Geometries & Operations

Geometries

Example of a Box

Open a new file, box.geo, and copy/paste the following line on top of the file:

  SetFactory("OpenCASCADE");

This command forces GMSH to use OpenCascade engine instead of the native one.

With this engine, you generally do not have to build the Point by hand, as ready-to-use geometries are provided. The mesh size must however still be set on every Point. A handy way to set the same mesh size to every Point is to use the two commands Mesh.CharacteristicLengthMin and Mesh.CharacteristicLengthMax at the beginning of the file :

SetFactory("OpenCASCADE");

h = 0.1; // or whatever
Mesh.CharacteristicLengthMin = h;
Mesh.CharacteristicLengthMax = h;

Now, we are going to build the box. Instead of creating the Point, Line, Surface and finally the Volume, add the following line to the file

Box(1) = {0, 0, 0, 1, 1, 1};

And here you go (⌐■_■) ! A nice box of size 1 in every direction (e.g a cube), in a single line!

The Box commands have the following syntax:

Box(index) = {x, y, z, lx, ly, lz};

where

• index: unique identifier of the resulting elementary Volume
• x,y,z: cartesian coordinates of the “bottom left” point
• lx,ly,lz: size in the (resp.) x-,y- and z- direction of the box

Some available geometries

Boolean operations: CAD like a boss (⌐■_■)

General Syntax

Four boolean operations are available in GMSH. They all need two input arguments: an object (first argument) and a tool (second argument). The index of the created element can be provided by the user but remember that the result can be “different” from what expected: a boolean operation can create multiple entities and hence, applying a single index does not make sense!

//Two possible syntax (beware the ";")
BooleanOperation{Object_List; Delete; }{Tool_List; Delete;} 
BooleanOperation(index) = {Object_List; Delete; }{Tool_List; Delete;} ;

The Object_List and Tool_List are not list in the programming point of view rather that an enumeration of entities (Point, Line, Surface, Volume). For example, the list of Line numbered 2, 3 and 6, Surface of every number from 42 to 50 and Volume 11 and 15 will be written as:

Line{2,3,6}; Surface{42:50}; Volume{11,15};

The 4 operations

Example: it’s a good day to dice

Code and expectation

There is nothing better as an example to understand a tool. Let’s build a 6-faces dice in a dice.geo file (copy/paste the following code):

SetFactory('OpenCASCADE');
Mesh.CharacteristicLengthMax = 0.1;
Mesh.CharacteristicLengthMin = 0.1;
Box(1) = {-0.5,-0.5,-0.5, 1, 1, 1};
Sphere(2) = {0,0,0, 0.65};
BooleanIntersection{ Volume{1}; Delete;}{ Volume{2}; Delete;}

Analyse of the code

First, the OpenCascade is set (line 1), then the cube is created (Box) and a sphere (Sphere). The associated Volume indices are respectively 1 and 2. Finally, the boolean operation is launch

BooleanIntersection{ Volume{1}; Delete;}{ Volume{2}; Delete;}

The intersection between Volume{1} (the cube) and Volume{2}(the sphere) is computed. Both Volume are then deleted due to Delete; but GMSH will create a new Volume and the possible Surface and Line associated and, obviously, will provide them a unique identifier. The indices are generally chosen as the “first number available”. As the Volume 1 and 2 has been deleted, there is “high chance” that the index of the newly created Volume will be 1 (because “1” has been freed). This can be check by going in the menu, Tools→Visiblity, and check the elementary entities indices (see remark below).

Draw this head with a conical hat as in the following figure. Be sure that, in the end, there is only one Volume.

To help you design this nice geometry: the sphere is centered at (0,0,0) with a radius equal to 1 while the cone is of parameter (0, 0, 0.5, 0, 0, 1, 1.5, 0).

A focus on BooleanFragments

Probably the most usefull but the less intuitive operation, BooleanFragments, does the following two operations:

1. Fragment the elementary entities: each intersection between entities are computed and become a newly entity with its own index
2. Delete every dupplicated entity, in particular common boundaries (e.g between two Surface or Volume)

Let us take the simple case of a geometry composed by a square and a disk with non empty intersection:

SetFactory("OpenCASCADE");
Mesh.CharacteristicLengthMin = 0.1;
Mesh.CharacteristicLengthMax = 0.1;
Rectangle(1) = {-0.5,-0.5, 0, 1, 1};
Disk(2) = {0.75, 0, 0, 0.75, 0.75};
Mesh 2; // Force GMSH to mesh

Opening this file in GMSH is a deceiving experience: there are 2 meshes and they are overlapping each other!

Let us now add the fragmentation:

SetFactory("OpenCASCADE");
Mesh.CharacteristicLengthMin = 0.1;
Mesh.CharacteristicLengthMax = 0.1;
Rectangle(1) = {-0.5,-0.5, 0, 1, 1};
Disk(2) = {0.75, 0, 0, 0.75, 0.75};
BooleanFragments{ Surface{1,2}; Delete; }{}
Mesh 2; // Force GMSH to mesh

Three entities are created (instead of only one) but there is only one (connected) mesh and no dupplicated boundaries. The three Surface can be regrouped lated into a single Physical Tag so this is absolutely not a problem.

Training examples

Create a nice mug as the below picture. You can use the Rotation operation to rotate the handle:

Rotate{{x,y,z}, {xp,yp,zp}, a}{List}

where (x,y,z) is a vector on the rotation axis, (xp,yp,zp) a point on the axis and a the angle of rotation (in rad). The List argument contains the entities to be modified (Line, Surface and Volume). The quantity π in GMSH is given by the hard coded command Pi.

Try and reproduce the following geometry