CADGeometrie

CADGeometrie is the mathematical description and manipulation of shapes within computer-aided design (CAD) systems. It encompasses the representation, construction, modification, and analysis of geometric entities used in engineering, architecture, and manufacturing. The core purpose is to enable precise, repeatable, and editable models that reflect real-world objects.

Geometric entities include points, lines, curves (Bézier, B-spline, NURBS), surfaces, and solids. They are organized in a geometry kernel providing operations such as intersection, union, difference, trimming, filleting, offsetting, and boolean modeling. Representations can be explicit (parametric equations), implicit (level-set or distance fields), or boundary-based (B-rep). Many CAD systems also use polygonal meshes for visualization.

Modeling approaches include parametric modeling, which links geometry to parameters and constraints, enabling design intent to be preserved; direct or facet-based modeling edits geometry directly; and feature-based modeling, which builds parts from named features that define history and reuse. Techniques include sketching, constraints, lofting, sweeping, and common boolean operations.

NURBS and splines provide smooth curves and surfaces. Managing precision, tolerances, and degeneracies is essential, as floating-point arithmetic can cause tiny gaps or overlaps. Robust kernels use exact predicates, reliable intersection routines, and tolerance control to maintain model integrity.

Interoperability relies on standards such as STEP and IGES, and clear topological representations (B-rep or CSG). Units and coordinate systems affect portability.

CADGeometrie supports applications from mechanical parts to architectural models, assemblies, and digital twins. Developments focus on real-time editing, parametric history, cloud collaboration, and integration with simulation and manufacturing.