The task of the mixed pure CAD generating method developed by the authors consists in finding only the points situated on the gear tooth surface. The use of the mixed CAD gear generating method results in a very large and particular type of Points Cloud: This contains points situated both in the tooth space, and on the tooth surface. The existing filtering programs and methods, as it was presented in previous papers, cannot deal with these particular point sets. The development of the named particular generating method claims an algorithm and a computer software which can find the envelope of the Points Cloud. This papers presents an Alpha Shape algorithm based filtering algorithm, adapted and developed to be used together with the mixed CAD generating software.
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 Tieming Xiang LizhiGu Leilei Xiao “Accurate modeling of logarithmic spiral bevel gear based on the tooth flank formation and Boolean addition operation” Sage Journals Proceedings of the Institution of Mechanical Engineers Part B: Journal of Engineering Manufacture Vol 230 Issue 9 pp. 1650 - 1658 2016.
 Di Puccio F. Gabiccini M. Guiggiani M. “An invariant approach for gear generation with supplemental motions” Science Direct Mechanism and Machine Theory 42 (2007) pp.275–295
 Li J.C. Wang T.Y. He G.Y. “3D solid accurate modeling of spiral bevel gear based on manufacture method and meshing theory” J Jilin Univ 2008; 38(6): 1315–1319.
 Jin XY Zhang TF Yang HL. “Research on the 3D solid modeling of high efficient gear tooth based on ProE” ProcediaEng 2012; 29(2): 2990–2994.
 Ding H Adayi XZD. “Methods of and outlook for the modeling of spiral bevel gear” Mach Des Manuf 2014; 51(1): 257–260.
 Tolvaly-Rosca F. Forgó Z. “Mixed CAD method to develop gear surfaces using the relative cutting movements and NURBS surfaces” Procedia Technology 2015; 19(2): 20–27.
 Tolvaly-Rosca F. Máté M. Forgó Z. Kakucs A. “Development of Helical Teethed Involute Gear Meshed with a Multi-Edge Cutting Tool Using a Mixed Gear Teeth Modeling Method” Procedia Engineering Vol.181 pp.153-158 2016.
 Li H.T. Wei W.J. Liu P.Y. “The kinematic synthesis of involute spiral bevel gears and their tooth contact analysis” Mech Mach Theory 2014; 79(9): 141–157.
 Tolvaly-Rosca F “Precision study of bevel gears using solid modeling methods” Phd.Thesis Universitatea Transilvania Brasov Romania 2006.
 Jiang Dan Wang Lancheng “Research on the method of accurate NURBS surface fitting to scattered points” The International Journal of Advanced Manufacturing Technology November 2006 Volume 31 Issue 1–2 pp 92–97
 Chazelle B. “An Optimal Convex Hull Algorithm In any Fixed Direction” Discrete Comput. Geom.10: 377-409(93) Springer Verlag 1993.
 Edelsbrunner H.; D. Kirkpatrick; R. Seidel “On the shape of a set of points in the plane” EEE Transactions on Information Theory (Volume: 29 Issue: 4 July 1983)
 Edelsbrunner H. “Smooth surfaces for multi-scale shape representation.” Foundations of software technology and theoretical computer science Bangalore 1995 pp. 391–412 Lecture Notes in Comput. Sci. 1026 Springer Berlin 1995.
 van Kreveld M. van Lankveld T. Veltkamp R. “On the shape of a set of points and lines in the plane” Technical Report UU-CS-2011-017 Department of Information and Computing Sciences Utrecht University The Netherlands 2011
 Preparata F.P. Hong S.J. “Convex Hulls of Finite Sets of Points in Two and Three Dimensions” Commun. ACM vol. 20 no. 2 pp. 87–93 1977