• Book Chapters/Reports
• Surface Reconstruction
• Medial axis
• Shape Features
• Curve Reconstruction
• Mesh Simplification and Decimation
• Rendering
• Computational Topology
• Triangulations/Mesh Generation
• Solid_Modeling
• Computational_Combinatorial_Geometry

Book Chapters/Reports

• T. K. Dey. Sample based geometric modeling.  AMS/DIMACS volume on Computer-Aided Design and Manufacturing, eds Dutta, Janardan, Smid. To appear.
  
• T. K. Dey. Curve and surface reconstruction. Chapter in Handbook of Discrete and Computational Geometry, Goodman and O' Rourke eds., CRC press, 2nd edition.
• One of the authors of Emerging Challenges in Computational Topology . (A NSF report), 1999.
• T. K. Dey, H. Edelsbrunner and S. Guha. Computational Topology .  Advances in Discrere and Computational Geometry, eds. B. Chazelle, J. E. Goodman and R. Pollack. Contemporary Mathematics, AMS, Providence, 1998.
• T. K. Dey. Section 13.4 on polyhedra of CRC Handbook of Discrete and Combinatorial Mathematics, Ken Rosen, Editor, CRC press (2000).

Surface Reconstruction

• T. K. Dey and S. Goswami. Provable surface reconstruction from noisy samples.  Proc. 20th  ACM Sympos. Comput. Geom. (2004), 330--339.  Extended version.
  
• T. K. Dey and S. Goswami. Tight Cocone: A water-tight surface reconstructor.  Proc. 8th ACM Sympos. Solid Modeling Applications (2003), 127--134. Journal version in J. of Computing and Infor. Sci. Engin. Vol. 30 (2003), 302--307.
• T.  K. Dey, J. Giesen, S. Goswami and W. Zhao. Shape dimension and approximation from samples. Disctere & Comput. Geom., vol 29, 419--434 (2003).
• N. Amenta, S. Choi, T. K. Dey and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Intl. Journal on Computational Geometry & Applications, vol. 12, (2002), 125--141.
• T.  K. Dey and J. Giesen. Detecting undersampling in surface reconstruction.  Proc. 17th ACM Sympos. Comput. Geom. (2001), 257--263. Journal version in Discrete and Comput. Geom. - The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, M. Sharir, eds.), Algorithms and Combinatorics Series, Springer-Verlag, Berline, 2003, to appear.
• T.  K. Dey, J. Giesen and J. Hudson. Delaunay based shape reconstruction from large data. Proc. IEEE Symposium in Parallel and Large Data Visualization and Graphics, (2001), 19--27.
• T.  K. Dey, J. Giesen, Samrat Goswami, J. Hudson, R. Wenger and W. Zhao. Undersampling and oversampling in sample based shape modeling.Proc. IEEE Visualization 2001, (2001), 83--90.
• T.  K. Dey, S. Funke and E. Ramos.  Surface reconstruction in almost linear time under locally uniform sampling. 17th European Workshop on Comput. Geom., Berlin, Germany, (2001).
• T.  K. Dey, J. Giesen and W. Zhao. Robustness issues in surface reconstruction. Proc. Intl. Conf. Comput. Sci., San Francisco, California, May 28-30, (2001).
• T. K. Dey, J. Giesen, N. Leekha and R. Wenger. Detecting boundaries for surface reconstruction using co-cones.Intl. J. Computer Graphics & CAD/CAM, vol. 16, (2001), 141--159.
• H-L. Cheng, T. K. Dey, H. Edelsbrunner and J. Sullivan. Dynamic skin triangulation.   Discrete Comput. Geom., vol. 25, (2001),  525--568.
• S. W. Cheng and T. K. Dey. Improved construction of Delaunay based contour surfaces. Proc. ACM Sympos. Solid Modeling and Applications 99 ,1999, 322-323.

• T. K. Dey and W. Zhao. Approximate medial axis as a Voronoi subcomplex. CAD, Vol. 36, Issue 2 (2003), 195--202. Preliminary version in Proc. 7th ACM Sympos. Solid Modeling Applications, 2002, 356--366.
• T. K. Dey and W. Zhao. Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee. R. Mohring and R. Raman (Eds.) ESA 2002, LNCS 2461, 387--398. An Extended version to appear in Algorithmica, vol. 38, 2004.

• T. K. Dey, J. Giesen and S. Goswami. Shape segmentation and matching with flow discretization.  Proc. Workshop Algorithms Data Strucutres (WADS 03), LNCS 2748, F. Dehne, J.-R. Sack, M. Smid Eds., 25--36.
• T. K. Dey, J. Giesen and S. Goswami. Shape segmentation and matching from noisy point clouds. Proc. Eurographics Sympos. Point -Based Graphics (2004), M. Alexa and S. Rusinkiewicz (eds).
  

Curve Reconstruction

• T. K. Dey and R. Wenger.  Fast  reconstruction of curves with sharp corners. Internat. J. Comput. Geom. Applications., vol. 12 (2002), 353--400.
• T. K. Dey and R. Wenger. Reconstructing curves with sharp corners. Computational Geometry: Theory and Applications, vol. 19, (2001), 89--99.
• T. K. Dey, K. Mehlhorn and E. Ramos. Curve reconstruction: connecting dots with good reason . Computational Geometry: Theory and Applications, Vol. 15, No. 4, 2000, 229--244.
• T. K. Dey and P. Kumar. A simple provable algorithm for curve reconstruction . Proc. 10th. ACM-SIAM Symposium on Discrete Algorithms (SODA '99) , 1999, 893--894.

Mesh Simplification and Decimation

• S.-W. Cheng, T. K. Dey and  S.-H. Poon. Hierarchy of surface models and irreducible triangulatiion. Computational Geometry : Theory & Applications, Vol. 27, No. 2 (2004), 135--150.
• T. K. Dey, J. Giesen and J. Hudson. Sample shuffling for quality hierarchic surface meshing. Proc. 10th Mehsing Roundtable Conf., Newport Beach, California, (2001), 143--154.
• T. K. Dey, J. Giesen and J. Hudson. Decimating samples for mesh simplification. Proc. 13th Canadian Conference on Computational Geometry, (2001), 85--88.
• T. K. Dey, H. Edelsbrunner, S. Guha and D. Nekhayev. Topology preserving edge contraction. . Publications de l' Institut Mathematique (Beograd), Vol. 60 (80), 23--45, 1999.

• T. K. Dey and J. Hudson. PMR: point to mesh rendering, a feature-based approach. Proc. IEEE Visualization 2002, (2002), 155--162.

Computational Topology

• S.-W. Cheng, T. K. Dey, E. Ramos and T. Ray. Sampling and meshing a surface with guaranteed topology and geometry. Proc. 20th Sympos. Comput. Geom. (2004), to appear.
  
• T. K. Dey, J. Giesen, M. John.  Alpha-shapes and flow shapes are homotopy equivalent. Proc. Sympos. Theory Computing (STOC 2003), 493--502.
• T. K. Dey, J. Giesen and S. Goswami. Shape segmentation and matching with flow discretization. Workshop on Data Structures and Algorithms (WADS 2003), LNCS 2748, 25--36.
  
• T. K. Dey, H. Edelsbrunner, S. Guha and D. Nekhayev. Topology preserving edge contraction. . Publications de l' Institut Mathematique (Beograd), Vol. 60 (80), 23--45, 1999.
• T. K. Dey, H. Edelsbrunner and S. Guha. Computational Topology . Invited paper in Advances in Discrere and Computational Geometry, eds. B. Chazelle, J. E. Goodman and R. Pollack. Contemporary Mathematics, AMS, Providence, 1998.
• T. K. Dey and S. Guha. Computing homology groups of simplicial complexes in $R^3$ . Journal of ACM , vol. 45, No. 2, (1998), 266-287. Preliminary version in 28th ACM STOC , 1996, 398-407.
• T. K. Dey and S. Guha. Transforming curves on surfaces . Journal of Computer and System Sciences, vol. 58, 1999, 297--325. Preliminary version in IEEE FOCS , 1995, 266-274.
• T. K. Dey. Optimal algorithms to detect null-homologous cycles on 2-manifolds. Intl. Journal of Computational Geometry & Applications, Vol. 7, No. 3, (1997), 167--174. Preliminary version in 5th CCCG , 1993, 273-278.
• T. K. Dey and H. Schipper. A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection. Discrete & Computational Geometry, Vol. 14, 93--110 (1995). Preliminary version in 10th SoCG, 1994, 277-284.

Triangulations/Mesh Generation

• S.-W. Cheng, T. K. Dey, E. Ramos and T. Ray. Sampling and meshing a surface with guaranteed topology and geometry. Proc. 20th Sympos. Comput. Geom. (2004), 280--289.
  
• S.-W. Cheng, T. K. Dey, E. Ramos and T. Ray. Quality meshing for polyhedra with small angles. Proc. 20th Sympos. Comput. Geom. (2004), 290--299.  Extended version.
  
• S.-W. Cheng and T. K. Dey.  Quality meshing with weighted Delaunay refinement.  SIAM J. Computing, Vol. 33 (2003), 69--93.
• T. K. Dey, J. Giesen and J. Hudson. Sample shuffling for quality hierarchic surface meshing. Proc. 10th Mehsing Roundtable Conf., Newport Beach, California, (2001), 143--154.
• S.-W. Cheng, T. K. Dey, H. Edelsbrunner, M. A. Facello and S.-H. Teng. Sliver exudation.  J. ACM, Vol. 47, (2000), 883--904.
• S.-W. Cheng and T. K. Dey. Approximate minimum weight Steiner triangulation in three dimensions . Proc. 10th ACM-SIAM Symposium on Discrete Algorithms , (1999).
• T. K. Dey, A. Roy and N. R. Shah. Approximating geometric objects through topological triangulations. Proc. 17th. FST&TCS Conference, Lecture Notes in Computer Science 1346, 6-21 (1997).
• T. K. Dey, M. Dillencourt, S. Ghosh and J. Cahil. Triangulating with high connectivity. Computational Geometry: Theory and Applications, Vol. 8, No. 1, (1997), 39--56. Preliminary version in 6th CCCG, 1994, 339-343.
• T. K. Dey, C. Bajaj and K. Sugihara. On good triangulations in three dimensions. Intl. Journal of Computational Geometry & Applications. Vol. 2 (1992), 75-95.
• T. K. Dey, C. Bajaj and K. Sugihara. Delaunay triangulations in three dimensions with finite precision arithmetic. Computer Aided Geometric Design, Vol. 9 (1992), 457-470.

Solid Modeling

• C. Bajaj and T. K. Dey. CSG operations on a MIMD distributed memory machines. Proc. CSG 94, Winchester, UK, 13-15 April, 1994.
• C. Bajaj and T. K. Dey. Convex decompositions of polyhedra and robustness. SIAM Journal Computing. Vol. 21 (1992), 339-364.
• T. K. Dey. Triangulation and CSG representation of polyhedra with arbitrary genus. Proc. 7th ACM Symposium Computational Geometry New Hampshire, USA, (1991), 364-372.
• T. K. Dey, C. Bajaj and K. Sugihara. On good triangulations in three dimensions. Proc. ACM Symposium on Solid Modeling, USA, (1991)
• C. Bajaj, V. Anupam, T. K. Dey, S. Klinkner, A. Royappa. CREMONA: A graphical editing system for algebraic boundary models. SIAM Conference on Geometric Design. Tempe, Arizona (1989)

Computational/Combinatorial Geometry

• B. Aronov and T. K. Dey. Polytopes in Arrangements .  Discrete & Computational Geometry, Vol. 25, (2001), 51--63.
• T. K. Dey. Improved bounds for planar k-sets and related problems. Invited paper in a special issue of Discrete & Computational Geometry, Vol. 19, No. 3, (1998), 373-382. Preliminary version in 37th IEEE FOCS, 1997, 156-161.
• T. K. Dey and J. Pach. Extremal problems for geometric hypergraphs. Discrete & Computational Geometry, Vol. 19, No. 4, (1998), 473--484. Preliminary version in ISAAC 96, LNCS 1178, 105-114.
• D. Chithraprasad, S. P. Pal and T. K. Dey. Visibility with multiple diffuse reflections . Computational Geometry:Theory and Applications, Vol. 10, (1998), 187--196.
• B. Aronov, A. Davis, T. K. Dey, S. P. Pal and D. C. Prasad. Visibility with multiple reflections . Discrete & Computational Geometry, Vol. 20, No. 61, (1998), 61--78. Preliminary version in 5th SWAT, 1996, LNCS 1097, 284-295.
• B. Aronov, A. Davis, T. K. Dey, S. P. Pal and D. C. Prasad. Visibility with one reflection. Discrete & Computational Geometry, Vol. 19, No. 4, (1998), 553-574. Preliminary version in 11th ACM SoCG, 1995, 316-325.
• T. K. Dey and N. Shah. On counting the number of simplicial complexes in $R^d$. Computational Geometry: Theory and Applications Vol. 8, No. 5, (1997). Preliminary version in 7th CCCG, 1995, 31-36.
• T. K. Dey and H. Edelsbrunner. Counting triangle crossings and halving planes. Invited paper in a special issue, Discrete & Computational Geometry, Vol. 12 (1994), 281--289.
• T. K. Dey and N. Shah. Many face complexity in incremental convex arrangements. Information Processing Letters. Vol. 51, 5, 227--231 (1994).
• T. K. Dey. On counting triangulations in d dimensions. Computational Geometry: Theory and Applications. Vol. 3 (1993), 315--325.
• C. Bajaj and T. K. Dey. Polygon nesting and robustness. Information Processing Letters. Vol. 1 (1990), 23-32.