{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T08:23:45Z","timestamp":1774599825750,"version":"3.50.1"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2006,10,1]],"date-time":"2006-10-01T00:00:00Z","timestamp":1159660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2006,10]]},"abstract":"<jats:p>The contour generator is an important visibility feature of a smooth object seen under parallel projection. It is the curve on the surface which seperates front-facing from back-facing regions. The apparent contour is the projection of the contour generator onto a plane perpendicular to the view direction. Both curves play an important role in computer graphics.Our goal is to obtain fast and robust algorithms that compute the contour generator with a guarantee of topological correctness. To this end, we first study the singularities of the contour generator and apparent contour for both generic views and generic time-dependent projections, for example, when the surface is rotated or deformed. The singularities indicate when components of the contour generator merge or split as time evolves.We present an algorithm to compute an initial contour generator by using a dynamic step size. An interval test guarantees the topological correctness. This initial contour generator can thus be maintained under a time-dependent projection by examining its singularities.<\/jats:p>","DOI":"10.1145\/1183287.1183288","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"1243-1280","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["Computing contour generators of evolving implicit surfaces"],"prefix":"10.1145","volume":"25","author":[{"given":"Simon","family":"Plantinga","sequence":"first","affiliation":[{"name":"University of Groningen, Groningen, The Netherlands"}]},{"given":"Gert","family":"Vegter","sequence":"additional","affiliation":[{"name":"University of Groningen, Groningen, The Netherlands"}]}],"member":"320","published-online":{"date-parts":[[2006,10]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Alberti G. Compte G. and Mourrain B. 2004. Meshing implicit algebraic surfaces: The smooth case. Tech. rep. 5405 INRIA Sophia-Antipolis. Alberti G. Compte G. and Mourrain B. 2004. Meshing implicit algebraic surfaces: The smooth case. Tech. rep. 5405 INRIA Sophia-Antipolis."},{"key":"e_1_2_1_2_1","unstructured":"Alliez P. Laurent N. Sanson H. and Schmitt F. 2001. Efficient view-dependent refinement of 3d meshes using sqrt(3)-subdivision. To appear in the Visual Computer. Alliez P. Laurent N. Sanson H. and Schmitt F. 2001. Efficient view-dependent refinement of 3d meshes using sqrt(3)-subdivision. To appear in the Visual Computer."},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1002\/cpa.3160290603","article-title":"Wave front evolution and equivariant Morse lemma","volume":"29","author":"Arnol'd V. I.","year":"1976","journal-title":"Comm. Pure Appl. Math."},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"Arnol'd V. I. 1986. Catastrophe Theory. Springer-Verlag Berlin. Arnol'd V. 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TR-1-99, Department of Computer Science","author":"Gu X.","year":"1999"},{"key":"e_1_2_1_14_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0096-3003(83)90001-2","article-title":"An interval Newton method","volume":"12","author":"Hansen E. R.","year":"1983","journal-title":"Appl. Math Comput."},{"key":"e_1_2_1_15_1","unstructured":"Hearn D. and Baker M. P. 1994. Computer Graphics 2nd ed. Prentice-Hall Englewood Cliffs NJ. Hearn D. and Baker M. P. 1994. Computer Graphics 2nd ed. Prentice-Hall Englewood Cliffs NJ."},{"key":"e_1_2_1_16_1","unstructured":"Hoffman C. M. 1989. Geometric and Solid Modeling. Morgan-Kaufmann San Fransisco CA. Hoffman C. M. 1989. Geometric and Solid Modeling. Morgan-Kaufmann San Fransisco CA."},{"key":"e_1_2_1_17_1","volume-title":"Artificial Intelligence","author":"Koenderink J. 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