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[SKK+06]  Perspective Silhouette of a General Swept Volume

Seong:2006:PSG (Article)
Author(s)Seong J.K., Kim K.J., Kim M.S. and Elber G.
Title« Perspective Silhouette of a General Swept Volume »
JournalThe Visual Computer
Volume22
Number2
Page(s)109--116
Year2006

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 Kt. The same instance of the moving object has a silhouette curve Lt on its own boundary. The intersection Kt?Lt 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 Kt and Lt 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.

BibTeX code
@article{Seong:2006:PSG,
  optpostscript = {},
  number = {2},
  month = feb,
  author = {Joon-Kyung Seong and Ku-Jin Kim and Myung-Soo Kim and Gershon
            Elber},
  optkey = {},
  optannote = {},
  localfile = {papers/Seong.2006.PSG.pdf},
  optkeywords = {},
  doi = {http://dx.doi.org/10.1007/s00371-006-0371-1},
  optciteseer = {},
  journal = j-TVC,
  opturl = {},
  volume = {22},
  optwww = {},
  title = {{P}erspective {S}ilhouette of a {G}eneral {S}wept {V}olume},
  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 Kt. The same instance of the
              moving object has a silhouette curve Lt on its own boundary. The
              intersection Kt?Lt 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 Kt and Lt 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.},
  pages = {109--116},
  year = {2006},
}

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