# csgdel

Delete boundaries between subdomains

## Description

`[`

deletes the boundaries between subdomains specified in `dl1`

,`bt1`

] = csgdel(`dl`

,`bt`

,`bl`

)`bl`

. If deleting
the boundaries in `bl`

makes the decomposed geometry matrix inconsistent,
then `csgdel`

deletes additional border segments (edge segments between
subdomains) to preserve consistency.

Deleting boundaries typically changes the edge IDs of the remaining boundaries.

`csgdel`

does not delete boundary segments (outer boundaries).

## Examples

### Delete Edges to Merge Faces of 2-D Geometry

Delete edges in a 2-D geometry created in the PDE Modeler app and
exported to the MATLAB^{®} workspace.

Create a geometry in the PDE Modeler app by entering the following commands in the MATLAB Command Window:

pdecirc(0,0,1,'C1') pdecirc(0,0,0.5,'C2') pderect([-0.2 0.2 0.2 0.9],'R1') pderect([0 1 0 1],'SQ1')

Reduce the geometry to the first quadrant by intersecting it with a square. To do
this, enter `(C1+C2+R1)*SQ1`

in the **Set formula**
field.

From the PDE Modeler app, export the geometry description matrix, set formula, and
name-space matrix to the MATLAB workspace by selecting **Export Geometry Description, Set
Formula, Labels** from the **Draw** menu.

In the MATLAB Command Window, use the `decsg`

function to decompose the exported geometry into minimal regions.
This creates an `AnalyticGeometry`

object `dl`

. Plot
`dl`

.

[dl,bt] = decsg(gd,sf,ns); pdegplot(dl,'EdgeLabels','on','FaceLabels','on') xlim([-0.1 1.1]) ylim([-0.1 1.1])

Remove edges 1, 2, and 13 using the `csgdel`

function. Specify the
edges to delete as a vector of edge IDs. Plot the resulting geometry.

[dl1,bt1] = csgdel(dl,bt,[1 2 13]); pdegplot(dl1,'EdgeLabels','on','FaceLabels','on') xlim([-0.1 1.1]) ylim([-0.1 1.1])

Now remove all boundaries between subdomains and plot the resulting geometry.

[dl1,bt1] = csgdel(dl,bt); pdegplot(dl1,'EdgeLabels','on','FaceLabels','on') xlim([-0.1 1.1]) ylim([-0.1 1.1])

## Input Arguments

`dl`

— Decomposed geometry matrix

matrix of double-precision numbers

Decomposed geometry matrix, returned as a matrix of double-precision numbers. It
contains a representation of the decomposed geometry in terms of disjointed minimal
regions constructed by the `decsg`

algorithm. Each edge segment of
the minimal regions corresponds to a column in `dl`

. Edge segments
between minimal regions (subdomains) are *border segments*. Outer
boundaries are *boundary segments*. In each column, the second and
third rows contain the starting and ending *x*-coordinates. The fourth
and fifth rows contain the corresponding *y*-coordinates. The sixth and
seventh rows contain left and right minimal region labels with respect to the direction
induced by the start and end points (counterclockwise direction on circle and ellipse
segments). There are three types of possible edge segments in a minimal region:

For circle edge segments, the first row is

`1`

. The eighth and ninth rows contain the coordinates of the center of the circle. The 10th row contains the radius.For line edge segments, the first row is

`2`

.For ellipse edge segments, the first row is

`4`

. The eighth and ninth rows contain the coordinates of the center of the ellipse. The 10th and 11th rows contain the semiaxes of the ellipse. The 12th row contains the rotational angle of the ellipse.

All columns in a decomposed geometry matrix have the same number of rows. Rows that are not required for a particular shape are filled with zeros.

Row number | Circle edge segment | Line edge segment | Ellipse edge segment |
---|---|---|---|

1 | 1 | 2 | 4 |

2 | starting x-coordinate | starting x-coordinate | starting x-coordinate |

3 | ending x-coordinate | ending x-coordinate | ending x-coordinate |

4 | starting y-coordinate | starting y-coordinate | starting y-coordinate |

5 | ending y-coordinate | ending y-coordinate | ending y-coordinate |

6 | left minimal region label | left minimal region label | left minimal region label |

7 | right minimal region label | right minimal region label | right minimal region label |

8 | x-coordinate of the center | x-coordinate of the center | |

9 | y-coordinate of the center | y-coordinate of the center | |

10 | radius of the circle | x-semiaxis before rotation | |

11 | y-semiaxis before rotation | ||

12 | Angle in radians between |

**Data Types: **`double`

`bt`

— Boolean table relating original shapes to minimal regions

matrix of 1s and 0s

Boolean table relating the original shapes to the minimal regions, returned as a matrix of 1s and 0s.

**Data Types: **`double`

`bl`

— Boundaries to delete

positive integer | vector of positive integers

Boundaries to delete, specified as a positive integer or a vector of positive integers. Each integer represents a boundary ID.

**Data Types: **`double`

## Output Arguments

`dl1`

— Modified decomposed geometry matrix

matrix of double-precision numbers

Modified decomposed geometry matrix, returned as a matrix of double-precision numbers.

**Data Types: **`double`

`bt1`

— Boolean table relating remaining original shapes to minimal regions

matrix of 1s and 0s

Boolean table relating the remaining original shapes to the minimal regions, returned as a matrix of 1s and 0s.

**Data Types: **`double`

## See Also

**Introduced before R2006a**

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