# Modeling Data

## Introduction

Based on Open Cascade - Modeling Data.

Boundary representation (BRep hereafter) is used to represent shapes in solid modeling.

In BRep the shape is represented as an aggregation of geometry within topology. The geometry is understood as a mathematical description of a shape, e.g. as curves and surfaces (simple or canonical, Bezier, NURBS, etc). The topology is a data structure binding geometrical objects together.

Geometry types and utilities provide geometric data structures and services for: - Description of points, vectors, curves and surfaces:

• their positioning in 3D space using axis or coordinate systems, and
• their geometric transformation, by applying translations, rotations, symmetries, scaling transformations and combinations thereof.

• Creation of parametric curves and surfaces by interpolation and approximation;

• Algorithms of direct construction;
• Conversion of curves and surfaces to NURBS form;
• Computation of point coordinates on 2D and 3D curves;
• Calculation of extrema between geometric objects.

Topology defines relationships between simple geometric entities. A shape, which is a basic topological entity, can be divided into components (sub-shapes):

• Vertex – a zero-dimensional shape corresponding to a point;
• 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 plane (in 2D) or a surface (in 3D) bounded by wires;
• Shell – a collection of faces connected by edges of their wire boundaries;
• Solid – a finite closed part of 3D space bounded by shells;
• Compound solid – a collection of solids connected by faces of their shell boundaries.

Complex shapes can be defined as assemblies of simpler entities.