995) The NURBS book. Springer, Berlin Heidelberg New York
Farin G (1988) Curve and surfaces for computer aided geometric design: a practical guide. Academic, New York
Piegl LA, Richard AM (1995) Tessellating trimmed NURBS surfaces. Comput Aided Des 27(1):16–26
Hamann B, Po-Yu T (1996) A tessellation algorithm for the representation of trimmed NURBS surfaces with arbitrary trimming curves. Comput Aided Des 28(6):461–472
Ng WMM, Tan ST (2000) Incremental tessellation of trimmed parametric surfaces. Comput Aided Des 32(4):279–294
Mantyla M (1988) An introduction to solid modeling. Computer Science Press, Rockville, Maryland, USA
Preparata FP, Shamos MI (1985) Computational geometry. Springer, Berlin Heidelberg New York
Park H, Kim K (1996) Smooth surface approximation to serial cross-sections. Comput Aided Des 28(12):995–1005
Jeong J, Kim K, Park H, Jung M (2000) A new method for solving branching problems in surface reconstruction. Int J Adv Manuf Technol 16(4):259–264
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Jang, D., Park, H. & Kim, K. Surface offsetting using distance volumes. Int J Adv Manuf Technol 26, 102–108 (2005). https://doi.org/10.1007/s00170-004-2216-2
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DOI: https://doi.org/10.1007/s00170-004-2216-2