﻿ Objects > sgCObject > sgC3DObject > Additional types > SgCBRep

sgCBRep

In the sgCore library all 3D solids are stored in the form of the polygonal surface representation - boundary representation – BRep. This representation defines a solid implicitly by describing its boundary surface. Each surface is approximated by a set of faces. The fragmentation is performed in such a way that each face has a compact mathematical representation.

Face boundaries are represented by edges.  Edges are selected like faces in such a way that each edge has a compact mathematical description. A part of the curve that forms an edge is ended by vertexes. It's necessary to introduce such a term as cycle (the description of each face contour) because every face can be a non-convex polygon with any number of holes.

A surface model which has only flat faces is called a polygonal model – this type of description is used in sgCore. So, every face is a polygon which consists of the vertex coordinates sequence. An object consists of the set of faces.

SgCore also introduces such a term as BRep piece. A BRep piece is a piece of simply connected boundary body surface.

This term has been introduced to accelerate the work of some algorithms (such as Boolean operations). Each BRepPiece has a limitary dimensional parallelogram. It was designed to avoid passes of each BRep pieces face in the cycles. All BRep pieces connected together form a full BRep.

Let's look at the BRep description on the solid example created by extruding a flat non-convex contour with one hole. This BRep is divided into 4 pieces – 2 bases, a side face and a hole surface.

Below you can see the table of the vertex and edge descriptions for all BRep pieces.

The vertex coordinate recurrence can be avoided by grouping the vertex coordinates in a separate array. In this case vertex coordinate indexes in the array (not the vertex coordinates themselves) get associated with faces and edges. In this case (see the picture) we have:

BRep Piece number and description

Vertexes

Edges

Name

Number

X

Y

Z

Name

Number

Begin

End

0

Bottom base

v0

v1

v2

v3

v4

v5

v6

v7

0

1

2

3

4

5

6

7

-2.0

1.0

0.0

0.0

-1.0

-0.4

-0.5

-1.0

0.0

2.0

0.0

-2.0

-0.6

-0.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

e0

e1

e2

e3

e4

e5

e6

e7

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

1

2

3

0

5

6

7

4

1

Side face

v0

v8

v1

v9

v2

v10

v3

v11

0

1

2

3

4

5

6

7

-2.0

-2.0

1.0

1.0

0.0

0.0

0.0

0.0

0.0

0.0

2.0

2.0

0.0

0.0

-2.0

-2.0

0.0

1.0

0.0

1.0

0.0

1.0

0.0

 1

e0

e16

e8

e1

e19

e9

e2

e18

e10

e3

e17

e11

0

1

2

3

4

5

6

7

8

9

10

11

0

0

1

2

2

3

4

4

5

6

6

7

2

1

3

4

3

5

6

5

7

0

7

1

2

Top base

v8

v9

v10

v11

v12

v13

v14

v15

0

1

2

3

4

5

6

7

-2.0

1.0

0.0

0.0

-1.0

-0.4

-0.5

-1.0

0.0

2.0

0.0

-2.0

-0.6

-0.8

0.0

0.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

e8

e9

e10

e11

e12

e13

e14

e15

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

1

2

3

0

5

6

7

4

3

Hole surface

v4

v12

v5

v13

v6

v14

v7

v15

0

1

2

3

4

5

6

7

-1.0

-1.0

-0.4

-0.4

-0.5

-0.5

-1.0

-1.0

-0.6

-0.6

-0.8

-0.8

0.0

0.0

0.0

0.0

0.0

1.0

0.0

1.0

0.0

1.0

0.0

1.0

e4

e20

e12

e5

e21

e13

e6

e22

e14

e7

e23

e15

0

1

2

3

4

5

6

7

8

9

10

11

0

0

1

2

2

3

4

4

5

6

6

7

2

1

3

4

3

5

6

5

7

0

7

1

A face is represented by a set of edges. An index of the initial face edge is set and the cycle structure determines each next face edge. In this way the outer contours of the faces and their holes can be set.