Constructing three-dimensional geometric objects defined by constraints

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Constructing three-dimensional geometric objects defined by constraints

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Symposium on Interactive 3D Graphics archive
Proceedings of the 1986 workshop on Interactive 3D graphics table of contents

Chapel Hill, North Carolina, United States

Pages: 111 - 129

Year of Publication: 1987

ISBN:0-89791-228-4

Author

Beat Brüderlin

Inst. für Informatik, ETH, CH-8092 Zürich, Switzerland

Sponsor

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 8, Downloads (12 Months): 34, Citation Count: 10

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ABSTRACT

We developed a system for automatically building three-dimensional geometric objects that are defined by their topology and by geometric constraints. A solid modeller is used for sketching the object. The geometric constraints are first evaluated symbolically by an algorithm written in Prolog. The symbolic solution is then numerically evaluated by procedures linked to Prolog.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	C.M. Brown. "PADL-2": A Technical Summary. IEEE Computer Graphics and Applications, Vol. 2, No. 2, pp. 69 - 84, March 1982.
	2	Beat Brüderlin, Using Prolog for Constructing Geometric Objects defined by Constraints, Research Contributions from the European Conference on Computer Algebra-Volume 2, p.448-459, April 01-03, 1985
	3	B. Briiderlin. A Half-Space Approach for Regularized Set Operations on Polyhedra. Report No 86-08, Mathematik, ETH Ziirich 1986.
	4	W F. Clocksin , Christopher S. Mellish, Programming in Prolog (2nd ed.), Springer-Verlag New York, Inc., New York, NY, 1984
	5	E. Engeler. Metamathematik der Elementarmathematik. Springer Verlag, Berlin, Heidelberg, New York 1983
	6	D. Hilbert. Foundations of Geometry. Open Court Publishing Company, La Salla, Illinois 1971
	7	D.E. Knuth, P.B. Bendix. Simple Word Problems in Universal Algebra. Computational Problems in Abstract Algebra, Conference ProceeAings, Oxford 1967, J. Leech ed., Pergamon 1970
	8	C. Muller. Modula-prolog, User Manual. Rep. No. 63, July 1985. Inst. fiJr Informatik, ETH Ziirich, Switzerland
	9	Greg Nelson, Juno, a constraint-based graphics system, Proceedings of the 12th annual conference on Computer graphics and interactive techniques, p.235-243, July 1985
	10	Aristides G. Requicha, Representations for Rigid Solids: Theory, Methods, and Systems, ACM Computing Surveys (CSUR), v.12 n.4, p.437-464, Dec. 1980 [doi>10.1145/356827.356833]
	11	W. Schwabh/iuser, W. Szmielev, A. Tarski, Metamathematische Methoden in der Geometrie (german), Springer Verlag Berlin, Heidelberg, New York 1983
	12	I. Sutherland. Sketchpad, A Man-Machine Graphical Communication System. PhD. thesis, MIT, January 1963
	13	Niklaus Wirth, Programming in MODULA-2 (3rd corrected ed.), Springer-Verlag New York, Inc., New York, NY, 1985

CITED BY 10

	David C. Gossard , Robert P. Zuffante , Hiroshi Sakurai, Representing Dimensions, Tolerances, and Features in MCAE Systems, IEEE Computer Graphics and Applications, v.8 n.2, p.51-59, March 1988
	Ioannis Fudos , Christoph M. Hoffmann, A graph-constructive approach to solving systems of geometric constraints, ACM Transactions on Graphics (TOG), v.16 n.2, p.179-216, April 1997
	C. Hsu , G. Alt , Z. Huang , E. Beier , B. Brüderlin, A constraint-based manipulator toolset for editing 3D objects, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.168-180, May 14-16, 1997, Atlanta, Georgia, United States
	Jean-François Dufourd , Pascal Mathis , Pascal Schreck, Formal resolution of geometrical constraint systems by assembling, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.271-284, May 14-16, 1997, Atlanta, Georgia, United States
	Wolfgang Sohrt , Beat D. Brüderlin, Interaction with constraints in 3D modeling, Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications, p.387-396, June 05-07, 1991, Austin, Texas, United States
	Ghassan Kwaiter , Véronique Gaildrat , René Caubet, Interactive constraint system for solid modeling objects, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.265-270, May 14-16, 1997, Atlanta, Georgia, United States
	Hervé Lamure , Dominique Michelucci, Solving geometric constraints by homotopy, Proceedings of the third ACM symposium on Solid modeling and applications, p.263-269, May 17-19, 1995, Salt Lake City, Utah, United States
	Mingxian Fa , Terrence Fernando , Peter M. Dew, Interactive constraint-based solid modeling using allowable motion, Proceedings on the second ACM symposium on Solid modeling and applications, p.243-252, May 19-21, 1993, Montreal, Quebec, Canada
	Hervé Lamure , Dominique Michelucci, Solving Geometric Constraints By Homotopy, IEEE Transactions on Visualization and Computer Graphics, v.2 n.1, p.28-34, March 1996
	Jiang Kun , Gao Yang Lv Xingfeng , Zhan Yang, Parallel algorithms on geometric constraint solving, Proceedings of the 2007 ACM symposium on Applied computing, March 11-15, 2007, Seoul, Korea