Boundary Representation Brep Solid model is defined by

Boundary Representation (B-rep) • Solid model is defined by their enclosing surfaces or boundaries. This technique consists of the geometric information about the faces, edges and vertices of an object with the topological data on how these are connected. • B-rep model is created using Euler operation • Data structure : • B-Rep graph store face, edge and vertices as nodes, with pointers, or branches between the nodes to indicate connectivity. http: //creativecommons. org/licenses/by-sa/4. 0/

B-Rep data structure [1]Mastering in cad/cam by ibrahim zeid , Tata publishing house

[1]Mastering in cad/cam by ibrahim zeid , Tata publishing house DHARANI KUMAR. S/AP/MECH

DHARANI KUMAR. S/AP/MECH

Boundary representation- validity • Validity also checked through mathematical evaluation • Evaluation is based upon Euler’s Law (valid for simple solid – no hole) F-E+V-L =2 (B-G) • F-E+V = 2 v 5 f 3 f 2 E 3 E 4 E 7 E 1 v 4 f 5 E 2 E 6 v 3 f 1 E 8 v 1 E 5 v 2 V = 5, E = 8, F = 5 5– 8+5=2 V- number of vertices E- number of edges F- number of faces [1]Mastering in cad/cam by ibrahim zeid , Tata publishing house

Boundary representation- validity • Expanded Euler’s law for complex polyhedrons (with holes) • Euler-Poincare Law: • F-E+V-H+2 P=2 B • H – number of holes in face, P- number of passages or through holes, B- number of separate bodies. V = 24, E=36, F=15, H=3, P=1, B=1 [1]Mastering in cad/cam by ibrahim zeid , Tata publishing house

DHARANI KUMAR. S/AP/MECH

B-Rep data structure v 5 f 3 E 4 E 1 v 4 f 4 E 8 v 1 E 5 edge 1 f 2 E 3 E 7 v 3 f 5 E 2 E 6 f 1 edge 2 vertex 1 v 2 face 1 solid face 2 face 3 edge 4 vertex 2 vertex 3 edge 5 (x, y, z) face 4 edge 6 vertex 4 face 5 edge 7 Combinatorial edge 8 structure / topology vertex 5 Metric information/ geometry [1]Mastering in cad/cam by ibrahim zeid , Tata publishing house

Boundary representation- advantages • Capability to construct unusual shapes that would not be possible with the available CSG aircraft • Less computational time to reconstruct the image

Boundary representationdisadvantages • Requires more storage • More prone to validity failure than CSG • Model display limited to planar faces and linear edges - complex curve and surfaces only approximated

Solid modeling - Advantages • Has all the advantages of surface models (uniqueness, non-ambiguous, realistic, surface profile) plus volumetric information. • Allows the designer to create multiple options for a design. • 2 D standard drawings, assembly drawing and exploded views are generated form the 3 D model. • Can easily be exported to different Finite Element Methods programs for analysis. • Mass and volumetric properties of an object can be easily obtained; total mass, mass center, area and mass moment of inertia, volume, radius of gyration.

Solid modeling - Disadvantages • More intensive computation than wireframe and surface modeling. • Requires more powerful computers (faster with more memory and good graphics)