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# Skills & Competence

## Geometric solver

The core technology of LGS (LEDAS Geometric Solver) consists of a combination of symbolic and numerical methods for solving systems of geometric and algebraic constraints.

Variation of constraint graph analysis based on abstract degree-of-freedom approach is one of symbolic methods used in LGS. Strong point of this method is its ability to decompose a complex geometrical problem (with hundreds of constraints) into a sequence of simpler ones. By solving them one by one, LGS provides a solution of the initial problem. Other decomposition algorithms used in LGS are decomposition by biconnected components and pattern-based decomposition of a constraint graph.

The simplest problems obtained after decomposition are solved algebraically; to solve more complex problems numerical methods are applied.

LGS contains powerful processor for numerical solving of algebraic equations. This processor includes some symbolic methods for rewriting of systems of equations; Among them algebraic decomposition method is the most efficient. It performs division of the system of equations into a set of smaller subsystems. Modified Newton method, Newton-Lagrange and gradient methods are numerical methods built in this processor. Newton method is greatly tuned for the class of system of equations generated from geometric specifications. It also applies efficient adaptive strategy of selection of Newton step size.

LGS uses special know-how technique in order to obtain the so called natural solution of geometric problem, i.e. solution that is expected by user. It allows us to avoid using of the homotopy continuation method that is a commonly used routine for finding of natural solutions. On all code levels LGS supports priorities of parameters that allow to obtain the solutions as natural as possible

The same technologies are used in both 2D and 3D solver, allowing to have rich functionality and competitive performance in both product lines. However technologies and methods are sometimes applied and tuned differently to solve different problems arising from 2D and 3D geometric models.

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