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The first surface loop defines the exterior boundary of the volume; all other surface loops define holes in the volume. A surface loop defining a hole should not have any surfaces in common with the exterior surface loop in which case it is not a hole, and the two volumes should be defined separately. Likewise, a surface loop defining a hole should not have any surfaces in common with another surface loop defining a hole in the same volume in which case the two surface loops should be combined.

Creates a sphere, defined by the 3 coordinates of its center and a radius. Additional expressions define 3 angle limits. Creates a box, defined by the 3 coordinates of a point and the 3 extents. Creates a cylinder, defined by the 3 coordinates of the center of the first circular face, the 3 components of the vector defining its axis and its radius. An additional expression defines the angular opening.

Creates a torus, defined by the 3 coordinates of its center and 2 radii.

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Creates a cone, defined by the 3 coordinates of the center of the first circular face, the 3 components of the vector defining its axis and the two radii of the faces these radii can be zero. Creates a right angular wedge, defined by the 3 coordinates of the right-angle point and the 3 extends.

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An additional parameter defines the top X extent zero by default. Creates a volume defined through curve loops. Same as ThruSections , but the surfaces created on the boundary are forced to be ruled. Creates a physical volume. Curves, surfaces and volumes can also be created through extrusion of points, curves and surfaces, respectively. Here is the syntax of the geometrical extrusion commands go to Structured grids , to see how these commands can be extended in order to also extrude the mesh :. Extrudes all elementary entities points, curves or surfaces in extrude-list using a translation.

The expression-list should contain three expression s giving the X, Y and Z components of the translation vector.

Extrudes all elementary entities points, curves or surfaces in extrude-list using a rotation. The first expression-list should contain three expression s giving the X, Y and Z direction of the rotation axis; the second expression-list should contain three expression s giving the X, Y and Z components of any point on this axis; the last expression should contain the rotation angle in radians. With the built-in geometry kernel the angle should be strictly smaller than Pi.

The first expression-list should contain three expression s giving the X, Y and Z components of the translation vector; the second expression-list should contain three expression s giving the X, Y and Z direction of the rotation axis, which should match the direction of the translation; the third expression-list should contain three expression s giving the X, Y and Z components of any point on this axis; the last expression should contain the rotation angle in radians.

Extrudes entities in extrude-list using a translation along their normal. Only available with the built-in geometry kernel. Extrudes entities in extrude-list along the give wire. Creates surfaces through the given curve loops or wires. Creates ruled surfaces through the given curve loops or wires. Fillets volumes first list on some curves second list , using the provided radii third list. The radius list can either contain a single radius, as many radii as curves, or twice as many as curves in which case different radii are provided for the begin and end points of the curves.

Chamfer volumes first list on some curves second list , using the provided distance fourth list measured on the given surfaces third list. The distance list can either contain a single distance, as many distances as curves, or twice as many as curves in which case the first in each pair is measured on the given corresponding surface. As explained in Floating point expressions , extrude can be used in an expression, in which case it returns a list of tags.

For example:. This behaviour can be changed with the Geometry. ExtrudeReturnLateralEntities option see Geometry options list. Boolean operations can be applied on curves, surfaces and volumes.

All boolean operation act on two lists of elementary entities. The first list represents the object; the second represents the tool. The general syntax for boolean operations is as follows:. Computes all the fragments resulting from the intersection of the entities in the object and in the tool, and makes all interfaces unique.

As explained in Floating point expressions , boolean can be used in an expression, in which case it returns the list of tags of the highest dimensional entities created by the boolean operation. An alternative syntax exists for boolean operations, which can be used when it is known beforehand that the operation will result in a single highest-dimensional entity:.

Computes the intersection of the object and the tool and assign the result the tag expression. Computes the union of the object and the tool and assign the result the tag expression.

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Geometrical transformations can be applied to elementary entities, or to copies of elementary entities using the Duplicata command: see below. The syntax of the transformation commands is:. Scales all elementary entities in transform-list by a factor expression. The expression-list should contain three expression s giving the X, Y, and Z coordinates of the center of the homothetic transformation.

Scales all elementary entities in transform-list using different factors along X, Y and Z the three expression s. Rotates all elementary entities in transform-list by an angle of expression radians. The first expression-list should contain three expression s giving the X, Y and Z direction of the rotation axis; the second expression-list should contain three expression s giving the X, Y and Z components of any point on this axis. Transforms all elementary entities symmetrically to a plane.

Applies a 4 x 4 affine transformation matrix 16 entries given by row; only 12 can be provided for convenience to all elementary entities. Translates all elementary entities in transform-list. Not a transformation per-se. Returns the entities on the boundary of the elementary entities in transform-list , with signs indicating their orientation in the boundary.

To get unsigned tags e. Returns the boundary of the elementary entities, combined as if a single entity, in transform-list. Useful to compute the boundary of a complex part. Returns all the geometrical points on the boundary of the elementary entities. Removes all duplicate elementary entities e. Note that with the built-in geometry kernel Gmsh executes the Coherence command automatically after each geometrical transformation, unless Geometry. AutoCoherence is set to zero see Geometry options list. Deletes all elementary entities whose tags are given in expression-list-or-all.

If an entity is linked to another entity for example, if a point is used as a control point of a curve , Delete has no effect the curve will have to be deleted before the point can. The Recursive variant deletes the entities as well as all its sub-entities of lower dimension. Deletes all the embedded entities in the elementary entities whose tags are given in expression-list-or-all. Hide the entities listed in expression-list-or-all , if General. VisibilityMode is set to 0 or 1. Hide all entities, if General. Show the entities listed in expression-list-or-all , if General. Show all entities, if General.

## Compiling Allegro Programs

The list of all the options that control the behavior of geometry commands, as well as the way model entities are handled in the GUI, is given in Geometry options list. All meshes can be subdivided to generate fully quadrangular or fully hexahedral meshes with the Mesh. SubdivisionAlgorihm option see Mesh options list.

Gmsh provides a choice between several 2D and 3D unstructured algorithms. Each algorithm has its own advantages and disadvantages.

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For all 2D unstructured algorithms a Delaunay mesh that contains all the points of the 1D mesh is initially constructed using a divide-and-conquer algorithm 5. Missing edges are recovered using edge swaps 6. After this initial step several algorithms can be applied to generate the final mesh:. If your version of Gmsh is compiled with OpenMP support see Compiling the source code , most of the meshing steps can be performed in parallel:.

The number of threads can be controlled with the -nt flag on the command line see Command-line options , or with the General. NumThreads , Mesh.

MaxNumThreads1D , Mesh.