Open CASCADE, the 3D modelling kernel
3D modeling & numerical simulation


BSpline Surface

Bezier Surface

vertex, edges, wires...


Modeling data

Modeling Data supplies data structures to represent 2D and 3D geometric and topological models.
These structures are organized in the following libraries:

2D Geometry
This library provides 2D geometric data structures.

The geometric package Geom2d provides STEP-compliant 2D geometric data structures handled by reference.

These objects are parameterized, and as a result, are oriented. They include Bezier, BSpline, and offset curves, and provide functions for conversion of Geom2d objects to gp (basic geometry) objects, which are non-oriented and non-parameterized.

Geom2dLProp local geometric properties package allows computing such properties of a parametric point on a 2D curve as:
- Derivative vectors;
- Tangent vectors (normal and curvature).

3D Geometry
This library provides 3D geometric data structures and topological orientation.

The geometric package Geom provides STEP-compliant 3D geometric data structures handled by reference. These objects are parameterized and are, as a result, oriented. They include Bezier, BSpline, offset curves, and surfaces, and provide functions for conversion of Geom3D objects to gp (basic geometry) objects, which are non-oriented and non-parameterized.

The geometric properties package GeomLProp allows you to compute such properties at the given parametric point on a 3D curve or surface as:
- Derivative vectors
- Tangent vectors (normal and curvature)

Geometry Utilities
This library provides standard high-level functions in 2D and 3D geometry such as:
- Direct construction of algorithms;
- Interpolation of a set of points to form a curve;
- Approximation of curves and surfaces from points;
- Conversion of more elementary geometry to BSpline curves and surfaces;
- Calculation of points on a 2D or 3D curve;
- Calculation of extrema between two geometries.

The topological library allows you to build pure topological data structures.

Topology defines relationships between simple geometric entities. In this way, you can model complex shapes as assemblies of simpler entities. Thanks to the built-in non-manifold (or mixed-dimensional) feature, you can build models mixing:
- 0D entities such as points
- 1D entities such as curves
- 2D entities such as surfaces
- 3D enitities such as volumes.

You can, for example, represent a single object made of several distinct bodies containing embedded curves and surfaces connected or not to the outer boundary.

Abstract topological data structure describes a basic entity, the shape, which can be divided into the following component topologies:
- Vertex, a zero-dimensional shape corresponding to a point in geometry
- Edge, a shape corresponding to a curve, and bounded by a vertex at each extremity
- Wire, a sequence of edges connected by their vertices
- Face, a part of a surface bounded by a number of closed wires
- Shell, a collection of faces connected by some of the edges of their wire boundaries
- Solid, a part of 3D space bounded by a number of closed shells
- Compound solid, a collection of solids

The wire and the solid can be either open (infinite) or closed.

A face with 3D underlying geometry may also refer to a collection of connected triangles that approximate the underlying surface. The surfaces can be undefined leaving the faces represented by triangles only. If so, the model is purely polyhedral.

As well as the above data structures and that for a generalized shape, this library also provides resources to define the location of shapes.

The foundations for Modeling Data C++ libraries were established 10 years ago, which insures the robustness of the model and the perpetuity of data.

Geometry and Topology both depend on the step standard and are defined in separate modules.

The data structure is incremental (sharing of the entities)

Topology defined in Open CASCADE allows regular and multidimensional descriptions of objects: physical objects (manifold objects) or abstract objects (non-manifold objects) and it thus covers a large number of professional domains.

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