# Modeling Algorithms

#### Modeling Algorithms containing a vast range of geometrical and topological algorithms.

Modeling Algorithms module groups a wide range of topological and geometric algorithms used in geometric modeling. Basically, there are two groups of algorithms in Open CASCADE Technology:

• High-level modeling routines used in the real design;
• Low-level mathematical support functions used as a groundwork for the modeling API;
• Low-level geometric tools provide the algorithms, which:
• Calculate the intersection of two curves, surfaces, or a curve and a surface;
• Project points onto 2D and 3D curves, points onto surfaces and 3D curves onto surfaces;
• Construct lines and circles from constraints;
• Construct free-form curves and surfaces from constraints (interpolation, approximation, skinning, gap filling, etc);
• Low-level topological tools provide the algorithms, which:
• Tessellate shapes;
• Check correct definition of shapes;
• Determine the local and global properties of shapes (derivatives, mass-inertia properties, etc);
• Perform affine transformations;
• Find planes in which edges are located;
• Convert shapes to NURBS geometry;
• Sew connected topologies (shells and wires) from separate topological elements (faces and edges).

Top-level API provides the following functionality:

• Construction of Primitives:
• Boxes;
• Prisms;
• Cylinders;
• Cones;
• Spheres;
• Toruses.
• Kinematic Modeling:
• Prisms - linear sweeps;
• Revolutions - rotational sweeps;
• Pipes - general-form sweeps;
• Lofting.

Shapes containing pipes with variable radius produced by sweeping

• Boolean Operations, which allow creating new shapes from the combinations of source shapes. For two shapes S1 and S2:
• Common contains all points that are in S1 and S2;
• Fuse contains all points that are in S1 or S2;
• Cut contains all points in that are in S1 and not in S2.

See Boolean Operations User's Guide for detailed documentation.

• Algorithms for local modifications such as:
• Hollowing;
• Shelling;
• Creation of tapered shapes using draft angles;
• Algorithms to make fillets and chamfers on shape edges, including those with variable radius (chord).
• Algorithms for creation of mechanical features, i.e. depressions, protrusions, ribs and grooves or slots along planar or revolution surfaces.

Please, see the details in Modeling Algorithms User's Guide.