Abstract
We present an efficient and robust algorithm for computing the perspective silhouette of the boundary of a general swept volume. We also construct the topology of connected components of the silhouette. At each instant t, a three-dimensional object moving along a trajectory touches the envelope surface of its swept volume along a characteristic curve K t. The same instance of the moving object has a silhouette curve Lt on its own boundary. The intersection K t∩L t contributes to the silhouette of the general swept volume. We reformulate this problem as a system of two polynomial equations in three variables. The connected components of the resulting silhouette curves are constructed by detecting the instances where the two curves K t and L t intersect each other tangentially on the surface of the moving object. We also consider a general case where the eye position changes while moving along a predefined path. The problem is reformulated as a system of two polynomial equations in four variables, where the zero-set is a two-manifold. By analyzing the topology of the zero-set, we achieve an efficient algorithm for generating a continuous animation of perspective silhouettes of a general swept volume.
Similar content being viewed by others
References
Alias-Wavefront Technology. Maya 5.0 Users Manual . http://www.alias.com (2003)
Bajaj, C., Hoffmann, C., Lynch, R., Hopcroft, J.: Tracing surface intersections. Comput. Aid. Geomet. Des. 5(4), 309–321 (1988)
Bajaj, C., Xu, G.: NURBS approximation of surface-surface intersection curves. Adv. Comput. Math. 2(1), 1–21 (1994)
Cipolla, R., Giblin, P.: Visual Motion of Curves and Surfaces. Cambridge University Press (2000)
Elber, G., Kim, M.-S.: Geometric constraint solver using multivariate rational spline functions. Proc. ACM Symposium on Solid Modeling and Applications, Ann Arbor, MI, June 4-8 (2001)
Elber, G., Chen, X., Cohen, E.: Mold accessibility via Gauss map analysis. Proc. Shape Modeling International ’04, Genova, Italy, pp. 263–272, June (2004)
Foley, J., van Dam, A., Feiner, S., Hughes, J.: Computer Graphics: Principles and Practice. 2nd ed, Addison Wesley, Reading, MA (1990)
FLTK, Fast Light Tool Kit. http://www.fltk.org/. Version 1.1, 2002
Gooch, B., Gooch, A.: Non-Photorealistic Rendering. A.K. Peters. ISBN: 1-56881-133-0 (2001)
Gooch, A., Gooch, B., Shirley, P., Cohen, E.: A non-photorealistic lighting model for automatic technical illustration. SIGGRAPH’98, pp. 447–452 (1998)
Isenberg, T., Freudenberg, B., Halper, N., Schlechtweg, S., Strothotte, T.: A developer’s guide to silhouette algorithms for polygonal models. IEEE Comput. Graph. Appl. 23(4), 28–37 (2003)
IRIT 9.0 User’s Manual, Technion, October (2002) http://www.cs.technion.ac.il/∼irit
Joy, K., Duchaineau, M.: Boundary determination for trivariate solid. Proc. of Pacific Graphics 99, Seoul, Korea, pp. 82–91, October 5–7 (1999)
Kalnins, R.D., Davidson, P.L., Markosian, L., Finkelstein, A.: Coherent stylized silhouette. ACM Trans. Graph. 22(3), 856–861 (2003)
Kim, K.-J., Lee, I.-K.: The perspective silhouette of a canal surface. Comput. Graph. Forum 22(1), 15–22 (2003)
Kim, M.-S., Elber, G.: Problem reduction to parameter space. In: Cipolla, R., Martin, R. (eds) The Mathematics of Surfaces IX (Proc. of the 9th IMA Conference), pp. 82–98. Springer, London (2000)
Martin, R., Stephenson, P.: Sweeping of three-dimensional objects. Comput. Aid. Des. 22(4), 223–234 (1990)
Patrikalakis, N., Maekawa, T.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Berlin Heidelberg New York (2002)
VTK, The Visualization Tool Kit. http://www.vtk.org/. Version 4.2 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Seong, JK., Kim, KJ., Kim, MS. et al. Perspective silhouette of a general swept volume. Visual Comput 22, 109–116 (2006). https://doi.org/10.1007/s00371-006-0371-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-006-0371-1