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 geometric objects are points, lines, circles, curves (both 2D and 3D), planes and arbitrary surfaces (3D only). 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, symmetry, etc.), dimensional constraints (that specify required values for given distances, radii, angles), or engineering constraints (like equal distances and radii, other mathematical relations on dimensions).

Here are some typical problems solved by geometric constraint solvers:

• Finding 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

Actually LGS offers all features that an end-user expects from a variational geometric solver:

• points,
• lines and segments,
• circles and circular arcs,
• ellipses and elliptic arcs,
• black-box curves,
• splines.

The list of supported constraints includes:

• fixation,
• coincidence,
• concentricity,
• distance,
• angle, perpendicularity and parallelism,
• tangency,
• midpoint,
• symmetry,
• equal distance and equal radii,
• fixation of ellipse radii and fixation of circle radius,
• angle with Ox coordinate axis,
• verticality,
• horizontality,
• vertical and horizontal distance.

Moreover, LGS operates with variables and equations. Equations are expressed in an explicit form (via mathematical notation) or as black-boxes evaluated by an application. Variables can be associated with parameters of geometrical constraints (e.g. distance or angle values); therefore algebraic constraints are solved simultaneously with the geometrical ones. In order to specify admissible domains for parameters of geometrical constraints or other variables application is able to use inequalities.

Set of supported constraints can be widened due to powerful mechanism of black-box constraints with semantics defined by an application, e.g. area constraint or contour length constraint can be modeled by an application and solved by LGS.

The following functions are available to the user:

• solving geometrical model, i.e. finding a configuration satisfying all imposed constraints;
• moving/rotating of any object or group of objects keeping constraints satisfied;
• preservation of design form;
• various algebraic and numerical methods;
• computations for underconstrained models and indication of overconstrainedness;
• indication of well-defined (rigid) or under-defined (non-rigid) parts of the sketch;
• automatic adding of constraints to an unconstrained or partially constrained model in order to make the model fully parametric;
• solving of different optimization problems under geometric and engineering 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.

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

Due to combined use of geometric problem decomposition (Hoffmann constraint graph analysis, articulation point decomposition, etc.) and a number of efficient computational methods, LEDAS Geometric Solver shows great performance on a broad range of geometry models.

LEDAS Geometric Solver has strong extensible design with incremental model processing. 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 to any application, from specialized, task-oriented systems and low-end, desktop CAD and modeling solutions to full-featured high-end systems.