Boundary view

The boundary representation of the model consists of two parts: topology and geometry (surfaces, curves, and points). The main topological elements: faces , edges and vertices . A face is a limited part of a surface, an edge is a limited part of a curve, and a vertex is a point. Other elements are the shell (a set of adjacent faces), the loop (the contour of the edges that bound the face), and the contour footnotes (also known as the footnotes of the winged edge or half-edge ) used to construct the contour from the edges.

The basic method of boundary representation was developed by Ian C. Braid in Cambridge (for CAD) and Bruce G. Baumgart in Stanford (for computer vision systems) independently in the early 1970s. Bride continued his work at the BUILD solid state research modeler, which was the forerunner to many scientific and commercial solid modeling systems. Bride worked on commercial ROMULUS systems, the predecessor of Parasolid , and on ACIS. Parasolid and ACIS are the foundation for many modern commercial CAD systems.

After Brid’s work on solids, the Swedish team, led by Professor Torsten Chelberg in the early 1980s, developed a philosophy and methods for working with hybrid models, wireframe, sheet objects and three-dimensional models. In Finland, Martti Mäntylä has developed a solid modeling system called GWB. Eastman and Weiler in the USA also worked on the boundary representation, and Professor Fumihiko Kimura and his team from the University of Tokyo in Japan created their own boundary modeling systems.

Compared to the representation in the form of structural block geometry ( CSG ), ( English CSG ), which uses only primitive objects and Boolean operations to combine them, the boundary representation is more flexible and has a much richer set of operations: extrusion , chamfering , mixing, training, shelling, tuning, and others. This makes the boundary view a more suitable choice for CAD. CSG was originally used by several commercial systems because it was easier to implement. The advent of robust commercial BREP modeling cores, such as the Parasolid and ACIS mentioned above, has led to the widespread adoption of boundary representation in CAD.

The boundary representation is essentially a local representation of adjacent faces, edges, and vertices. An extension to this was the grouping of sub-elements of a form into logical units called geometric parts , or simply, ' parts' . The groundbreaking work was done by Cyprian at Cambridge also using the BUILD system and continued and expanded by Jared and others. Details underlie many other developments that allow for high-level "geometric reasoning" about the form for comparison, planning processes, production, etc.

The boundary representation was also expanded by the introduction of special non-monolithic types of models called non-assembled models . According to Bride's description, normal solids in nature have the property that for each point on the boundary, any cleavage or small sphere around it is divided into two parts: one inside and the other outside the object. Simple models violate this rule. An important subclass of simple models are sheet objects, which are used to represent flat objects and integrate surface modeling into solid modeling.

STEP Simulation Data Exchange Standard   Defines some data models for displaying boundaries. Generalized topological and geometric models are defined in ISO 10303-42 "Geometric and topological representations . " The following integrated resources applications (AIC) define the boundaries of the model, the limitations of universal geometric and topological capabilities:

• ISO 10303-511 A topologically bounded surface , the definition of an expanded face , which is the boundary surface when the surface is of the elementary type (planes, cylindrical, conical, spherical or toroidal), or a surface along a path, or a B spline surface. Borders are defined by lines, conics, polylines, curved surfaces, or B spline curves
• ISO 10303-514 extended boundary representation , solid, defining the volume with possible voids that make up the forefront
• ISO 10303-509 surface collector without crossing terrain in 3D, which consists of advanced faces
• ISO 10303-521 subsurface collector , sub-corner from collector surface
• ISO 10303-508 uncomplicated surface of any prior arrangement by a person
• ISO 10303-513 elementary boundary representation similar to ISO 10303-514, but limited to elementary surface only
• ISO 10303-512 faceted boundary representation of a simplified surface model constructed on a flat surface only

Additional information on boundary representation can be found in various articles and the following books:

• Mäntylä, Martti. An Introduction to Solid Modeling. - Computer Science Press , 1988. - ISBN 0-88175-108-1 .
• Chiyokura, H. Solid Modeling with DESIGNBASE. - Addison-Wesley Publishing Company , 1988. - ISBN 0-201-19245-4 .
• Stroud, Ian. Boundary Representation Modeling Techniques. - Springer , 2006. - ISBN 1-84628-312-4 .

• Opencascade

• OpenCascade - An open source library for solid modeling BREP
• Real Example Borders of the Original Step View
• SimpleGeo - BREP / CWG Hybrid Simulation Monte Carlo Particle Transport Simulation System
• FreeREP - open source kernel development geometry
• Brep by - boundary view based Modeller