Features and benefits

Geometric modeling is widely used in many software products, but mainly in CAD/CAM/CAE/PLM systems. Other examples include computer games, geometric theorem proving, molecular modeling, publishing, etc. A Geometric Constraint Solver is a computation engine that supports creation and modification of geometric models by means of (explicit or implicit) constraints.

Typical 3D geometric objects are points, lines, planes, arbitrary curves and surfaces. Objects can be fixed in absolute coordinate system or with respect to each other (so called rigid sets of objects). Geometric constraints include logical constraints between geometric entities (like incidence, parallelism, tangency, etc.), dimensional constraints (that specify required values for given distances or angles), or engineering constraints (usually defined by a user). For now, LGS 3D supports many types of logical and dimensional constraints, as well as user-defined white-box equations.

Here are some typical problems solved by geometric constraint solvers:

• find a configuration for a set of geometric objects which satisfies a given set of constraints between the geometric elements;
• if such a configuration does not exist, provide both a partial solution (that satisfies only a subset of given constraints) and information about over-constrained parts of the geometric model;
• drag a given geometric object along a given trajectory keeping all the constraints satisfied.

Objects, constraints, functions

Currently LGS 3D supports the following set of geometric objects:

• points,
• lines,
• planes,
• circles,
• cylinders,
• spheres,
• black-box curves and surfaces,
• swept surfaces defined by a parametric curve and a sweep direction.

A list of supported constraints includes:

• fixation,
• coincidence,
• concentricity,
• distance,
• angle and planar angle,
• perpendicularity and parallelism,
• tangency.

Moreover, LGS 3D operates with variables and equations. Equations are expressed in an explicit form via mathematical notation. Variables can be associated with parameters of geometrical constraints (distance or angle values); therefore algebraic constraints are solved simultaneously with the geometrical ones.

The following functions are available to the user:

• solution of specified set of constraints;
• moving/rotating any objects or groups of objects with respect to given constraints;
• diagnostics of the states of objects and constraints.

Major benefits

Variational functionality is required in a broad spectrum of geometrical applications and the implementation of computational engine for variational solving with necessary performance characteristics is very promising. Based on many years of experience in constraint-based technologies, LEDAS team considers computational power as one of the main advantages of the LEDAS Geometric Solver 3D.

With the benefits of constraint-based technology powered by effective algebraic solver and special geometry-oriented algorithms, LGS 3D can approach almost any end-user task. This, in turn, gives customers a possibility to use LGS 3D not only as a parametrical engine but also as a computation and optimization engine.

Due to combined use of geometric problem decomposition based on constraint graph analysis and a number of efficient computational methods, LEDAS Geometric Solver 3D shows great performance on a broad range of geometry models.

LGS 3D has strong extensible design. It allows incorporation of the solver into a CAD or modeling system as a computational engine. Constraints will be applied immediately as the user adds them to the sketch.

LEDAS offers an attractive pricing policy. Different configurations are available which allow tailoring LGS 3D to any application, from specialized, task-oriented systems and low-end, desktop CAD and modeling solutions to full-featured high-end systems.