Geometric solver ( Geometric Constraint Solver ), geometric constraint solver, geometric constraint solver is a software component that integrates into CAD and allows the engineer to accurately position geometric elements relative to each other.
Two-dimensional geometric solvers work with geometric objects on the plane, and allow you to create two-dimensional drawings, and three-dimensional geometric solvers are usually used to assemble parts of mechanisms and other structures. An engineer imposes geometric constraints (parallelism, perpendicularity, coincidence, alignment, etc.) on geometric objects (points, lines, planes, circles, spheres, etc.) and after the solver works, he receives a solution to the problem - the new coordinates of the objects and the values of their parameters ( such as the radii of circles or the angles of cones) satisfying the constraints. In case of unsolvability of the problem, the geometric solver gives a message about the incompatibility of the model. As a rule, geometric solvers also contain implementations of related functions: determining the under- and overdetermination of the problem, auto-generation of constraints, movement of objects while maintaining the constraints imposed on them, etc.
Content
Methods
The general scheme of the work of geometric solvers consists in generating a system of nonlinear equations that models geometric constraints imposed on objects, and solving this system, as a rule, using iterative methods, such as the Newton-Raphson method. Essential for the correctness and performance of geometric solvers is the modeling method.
To accelerate the work of solvers, various methods of problem decomposition are used: [1] decomposition-recombination, [2] [3] tree-like decomposition, [4] C-tree decomposition, [5] graph reduction, [6] re-parametrization and reduction, [ 7] computing fundamental circuits, [8] body-and-cad structure, [9] and witness configuration method. [ten]
Some other methods and approaches include the analysis of degrees of freedom, [11] [12] symbolic calculations , [13] application of rule systems, [14] programming in constraints , [14] [15] and genetic algorithms . [sixteen]
Systems of nonlinear equations are mainly solved using iterative methods; a linear problem is solved at each iteration. The Newton-Raphson method is one of the most famous examples. [14]
The solver passes the information on to the geometric core , which performs the construction of the geometric model using the coordinates and parameters of the objects obtained by the solver.
Applications and software
The main field of application of geometric solvers is CAD. They are also used to solve the problems of reverse kinematics, robotics, architectural design, geometric modeling of molecules and other applied fields.
Geometric solvers include:
- 2D Dimensional Constraint Manager (DCM), 3D DCM ( D-Cubed ), owned by Siemens PLM Software , integrated into AutoCAD , SolidWorks , Creo and many other popular CAD systems; [17]
- 2D LEDAS Geometric Solver (LGS), 3D LGS ( LEDAS );
- C3D Solver parametric core ( C3D Labs ), integrated into KOMPAS-3D ; [18]
- GeoSolver, [19] a Python package for solving geometric constraints, distributed under the GNU General Public License .
See also
- Geometric core
- Parametric modeling
Notes
- ↑ Pascal Mathis, Simon EB Thierry. A formalization of geometric constraint systems and their decomposition .
- ↑ Christoph M. Hoffman, Andrew Lomonosov, Meera Sitharam. Decomposition Plans for Geometric Constraint Systems, Part I: Performance Measures for CAD .
- ↑ Christoph M. Hoffman, Andrew Lomonosov, Meera Sitharam. Decomposition Plans for Geometric Constraint Problems, Part II: New Algorithms .
- ↑ Marta Hidalgoa, Robert Joan-Arinyo. h-graphs: A new representation for tree decompositions of graphs .
- ↑ Xiao-Shan Gao, Qiang Lin, Gui-Fang Zhang. A C-tree decomposition algorithm for 2D and 3D geometric constraint solving .
- ↑ Samy Ait-Aoudia, Sebti Foufou. A 2D geometric constraint solver using a graph reduction method .
- ↑ Hichem Barki, Lincong Fang, Dominique Michelucci, Sebti Foufou. Re-parameterization reduces irreducible geometric constraint systems .
- ↑ R. Joan-Arinyo, M. Tarres-Puertas, S.Vila-Marta. Decomposition of geometric constraint graphs based on computing fundamental circuits. Correctness and complexity .
- ↑ Kirk Haller, Audrey Lee-St. John, Meera Sitharam, Ileana Streinu, Neil White. Body-and-cad geometric constraint systems .
- ↑ Dominique Michelucci, Sebti Foufou. Geometric constraint solving: The witness configuration method .
- ↑ Kramer Glenn A. Solving geometric constraint systems: a case study in kinematics . - 1: a upplagan. - Cambridge, Mass. : MIT Press, 1992. - ISBN 9780262111645 .
- ↑ Xiaobo Peng, Kunwoo Lee, Liping Chen. A geometric constraint solver for 3-D assembly modeling .
- ↑ Xiao-Shan Gao, Shang-Ching Chou. Solving Geometric Constraint Systems II. A Symbolic Approach and Decision of Rc-constructibility .
- ↑ 1 2 3 William Bouma, Ioannis Fudos, Christoph M. Hoffmann, Jiazhen Cai, Robert Paige. A Geometric Constraint Solver . - 1993.
- ↑ Michela Farenzena, Andrea Fusiello. Stabilizing 3D modeling with geometric constraints propagation .
- ↑ R. Joan-Arinyo, MV Luzón, A. Soto. Constructive Geometric Constraint Solving: A New Application of Genetic Algorithms .
- ↑ D-Cubed Customers .
- ↑ Evgeny Ermakov, Sergey Mitin, Sergey Rotkov, Alexander Maksimenko. Using C3D Solver to solve the kinematic problems of mechanism nodes . LEDAS Ltd. (January 6, 2017).
- ↑ GeoSolver Project Page .
Links
- W. Bouma. A Geometric Constraint Solver . - DOI : 10.1016 / 0010-4485 (94) 00013-4 .
- Geometric constraint solver . www.v-rep.eu. Date of treatment January 21, 2017.
- Geometric constraint solver - PLMpedia . plmpedia.ru. Date of treatment January 21, 2017.
- Ershov A.G. How world-class engineering software is created. Geometric Solver - “The Great Combinator” (Russian) // First-hand Science: Journal. - 2013. - July 22 ( t. 50 , No. 2 ).
- Price S. LGS - An Effective and Affordable Solver of Geometric Problems (Russian) // CAD and Graphics: Journal. - 2003. - No. 9 .
- Vladimir Malyukh. Geometric constraint solver // Introduction to modern CAD. Course of lectures . - Litres, 2017-01-03. - S. 186. - 190 p. - ISBN 9785457517165 .
- Ushakov D.M. Variational geometric solver // Introduction to the mathematical foundations of CAD, Course of lectures. - 2011 .-- S. 84.