The geometric modelling technique has revolutionised design and manufacture of products to a great extent. Although there have been various ways of representing an object, the most commonly used modelling technique is Solid Modelling. The two prominent ways to express solid models are Boundary Representation modelling and Constructive Solid Geometry modelling.


In solid modelling and computer-aided design, boundary representation or B-rep / BREP—is the process of representing shapes using the limits. Here a solid is described as a collection of connected surface elements. BREP was one of the first computer-generated representations to represent three-dimensional objects.

BREP defines an object by their spatial boundaries. It details the points, edges, surfaces of a volume, and sends commands to rotate, sweep a binds facets into a three dimensional solid. The union, thus, enables the formation of a surface that notably encloses a volume

Boundary representation of models consists of two kinds of information:

Topology: The main topological entities are: faces, edges, and vertices.

Geometry: The main geometrical entities are: surfaces,  curves, and points.

The topological and geometrical entities are intertwined in a way where:

the face is a bounded portion of a surface;

an edge is an enclosed piece of a curve and;

A vertex lies at a point. Topological items allow making links between geometrical entities.

BREP comes with its share of advantages and disadvantages, which are:

  • It is appropriate for constructing solid models of unusual shapes.
  • A BREP model is relatively simple to convert to the wireframe model.
  • BREP uses only primitive objects and Boolean operations to combine them, unlike CSG (Constructive Solid Geometry).
  • BREP is more flexible with a more rich operation set.
  • In addition to the Boolean operations, B-rep has extrusion (or sweeping), chamfer, blending, drafting, shelling, tweaking and other actions which make use of these.
  • The BREP library does not store geometric or other information associated with topological entities.
  • BREP is not suitable for applications like tool path generation.

Constructive solid geometry or C-REP/CREP, previously known as computational binary solid geometry, is a solid modelling technique that allows creating a complex object from simple primitives using Boolean operations. It is based on the fundamental that a physical object can be divided into a set of primitives or basic elements that can be combined in a particular order by following a set of rules (Boolean operations), to create an object. Typically, they are objects of simple shapes such as cuboids, cylinders, prisms, pyramids, spheres, and cones.

The primitives themselves are regarded as valid CSG models, where each primitive is bounded by orientable surfaces (Half-spaces).

These simple primitives are in some generic form and must be confirmed by the user to be used in the design. The primitive may require transformations like scaling, translation, and rotation to be assigned a coveted position.

There are two kinds of CSG schemes:

Primitive based CSG: It is a popular CSG scheme which is based on bounded solid primitives, R-sets.

Half-space based CSG: This CSG scheme uses unbounded Half-spaces. Bounded solid primitives and its boundaries are considered composite half-spaces and the surfaces of the component half-spaces, respectively.

Some attributes of CSG are as follows:

  • CSG is fundamentally different from the BREP model, where it does not store faces, edges and vertices. Instead, it evaluates them as needed by algorithms.
  • CSG database stores topology and geometry.
  • The validity checking in CSG scheme occurs indirectly. Each primitive that is combined using a Boolean operation (r-sets) to build the CSG model is checked for its validity.
  • The standard data structures used in CSG are graphs and trees.
  • CSG representation is of considerable importance to manufacturing.


Boundary Representation (BREP) Constructive Solid Geometry (CSG)
BREP describes only the oriented surface of a solid as a data structure composed of vertices, edges, and faces. A solid is represented as a set of Boolean expression of primitive solid objects, of a simpler structure.
A BREP object is easily rendered on a graphic display system. A CSG object is always valid in the sense that its surface is closed and orientable and encloses a volume, provided the primitives are authentic in this sense.
For B-rep, we review the possible surface types, the winged-edge representation schema, and the Euler operators. For CSG, The basic operations include classifying points, curves, and surfaces concerning a solid; detecting redundancies in the representation; and approximating CSG objects systematically.