Abstract
After presenting a classification of blending techniques and the types of blends a method for blending B-rep solid models is described. Free-form parametric surfaces are used to provide a wide range of blend definitions, allowing blending of free-form faces and reblending of blends. Considering blending as a local operation, the most important issues of restructuring the topology of the solid model to be blended are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Braid, I.C.(1980) Superficial Blends in Geometric Modelling, CAD Group Document No. 105, University of Cambridge Computer Laboratory.
Chiyokura, H. and Kimura, F.(1983) Design of Solids with Free-Form Surfaces, Computer Graphics, 17 (Proc. SIGGRAPH’83, Detroit) pp 25–29.
Chiyokura, H.(1987) An Extended Rounding Operation for Modelling Solids with Free-Form Surfaces, in: Computer Graphics 1987 (Proc. CG International’87), Ed. T.L. Kunii, Springer-Verlag, pp 249–268.
Doo, D.W.H.(1978) A recursive subdivision algorithm for fitting quadratic surfaces to irregular polygons, PhD Thesis, Brunei University.
Faux, I.D. and Pratt, M.J.(1979) Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester.
Fjallström, P.O.(1986) Smoothing of Polyhedral Models, Proc. ACM 2nd Symposium on Computational Geometry, Yorktown Heights, pp 226–235.
Hoffman, C. and Hopcroft, J.(1987) The Potential Method for Blending Surfaces, in: Geometric Modelling: Algorithms and New Trends, Ed. Farin, G.E., SIAM, pp 347–366.
Holmström, L.(1987) Piecewise Quadratic Blending of Implicity Defined Surfaces, Computer Aided Geometric Design, 4, pp 171–189.
Jared, G.E.M. and Varady, T.(1984) Synthesis of Volume Modelling and Sculptured Surfaces in BUILD, Proc. CAD 84 Conference, Butterworths, pp 481–495.
Martin, R.R.(1982) Principal Patches for Computational Geometry, Ph.D. Thesis, Cambridge University Engineering Department
Martin, R.R.(1988) Notes on the topological aspects of the FFSolid blending model, Study, Computer and Automation Institute, Hungarian Academy of Sciences (in preparation)
Middleditch, A.E. and Sears, K.H.(1985) Blend Surfaces for Set Theoretic Volume Modelling Systems, Computer Graphics, 19 (Proc. SIGGRAPH’85, San Francisco), pp 161–170.
Nasri, A.H.(1984) Polyhedral Division Methods for Free-Form Surfaces, University of East Anglia, PhD Thesis.
Nutbourne, A.W., Martin, R.R.(1988) Differential Geometry Applied to Curve and Surface Design, Vol 1. Foundations. Ellis Horwood, Chichester.
Pratt, M.J.(1988) Blending with Cyelide Patches, 3rd IMA Conference on the Mathematics of Surfaces, Oxford
Rockwood, A.P. and Owen, J.C.(1987) Blending Surfaces in Solid Modelling, in: Geometric Modelling: Algorithms and Trends, Ed. Farin, G.E., SIAM, pp 367–384.
Rockwood, A.P.(1987) Blending Surfaces in Solid Geometrical Modelling, PhD Thesis, DAMTP, University of Cambridge
Rossignac, A.R. and Requicha, A.A.G.(1984) Constant Radius Blending in Solid Modelling, Computers in Mechanical Engineering, pp 65–73.
Sederberg, T.W. and Anderson, D.C.(1985) Steiner Surface Patches, IEEE Computer Graphics and Applications, 5, (5), pp 23–36.
Varady, T.(1985) Integration of Free-Form Surfaces into a Volumetric Modeller, Dissertation, Computer and Automation Institute, Hungarian Academy of Sciences.
Varady, T., Vida, J. and Martin, R.R.(1988) Parametric Blending in a Boundary Representation Solid Modeller, 3rd IMA Conference on the Mathematics of Surfaces, Oxford
Woodwark, J.R.(1987) Blends in Geometric Modelling, in: The Mathematics of Surfaces II, Ed. R.R. Martin, Oxford University Press, pp 255–297.
Zhang, D.Y. and Bowyer, A.(1986) CSG Set-Theoretic Solid Modelling and NC Machining of Blend Surfaces, Proc. ACM 2nd Symposium on Computational Geometry, Yorktowri Heights, pp 236–245.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Varady, T., Martin, R.R., Vida, J. (1989). Topological considerations in blending boundary representation solid models. In: Straßer, W., Seidel, HP. (eds) Theory and Practice of Geometric Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61542-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-61542-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64866-3
Online ISBN: 978-3-642-61542-9
eBook Packages: Springer Book Archive