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4.11. Geometric Operations

4.11.1. Boolean Operations

The Boolean operations allow combining two surfaces/set of surfaces/objects (the operations only works with NURBS surfaces that may be introduced in different ways), named in the commands as “objectA”, and “objectB” with different criteria. The following Boolean operations are available: union (OR), intersection (AND), difference (MINUS), union-exclusive (XOR), inside (inner surfaces), outside (outer surfaces) and split (mutual split). Every Boolean operation commands are named in the way of “booleanNAME”, where “NAME” is the specific operation.

In the following, every operation is explained by taking into account the examples of a plane with a disk and a box with a sphere.

4.11.1.1. Union

The union operation computes the total regions where at least one of the two candidate objects exits, i.e., the OR logical operation. The order of the selected objects does not modifies the result.

 Object A Object B OR 0 1 1 1 0 1 1 1 1

4.11.1.2. Intersection

The intersection operation computes the mutual regions of two different objects, i.e., the AND logical operation. The order of the selected objects does not modifies the result.

 Object A Object B AND 0 1 0 1 0 0 1 1 1

4.11.1.3. Difference

The difference operation computes the regions of the first object after subtracting the second one, i.e., the MINUS operation.

4.11.1.4. XOR

The union-exclusive operation computes the regions where only one of the two objects exits, i.e., the XOR logical operation. The order of the selected objects does not modifies the result.

 Object A Object B XOR 0 1 1 1 0 1 1 1 0

4.11.1.5. Inside

The inside operation computes the regions of the first object that is completely contained in the second one.

4.11.1.6. Outside

The outside operation computes the regions of the first object that is not contained in the second one.

4.11.1.7. Split

The split operation computes the cuts that an objects produce in the other one. The command may process both surfaces and objects, and the result is returned in the same format, i.e., after splitting a surface, the resulting sections is returned in multiple surfaces; however, an object is returned as the same object but with the resulting surfaces of the operation (explode it if necessary). Intersections only is computed between different objects.

4.11.2. Arrays

This menu contains the available options for arrays generation.

4.11.2.1. 3D Array

This is an option to create an array from an existing geometry. This option lets the user easily create a matrix of geometries. It is possible to create a circular array using the array command with the parameter -cir <radius>.

First, create any geometry (for example a sphere). To create it, click on “Geometry”, “Solids”, and click on “Sphere”. Now click on “Edit”, “Geometric Operations”, and click on “Array”.

This option is used to double up the selected surface. To do this, enter the number of copies in X, Y and Z and the distance between them using a starting point and end point.

For example, create a rectangle and press the option array. Then select the desired surface as shown in the next Figure.

Selecting the sphere to replicate

Then introduce the parameters shown in the command line of the figure below and press enter. The results are seen in the next Figure.

After applying the array function

4.11.2.2. ArrayOnSurface

This is an option to create an array from planar elements conformed to the selected surface.

Defining the cell structure on XY Plane and centered at the origin is the first step. In the example below, a disk with center in 0,0,0 and radius 0.04 is considered.

The next step is the creation of the object or surface where the cell structure will be placed on. For example, a sphere is created with center in 0,0,0 and radius 0.5, then it is exploded for extracting its surfaces.

Now click on Edit - Geometric Operations – Arrays – ArrayOnSurface option to start with the array generation.

The command ask the selection of the surfaces where the cell will be placed. This selection is only valid over surfaces entities, so objects should be exploded before using the command.

The first required option is the mode of array generation. Four different ways of cell distributions are available:

• Parametric: This option generates a quasi-regular distribution of cells along the parametric dimensions of the surfaces, i. e., the cells sizes may vary in the surfaces but the structure shape is guaranteed. It is recommended for non-degenerated surfaces or when the size of the cell in X and Y dimension must be different.
• Global: This option generates a more regular distribution of cells on the surfaces, i. e., the cells sizes and the structure shape may be slightly varied but the global quality of the array is improved. It is recommended for most of structures but it is only available when the size of the cell in X and Y dimension are identical.
• Projected: This option generates a full regular distribution of cells along the reference plane and then they are projected onto the target surfaces, i. e., both the cells sizes and the structure shape are guaranteed whenever the curvature of the surfaces is soft enough. It is only recommended for soft-curvature surfaces. When this mode is selected, the command ask whether the cells have to be projected onto the surfaces bounds or not:
• Yes (by default) option generates and projects the cells on full surfaces, and the bounding cells are trimmed.
• No option only generates cells on the rectangles (Tx Ty) that are completely inside the surfaces.
• Manual: This option place cells on the closest point on the surfaces to the introduced by the user, i. e., both the cells sizes and the structure shape are guaranteed whenever the curvature of the surfaces is soft enough in the selected points. It is recommended for customizing the cells distribution in most of structures.

The next parameter required is the type of array. Two different types of array types are available:

• Capacitive: Metallic cell structures are generated as the original one.
• Inductive: Metallic cell structured are inverted to the original one, i.e., the generated cells are rectangular cells with holes with the shapes of the original cell.

Then, the size of the cell structure (in the units selected) is required. As a planar cell is considered, the size in X and Y dimensions are required. In the considered example, 0.1, 0.1 are introduced.

When the sizes of cell structure in X and Y are different, the global option returns an error because the two sizes must be identical for this mode.

The last parameter required is the selection of the planar object used as reference cell. Note that these objects must be centered at the origin of coordinates, contained in the XY plane and surrounded by the red rectangle (of Tx Ty sizes) highlighted. If multiple surfaces are required for the cell definition, all of them must be grouped in one unique object.

When the array operation is finished, the original surfaces and cells are in the geometry. It may be removed by using the Delete command.

The next figure shows the full example of the disk array on the sphere with all the parameters required by default (the original objects have not been deleted).

Disk array on sphere with global mode and capacitive type

The next figure shows the full example of the disk array on the sphere generated with parametric mode (the original objects have not been deleted).

Disk array on sphere with parametric mode and capacitive type

The next figure shows the full example of the disk array on the sphere generated with manual mode (the original objects have not been deleted).

Disk array on sphere with manual mode and capacitive type

The next figure shows again the full example of the disk array on the sphere generated with the global mode and the inductive type (the original objects have been deleted).

Disk array on sphere with global mode and inductive type

The next figure shows the full example of the disk array on the sphere generated with the parametric mode and the inductive type (the original objects have been deleted).

Disk array on sphere with parametric mode and inductive type

The next figure shows the full example of the disk array on the sphere generated with the manual mode and the inductive type (the original objects have been deleted).

Disk array on sphere with parametric mode and inductive type

In the last part of this section, a paraboloid is considered to evaluate the generation of a crosses array with the projected mode.

The next figure shows the full example of the crosses array on the paraboloid with the rest of required parameters by default (the original objects have not been deleted).

Cross array on paraboloid with projected mode, projecting onto surface bounds and capacitive type

The next figure shows the full example of the cross array on the paraboloid without projecting onto surface bounds, and the rest of required parameters by default (the original objects have not been deleted).

Cross array on paraboloid with projected mode, without projecting onto surface bounds and capacitive type

The next figure shows the full example of the cross array on the paraboloid with inductive mode and the rest of required parameters by default (the original objects have been deleted).

Cross array on paraboloid with projected mode, projecting onto surface bounds and inductive type

The next figure shows the full example of the cross array on the paraboloid without projecting onto surface bounds inductive mode, and the rest of required parameters by default (the original objects have been deleted).

Cross array on paraboloid with projected mode, without projecting onto surface bounds and inductive type

4.11.3. Scale

Scaling any geometry is also possible by using the Scale menu. When the Edit – Geometric Operations - Scale button is clicked, different options to select the objects to be scaled are available:

• Scale Selection: multiple objects can be selected by pressing simultaneously “Ctrl + Left Mouse button”.
• Scale All: to select all existing objects in the geometry.

Several options of scaling are available in this menu. To select one of them, click on Edit - Geometric Operations – Scale menu. A cylinder centered at the origin with radius of 0.25 and height of 1 has been generated for the following sections.

4.11.3.1. Scale 1D

By using this option, only the X, Y or Z dimension is scaled by the scale factor.

Example of a cylinder scaled in the X dimension

4.11.3.2. Scale 2D

By using this option, only two of the X, Y or Z dimensions are scaled by the same scale factor.

Example of a cylinder scaled in the X and Z dimensions

4.11.3.3. Scale 3D

By using this option, the three X, Y and Z dimensions are scaled by the same scale factor. This function is the corresponding to the “scale” or “scale3D” commands.

Example of a cylinder scaled in the three dimensions

4.11.3.4. Scale Non-Uniform

By using this option, the three X, Y and Z dimensions are scaled by the corresponding scale factor each one.

Example of a cylinder scaled in the three dimensions with different factors

4.11.4. Rotate

This option is used to rotate the selected objects. The user will select the objects and enter the coordinates of the points that form the rotation axis and the angle of rotation and press enter, as shown in the following figure.

Selecting the surface to rotate

After selecting the surface and having selected the option to rotate, introduce the desired points. The result appears in the next Figure.

Rotate

4.11.5. Symmetric

The symmetry operation can be used to generate new objects. After clicking on the Edit – Geometric Operations – Symmetric button, different options to select the objects are available:

• Symmetry Selection: multiple objects can be selected by pressing simultaneously “Ctrl + Left Mouse button”.
• Symmetry All: to select all existing objects in the geometry.

By selecting the proper surface or figure, the system will require to introduce two points. These two points form a vector which is the vector normal to the plane of symmetry. Pressing enter creates the symmetric of the selected surface from this plane.

Note that this option modifies the original input object. In case of wanting a copy and then symmetry operation on the copied objects, the two operations may be grouped by using the command 'symmetric -c'.

For example, introduce a cylinder and click on Edit - Geometric operations and symmetric, and select the surface as shown in the figure, pressing enter, introduce points as those seen in the following Figure and the result is shown in the subsequent Figure.

Symmetric

Symmetric

4.11.6. Transform to reference plane

This option applies the transformation of the Reference Plane to the selected objects, and also can be used by using the localTransform command. It is useful to create geometrical objects in the default origin and then translate and orientate them with the desired reference plane.

The figure below shows two planes of different sizes that have been created in the default system.

2 planes created with the default reference plane

Then, the reference plane has been centred in the right edge of the first plane. It has been also oriented to be contained in the YZ plane, so its Z-Axis is pointing to the X axis. By using the new reference plane, select the second created plane and then click on Edit - Geometric Operations - Transform to reference plane option. Note that the selected plane has been moved an rotated according to the reference plane parameters, as shown in next figure.

Dihedral after applying the 'localTransform' command to the second plane.

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