Abstract
Up to now, assuming a geometric object as being a set of points, a deformation was defined as a mathematical function which mapped the original object set of points into a new one. In short, a new point was linked with each object point in the zone of influence of the deformation. With such a statement, it was not possible to apply several deformations simultaneously as soon as their zones of influence overlapped each other. A new formal definition of a deformation is brought out in this paper. Instead of a new point, this definition links a displacement with each object point in the zone of influence of the deformation. Thus, applying several deformations simultaneously is made feasible by blending, for each point of the original object, the displacement due to each deformation.
Chapter PDF
Similar content being viewed by others
References
Barr, A. H.: Global and Local Deformations of Solid Primitives. ACM Computer Graphics (SIGGRAPH’84). 18(3) 21–34, 1984.
Bechmann D.: Multidimensional Free-Form Deformation Tools. State of the Art Report (EUROGRAPHICS’98), Lisbon (Portugal), 1998.
Cook R. L.: Shade Trees. ACM Computer Graphics (SIGGRAPH’84). 18(3) 223–231, 1984.
Feng J., Ma L. and Peng Q.: A new Free-Form Deformation Through the Control of Parametric Surfaces. Computer and Graphics, Pergamon Press. 20(4) 531–539, 1996.
Lazarus F., Coquillart S. and Jancène P.: Axial Deformations: An intuitive Technique. Computer-Aided Design. 26(8) 607–613, 1994.
Lewis J. P.: Algorithms for Solid Noise Synthesis. ACM Computer Graphics (SIGGRAPH’89). 23(3) 263–270, 1989.
Pedersen H. K.: Displacement Mapping Using Flow Fields. ACM Computer Graphics Proceedings (SIGGRAPH’94), Annual Conference Series. 279–286, 1994.
Sederberg T. W. and Parry S. R.: Free-Form Deformation of Solid Geometric Models. ACM Computer Graphics (SIGGRAPH’86). 20(4) 151–160, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peyré, H., Bechmann, D. (2002). Deformations Expressed as Displacement Maps An Easy Way to Combine Deformations. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46080-2_23
Download citation
DOI: https://doi.org/10.1007/3-540-46080-2_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43593-8
Online ISBN: 978-3-540-46080-0
eBook Packages: Springer Book Archive