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CREATING A GEOMETRY MODEL IN HOBBIES

4.0 SUMMARY

A Higher Order Basis Based Integral Equation Solver (HOBBIES) project consists of a geometry model, the electrical properties of the electromagnetic materials associated with that model, and the parametric settings of the solution. As is well known, the geometry modeling is very important since it describes the object that is essential in an electromagnetic simulation.

In general, HOBBIES provides two ways to create a model of the electromagnetic structure:

• Using the HOBBIESStructure menu to create a simple shaped model
• Using the Geometry menu to create an arbitrarily shaped model

Users can draw arbitrary one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) objects using either of the procedures, as discussed in detail in this chapter. HOBBIES can also import geometric models of structures from other software, such as AutoCAD, Rhinoceros, and Pro/E, as described in Section 3.5.2 of Chapter 3.

To draw a model efficiently, one can perform various operations and manipulations with previously created objects (points, wires, surfaces, etc.). The operations include moving a point, dividing lines/surfaces, collapsing, Boolean operations, and so on. The manipulations include translation, rotation, mirroring, scale, offset, sweep, and align. These operations and manipulations of the model are discussed at the end of this chapter.

4.1 CREATING A SIMPLE MODEL USING THE STRUCTURE MENU

The geometric properties of a structure can be defined using nodes, wires, surfaces, junctions, volumes, or objects. In a HOBBIES project, the geometric modeling is implemented using HOBBIESStructureNodes, Wires, Surfaces, Volumes, Junctions, and Objects menus. Each menu will be described in detail in the next section.

4.1.1 Nodes

A node is a point in space completely determined by its x-, y-, and z-coordinates. Click the HOBBIESStructureNodes menu, and the Node list window appears, as shown in Figure 4.1.

Figure 4.1. Node list window including six nodes.

The following can be accomplished in the Node list window:

• : add a new node
• : delete an existing node
• : go to the first page
• : go to the previous page
• : go to the next page
• : go to the last page
• : find a node according to the ID of the node
• : show/hide all the node labels. See also the icon in the Toolbar in Section 3.4.3.

These commands will now be described in detail.

Add a node

1. Click on the Add icon in the Node list window. A new node is created. The default values for all coordinates are zero. The numbers in the Node column (first column in the Node list window) are the ID of the nodes in HOBBIES.

2. One can edit the node coordinates in the Node list window. Select the x-coordinate edit field of one node in the X column, and enter the new value. Then press the tab key or use the left mouse button to switch to the y-coordinate field (Y column) and enter the new value. The z-coordinate (Z column) can be edited as the x- and y-coordinates.

Delete a node

1. Click on the box in front of a node number to select the node, as shown in Figure 4.2.

Figure 4.2. Select node 3.

2. Click on the Delete icon in the Node list window, and the selected node will be removed from the list, as shown in Figure 4.3.

Figure 4.3. Delete node 3. (The original node numbers 4, 5, and 6 in Figure 4.2 change to the new node numbers 3, 4, and 5 in Figure 4.3, respectively.)

Figure 4.4. Nodes selected: (a) nodes 1, 2, 3, 4, (b) their labels are displayed through 1, 2, 3, and 4.

Go to the first/last/previous/next page of the Node list window

In the Node list window, each page contains at most 100 nodes. If there are more than 100 nodes, the Node list window will include more than one page. The icons , , , and allow one to go to the first, previous, next, and last page of the Node list window, respectively.

Search for a node

One can search for a node in the Node list window according to the node ID:

1. Click on the Search icon in the Node list window, and then a window appears, as shown in Figure 4.5.
2. Enter the ID of a node, e.g., 200, in the Node ID field, as shown in Figure 4.6.

Figure 4.5. Search the node dialog window.

Figure 4.6. Enter the Node ID.

3. Click Ok in the Search node window, and the node with the ID of 200 will appear in current Node list window, as marked in Figure 4.7.

Figure 4.7. Result of the search for a node.

Show/hide node labels

Click on the Label icon in the Node list window to show all the node labels {Figure 4.8 (a)}, and click it again to hide the labels {Figure 4.8 (b)}. The nodes are labeled by 1, 2, 3, and so on. The function of this icon is the same as that of in the Toolbar (see Section 3.4.3).

Figure 4.8. Six nodes: (a) show node labels, (b) hide node labels.

4.1.2 Wires

Wires are modeled by right-truncated cones in the geometry. As discussed in Chapter 1, a method of moments (MoM) model of a right-truncated wire cone can be considered as a line with a radius and associated with it are properties of the medium in which it is embedded.

In general, a right-truncated cone is defined by its start and end points (nodes) and by its starting and ending radii. Wire nodes are specified by their ID, given in the Node list window.

A wire in HOBBIES is specified by (Figure 4.9):

• Starting and ending points of its axis (Nodes 1st and 2nd).
• Starting and ending radii (Radii 1st and 2nd).
• Domain in which the wire is immersed (Dom). By default, this is Domain 1. The significance of Domain will be described in detail in Section 6.4.
• Degree of polynomial approximation for current along the wire (Nds). By default, it is set to 0, which means that the degree is automatically determined by the code and the value is determined by the electrical length of the wire. See also Order of Current Approximation in Section 6.10.2.
• The number of uniformly distributed points along the wire at which the current is calculated (Ncs). See also Current in Section 6.9.1.

Figure 4.9. Wire list window.

The following can be accomplished in the Wire list window:

• : add a new wire.
• : delete an existing wire.
• : go to the first page.
• : go to the previous page.
• : go to the next page.
• : go to the last page.
• : find a wire according to the Line ID of the wire.
• : show/hide all wire labels. See also the icon in the Toolbar in Section 3.4.3.

These commands will now be described in detail.

Add a wire

1. Click on the Add icon in the Wire list window. For example, enter the node IDs of 5 and 6 in Figure 4.8 (a) in the Nodes ID field (Figure 4.10) and click Ok; a line is created {Figure 4.11 (a)}, and an entry is added in the Wire list window {Figure 4.11 (b)}, which connects the two nodes.

Figure 4.10. Enter two different node IDs for defining a line.

Figure 4.11. (a) A wire connecting nodes 5 and 6, (b) a line is added in the Wire list.

2. Edit the wire parameters in the Wire list window.

• Starting and ending radii of the wire (Radius column), select the 1st edit field in the Radius column, and enter the value of the radius at the first node of the wire. Then press the tab key or use the left mouse button to switch to the 2nd field and enter the value of the radius at the second node of the wire. The starting and ending radii may be the same or different. By default, the values of the two radii are zero.

• Domain (Dom column): select the domain edit field in the Dom column, and enter the number of the domain, in which the wire is immersed. By default, this is Domain 1, which means that the wire is immersed in vacuum. The Domains will be described in detail in Section 6.4.
• Nds: select the Nds edit field, and enter the degree of polynomial approximation for current along the wire. By default, it is 0, which means that the degree is automatically determined by the electrical length of the wire. See Order of Current Approximation in Section 6.10.2 for details.
• Ncs: select the Ncs edit field, and enter the number of uniformly distributed points along the wire at which the current is calculated. This will be specified in Section 6.9.1.

Example:

In the Wire list window shown in Figure 4.12, the wire number is 1 and the Line ID of the wire is also 1. The first (starting) and second (ending) nodes of the wire are nodes 5 and 6, respectively. The nodes 5 and 6 should have been defined in the Node list window (Section 4.1.1). The radii at the first and second nodes are both 3 mm. Domain 1 means that the wire is immersed in vacuum (Section 6.4 in Chapter 6). Nds is 0, which means that the degree of the polynomial basis for the current along the wire is automatically determined according to the electrical length of the wire (Section 6.10.2). Ncs is 0, which means the values of the current will not be displayed in the output results for the wire (Section 6.9.1). One can add multiple wires by following this process.

Figure 4.12. A wire example: Wire list.

Delete a wire

1. Click the left mouse button on the box in front of a wire number to select the wire, as shown in Figure 4.13 (a).

2. Click the left mouse button on the Delete icon in the Wire list window, and the selected wire will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

Figure 4.13. (a) A selected wire, (b) wire label denoted by 1.

The icons , , , , and in the Wire list window have the same functions as those in the Node list window (Section 4.1.1), and thus, their descriptions are omitted.

Show/hide wire labels

Click the Label icon in the Wire list window to show all the wire labels {Figure 4.14 (a)} and click it again to hide the labels {Figure 4.14 (b)}. The wires are labeled by 1, 2, 3, and so on. See the function of this icon is the same as that of in the Toolbar (Section 3.4.3). Wire labels are shown with radii of wires, and wire labels can be shown together with node labels, as depicted in Figure 4.14 (c).

Figure 4.14. Six wires with nine nodes: (a) showing wire labels, (b) hiding labels, (c) showing wire and node labels.

4.1.3 Surfaces

Quadrilateral surfaces are modeled by bilinear surfaces. In the general case, a bilinear surface is a curved quadrilateral completely determined by its four corner points (nodes), arbitrarily positioned in space. The nodes of a quadrilateral surfaces are specified by their IDs, given in the Node list window. The sequence of nodes defines the contour of the surface. A quadrilateral surface is modeled as a bilinear surface completely specified by:

• Four corner points arbitrarily positioned in space.
• Domains in which the quadrilateral surface is immersed (Domains 1st and 2nd). By default, these are Domains 1 and 0.
• Degrees of polynomial approximation of the current along p- and s-coordinates (Ndp, Nds).
• Numbers of uniformly distributed points along p- and s-coordinates at which the current is calculated (Ncp, Ncs).

Figure 4.15. Window displaying a list of all the surfaces.

The following can be done in the Surface list window, as shown in Figure 4.15:

• : add a new surface.
• : delete an existing surface.
• : go to the first page.
• : go to the previous page.
• : go to the next page.
• : go to the last page.
• : find a surface according to the ID of the surface.
• : show/hide all surface labels. See also the icon in the Toolbar in Section 3.4.3.

These commands will be described in the next section.

Add a quadrilateral surface

1. Click the left mouse button on the Add icon in the Surface list window (Figure 4.15). If four different nodes are already defined in the Node list, the window shown in Figure 4.16 appears. Type in four different node IDs in the Nodes ID field and click Ok. A quadrilateral surface is created and added in the Surface list window (Figure 4.17). For example, from Figure 4.4, enter the nodes 1, 2, 3, and 4 in the Nodes ID window, as shown in Figure 4.16, and press the ESC key.

Figure 4.16. Enter four different node IDs for defining a quadrilateral surface.

Figure 4.17. A surface added in the Surface list.

2. Edit the surface parameters in the Surface list window.

• Domains (1st, 2nd): select the 1st or 2nd domain edit field in the Domains column by using the left mouse button and editing the number. By default, the 1st domain is Domain 1 and the 2nd domain is Domain 0. Domain 1 means that the surface is immersed in the outer space filled by vacuum, and Domain 0 means that the surface is made of a perfect electric conductor (PEC). The Domains will be described in detail in Section 6.4.
• Degrees (Ndp, Nds): select the Ndp or Nds edit field in the Degrees column by using the left mouse button, and edit the degree of polynomial approximation of the current along p- or s-coordinates of the surface. By default, these are both 0, which mean that the degrees are automatically determined according to the surface's electrical length. (See Section 6.10.2 for further information about how to change the order of the current approximation.)
• Current (Ncp, Ncs): select the Ncp or Ncs edit field in the Current column by using the left mouse button, and edit the number of uniformly distributed points along the p- or s-coordinates of the surface at which the current is calculated. This will be specified in Section 6.9.1.

One can add multiple surfaces by following the process described so far.

Delete a quadrilateral surface

1. Click the left mouse button on the box in front of a surface number to select the surface.

2. Click the left mouse button on the Delete icon in the Surface list window, and then the selected surface will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

Figure 4.18. A surface and its label: (a) A selected surface, (b) label denoted by 1.

The icons , , , , and in the Surface list window have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

Show/hide quadrilateral surface labels

Click the Label icon in the Surface list window to show all the surface labels {Figure 4.19 (a)}, and click it again to hide the labels (Figure 4.19 (b)). The surfaces are labeled by 1, 2, 3, and so on. The function of this icon is the same as that of in the Toolbar (see Section 3.4.3). Surface labels can be shown together with node labels, as depicted in Figure 4.19(c).

Figure 4.19. One quadrilateral surface with four nodes: (a) showing the surface label, (b) hiding label, (c) showing surface and node labels.

4.1.4 Junctions

Two wires having a common node and two quadrilateral surfaces having two common nodes (that define their common edge) are automatically considered to be connected. However, the wire-to-surface junction must be specified by the user, using the Junction list window (Figure 4.20). The junction is completely specified by a node of a wire situated on a surface. In the general case, the ends of a wire and a surface's short edges that are placed in an electrically small region can also be specified by the user to be electrically connected. A junction, in the general case, is completely specified by all nodes in the junction domain.

Figure 4.20. Junction list window.

The following can be done in the Junction list window:

• : add a new junction.
• : delete an existing junction.
• : go to the first page.
• : go to the previous page.
• : go to the next page.
• : go to the last page.
• : find a junction according to the ID of the junction.
• : show/hide all junction labels. See also the icon in the Toolbar in Section 3.4.3.

These commands will be described in the next section.

Add a junction

1. Click the left mouse button on the Add icon in the Junction list window and an information window appears (Figure 4.21). Note that the information window will not appear unless the Popup message in the Interface options frame on the General tab of Preferences (Appendix A) is set as Beginner.

2. Click OK in the information window, and select all nodes in the junction domain with the left mouse button. Press the ESC key and a junction is added in the Junction list window (Figure 4.22). Each row in the Junction list window defines one junction.

Figure 4.21. Information window.

Figure 4.22. Junction list containing one junction with one node.

Delete a junction

1. Click the left mouse button on the box in front of a junction number to select the junction.

2. Click the left mouse button on the Delete icon in the Junction list window, and then the selected junction will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

The icons , , , , and in the Junction list window have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

Show/hide junction labels

Click the Label icon in the Junction list window to show all junction labels {Figure 4.24 (a)}, and click it again to hide the labels {Figure 4.24 (b)}. The junctions are labeled by 1, 2, 3, and so on. The function of this icon is the same as that of in the Toolbar (see Section 3.4.3).

Figure 4.23. A junction and its label: (a) a selected junction, (b) label denoted by 1.

Figure 4.24. A wire-to-surface junction: (a) showing junction label, (b) hiding junction label.

Figure 4.25. Combined wire-to-surface junctions: (a) the junction between a wire and a corner of a surface, (b) the junction of a wire and a surface edge (that is not electrically short), (c) the junction of a wire and the middle point of a surface, (d) complex junctions (junction 1 includes one node and junction 2 includes four nodes). It is important to note that there are multiple junction labels 2 because the software labels every point of the junction. It should have 4 labels for junction 2. But the other 2 labels are overlapped by the plates and hence not visible.

4.1.5 Volumes

A volume is an entity formed by a closed set of surfaces that share the lines between them. The HOBBIES computational kernel is based on the surface integral equation (see Chapter 1) and cannot use the volume entities or the mesh of volumes. The purpose of introducing volumes in HOBBIES is to utilize the volume Boolean operations for geometric modeling, which will be described in detail in Section 4.3.16.

The following can be done in the Volume list window, as shown in Figure 4.26:

• : add a new volume.
• : delete an existing volume.
• : go to the first page.
• : go to the previous page.
• : go to the next page.
• : go to the last page.
• : find a volume according to the Volume ID of the volume.
• : show/hide all volume labels.

These commands will be described in the following section.

Figure 4.26. Volume list.

Add a volume

Click the left mouse button on the Add icon in the Volume list window and then select some surfaces in the HOBBIES window with the left mouse button. Press the ESC key and a volume is added in the Volume list. Each row of the Volume list defines one volume.

To create a volume, some surfaces must be selected. The order of selection is not important but they all must join each other by sharing common lines and they must form a closed contour. Otherwise, there is an error and the volume is not created, and a window appears with some useful information.

For example, the information for a sphere is shown in the Volume list in Figure 4.27. It is seen that the sphere volume includes 4 surfaces, 4 lines and 2 points. The sphere with and without the volume element is shown in Figure 4.28.

Figure 4.27. Volume list containing a sphere volume.

Figure 4.28. A sphere: (a) without a volume element, (b) with the volume element.

Delete a volume

1. Click the left mouse button on the box in front of a volume number to select the volume.

2. Click the left mouse button on the Delete icon in the Volume list window, and then the selected volume will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

The icons , , , , and in the Volume list window have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

Show/hide volume labels

Click the Labels icon in the Volume list window to show all the volume labels {Figure 4.30 (a)}, and click it again to hide the labels {Figure 4.30 (b)}. The volumes are labeled by 1, 2, 3, and so on.

Figure 4.29. A volume and its label: (a) A selected volume, (b) label denoted by 1.

Figure 4.30. A sphere volume: (a) showing a volume label, (b) hiding the volume label.

4.1.6 Objects

One can create typical models in the Object list. The models include:

• Spheres
• Cylinders
• Cones
• Prisms
• Parametric surfaces
• Parametric lines

The Object list is shown in Figure 4.31. The default tab is Spheres. One can switch to other tabs by clicking Cylinders, Cones, and so on. in the Object list.

Figure 4.31. Object list.

The following can be done in each tab of the Object list:

• : add a new sphere/cylinder/cone/prism/parametric surface/parametric line.
• : delete an existing object.
• : go to the first page.
• : go to the previous page.
• : go to the next page.
• : go to the last page.
• : find an object according to the ID of the object.
• : show/hide object labels.

Symbols can be used in the definition of models in the Object list (symbols will be described in Section 4.1.7). In addition, the mesh of models can be controlled in the Object list.

Each type of object in the Object list will now be described one by one in the next section.

4.1.6.1 Spheres

The Spheres tab is shown in Figure 4.32. Each row of the list defines one sphere, which includes three parameters: Center, Radius, and Auto-mesh divisions.

Add a sphere

1. Click the left mouse button on the Add icon in the Sphere tab, and Press the ESC key. A new sphere is created (Figure 4.32). By default, the coordinates for the Center of the sphere (X, Y, Z) are zeros, the Radius is 1.0 m, and the Auto-mesh division is 0.0. Then the sphere will be displayed in the HOBBIES window as shown in Figure 4.33.

2. One can edit the geometric parameters and mesh size of the sphere in the list.

• Center (X, Y, Z): select the edit field of the X/Y/Z coordinate by using the left mouse button, and enter the new value. By default, the sphere is centered at the origin of the Cartesian coordinate system.
• Radius: select the edit field of Radius by using the left mouse button, and enter the new value.
• Auto-mesh divisions: select the edit field of Auto-mesh divisions by using the left mouse button, and enter the new value. The value denotes the number of divisions per quarter of the circumference, which will determine the mesh size. The default value is zero, which means that the mesh size is determined by the MeshGenerate mesh menu (Section 5.7 in Chapter 5). Note that the value of Auto-mesh divisions will not be used for meshing if the Automatic correct sizes option on the Meshing tab of Preferences (Appendix A) is not set as None.

Figure 4.32. Sphere tab containing one sphere.

Figure 4.33. The sphere shown in the HOBBIES window.

Delete a sphere

1. Click the left mouse button on the box in front of a sphere ID to select the sphere.

2. Click the left mouse button on the Delete icon in the Spheres tab, and the selected sphere will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

Figure 4.34. A sphere: (a) a selected sphere, (b) the display of a sphere with a transparent green color.

Highlight spheres

Click the icon in the Spheres tab to highlight all spheres with the transparent green color {Figure 4.35 (a)}, and click it again to cancel the highlight {Figure 4.35 (b)}.

Figure 4.35. Two spheres: (a) showing highlight, (b) hiding highlight.

Other commands

The commands , , , and in the Spheres tab have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

4.1.6.2 Cylinders

The Cylinders tab is shown in Figure 4.36. Each row of the list defines one cylinder, which includes five parameters: Base Center, Normal Vector, Radius, Height, and Auto-mesh divisions.

Figure 4.36. Cylinders tab.

Add a cylinder

1. Click the left mouse button on the Add icon in the Cylinders tab and press the ESC key. A new cylinder is created (Figure 4.37). By default, the Base Center coordinates (X, Y, Z) are zeros, the Normal Vector is (0.0, 0.0, 1.0), the Radius is 1.0 m, the height is also 1.0 m, and the Auto-mesh divisions is 0.0.

2. One can edit the geometric parameters and mesh size of the cylinder in the list.

• Base Center (X, Y, Z): select the edit field of the X/Y/Z coordinate in the Base Center column by using the left mouse button, and enter the new value. By default, the Base Center of the cylinder is at the origin of the Cartesian coordinate system.
• Normal Vector (X, Y, Z): select the edit field of the X/Y/Z coordinate in the Normal Vector column by using the left mouse button, and enter the new value. The default Normal Vector of the cylinder is along the direction of the z-axis.
• Radius: select the edit field of Radius by using the left mouse button, and enter the new value. The default radius is 1.0 m.
• Height: select the edit field of Height by using the left mouse button, and enter the new value. The default height is 1.0 m.
• Auto-mesh divisions: select the edit field of Auto-mesh divisions by using the left mouse button, and enter the new value. The value denotes the number of divisions per quarter of the circumference, which will determine the mesh size. The default value is zero, which means that the mesh size is determined by the MeshGenerate mesh menu (Section 5.7 in Chapter 5). Note that the value of Auto-mesh divisions will not be used for meshing if the Automatic correct sizes option on the Meshing tab of Preferences (Appendix A) is not set as None.

Figure 4.37. An added cylinder: (a) cylinders tab containing one cylinder, (b) the cylinder shown in the HOBBIES window.

Delete a cylinder

1. Click the left mouse button on the box in front of a cylinder ID to select the cylinder.

2. Click the left mouse button on the Delete icon in the Cylinders tab, and the selected cylinder will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

Figure 4.38. A selected cylinder: (a) in the object list, and (b) its display with transparent green color.

Highlight cylinders

Click the icon in the Cylinders tab to highlight all cylinders with a transparent green color (Figure 4.39(a)), and click it again to cancel the highlight (Figure 4.39(b)).

Other commands

The commands , , , , and in the Cylinders tab have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

Figure 4.39. Two cylinders: (a) two cylinders that are highlighted, (b) two cylinders hiding the highlight.

4.1.6.3 Cones

The Cones tab is shown in Figure 4.40. Each row of the list defines one cone, which includes five parameters: Base Center, Normal Vector, Radius, Height, and Auto-mesh divisions.

Figure 4.40. Cones tab.

Add a cone

1. Click the left mouse button on the Add icon in the Cones tab, and press the ESC key. A new cone is created (Figure 4.41). By default, the Base Center coordinates (X, Y, Z) are zeros, the Normal Vector is (0.0, 0.0, 1.0), the Radius is 1.0 m, the Height is also 1.0 m, and the Auto-mesh divisions is 0.0.

2. One can edit the geometric parameters and the mesh size of the cone in the list.

• Base Center (X, Y, Z): select the edit field of the X/Y/Z coordinate in the Base Center column by using the left mouse button, and enter the new value. By default, the Base Center of the cone is at the origin of the Cartesian coordinate system.
• Normal Vector (X, Y, Z): select the edit field of the X/Y/Z coordinate in the Normal Vector column by using the left mouse button, and enter the new value. The default Normal Vector of the cone is along the z-axis direction.
• Radius: select the edit field of Radius by using the left mouse button and enter the new value. The default radius is 1.0 m.
• Height: select the edit field of Height by using the left mouse button and enter the new value. The default height is 1.0 m.
• Auto-mesh divisions: select the edit field of Auto-mesh divisions by using the left mouse button and enter the new value. The value denotes the number of divisions per 1/3 of the circumference, which will determine the mesh size. The default value is zero, which means that the mesh size is determined by the MeshGenerate mesh menu (Section 5.7 in Chapter 5). Note that the value of Auto-mesh divisions will not be used for meshing if the Automatic correct sizes option on the Meshing tab of Preferences (Appendix A) is not set as None.

Figure 4.41. Geometrical generation of a cone: (a) the cones tab containing one added cone, (b) the cone shown in the HOBBIES window.

Delete a cone

1. Click the left mouse button on the box in front of a cone ID to select the cone.

2. Click the left mouse button on the Delete icon in the Cones tab, and the selected cone will be removed from the list.

This is similar to the procedure of deleting a node (Section 4.1.1).

Figure 4.42. Display of a cone: (a) a selected cone, (b) the cone is displayed with a transparent green color.

Highlight cones

Click the icon in the Cones tab to highlight all cones with a transparent green color {Figure 4.43 (a)}, and click it again to cancel the highlight {Figure 4.43 (b)}.

Figure 4.43. Two cones: (a) are highlighted, (b) two cones without the highlight.

Other commands

The commands , , , , and in the Cones tab have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

4.1.6.4 Prisms

The Prisms tab is shown in Figure 4.44. Each row of the list defines one prism, which includes five parameters: Base Center, Normal Vector, Radius, Height, and Auto-mesh divisions.

Figure 4.44. Prisms tab.

Add a prism

1. Click the left mouse button on the Add icon in the Prisms tab and an information window appears (Figure 4.45). Enter the number of sides for the prism, click Ok, and a new prism is created (Figure 4.46). By default, the number of sides is 4, the Base Center coordinates (X, Y, Z) are zeros, the Normal Vector is (0.0, 0.0, 1.0), the Radius is 1.0 m, and the Height is also 1.0 m. Note that the Auto-mesh divisions is not available for prisms.

Figure 4.45. Information window for creation of a prism.

2. One can edit the geometric parameters of the prism in the list.

• Base Center (X, Y, Z): select the edit field of the X/Y/Z coordinate in the Base Center column by using the left mouse button and enter the new value. By default, the Base Center of the prism is at the origin of the Cartesian coordinate system.
• Normal Vector (X, Y, Z): select the edit field of the X/Y/Z coordinate in the Normal Vector column by using the left mouse button and enter the new value. The default Normal Vector of the prism is oriented along the z-axis.
• Radius: select the edit field of Radius by using the left mouse button and enter the new value. The radius is that of a circle, which circumscribes the prism. The default radius is 1.0 m.
• Height: select the edit field of Height by using the left mouse button and enter the new value. The default height is 1.0 m.
• Auto-mesh divisions: this option is not available for prisms.

Figure 4.46. An added prism: (a) prisms tab containing a four-sided prism, (b) the prism shown in the HOBBIES window.

Delete a prism

1. Click the left mouse button on the box in front of a prism ID to select the prism.

2. Click the left mouse button on the Delete icon in the Prisms tab, and the selected prism will be removed from the list.

Figure 4.47. A selected prism: (a) with object list, (b) its display with transparent green color.

Highlight prisms

Click the icon in the Prisms tab to highlight all prisms with a transparent green color {Figure 4.48 (a)}, and click it again to cancel the highlight {Figure 4.48 (b)}.

Other commands

The commands , , , , and in the Prisms tab have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

Figure 4.48. A four-sided and six-sided prism: (a) showing the highlight, (b) hiding the highlight.

4.1.6.5 Parametric Surfaces

The Parametric Surfaces tab is shown in Figure 4.49. Each row of the list defines one parametric surface, which includes three parameters: Parametric Equations, U, and V.

Add a parametric surface

1. Click the left mouse button on the Add icon in the Parametric Surfaces tab and an information window appears (Figure 4.50). The required input data are the mathematical formulas of the coordinates X(u,v), Y(u,v), and Z(u,v), where u and v are the parameters of the surface, and their values belong to the intervals set in U from…to… and V from…to…, respectively. The surface is created by approximation and is a NURBS (Non-Uniform Rational B-Spline) surface, which is created with multiple points along the u and v directions.

Figure 4.49. A window to input the variables for a parametric surface.

Figure 4.50. A window to input the mathematical formula for the parametric surface.

One can also input the mathematical formulas manually or select the formulae in the drop-down menu of the Examples in Figure 4.51 (a). There are four types of parametric surfaces in the Examples drop-down menu: Band, Helicoid, Catenoid, and Dinni {Figure 4.51 (a)}. Select one of the Examples (e.g., Band), and the mathematical formulas are filled automatically in the corresponding fields {Figure 4.51 (b)}. Click Ok and the parametric surface is created and added in the Parametric Surfaces tab, as shown in Figure 4.52. Press the ESC key to leave the NURBS surface creation.

Figure 4.51. Examples of a parametric surface: (a) use of the drop-down menu, (b) an example of a Band parametric surface.

Figure 4.52. An added parametric surface: (a) Parametric Surfaces tab containing a Band surface, (b) the surface displayed in the HOBBIES window.

The valid mathematical operators are: + − * / % **.

The valid mathematical functions are as follows:

abs (arg): Returns the absolute value of arg. Arg may be either an integer or a floating-point, and the result is returned in the same form.

acos (arg): Returns the arc cosine of arg, in the range [0, π] radians. Arg should be in the range [−1, 1].

asin (arg): Returns the arc sine of arg, in the range [−π/2, π/2] radians. Arg should be in the range [−1, 1].

atan (arg): Returns the arc tangent of arg, in the range [−π/2, π/2] radians.

atan2 (y, x): Returns the arc tangent of y/x, in the range [−π, π] radians, x and cannot both be 0.

ceil (arg): Returns the smallest integral floating-point value (i.e., with a zero fractional part) not less than arg. The argument may be any numeric value.

cos (arg): Returns the cosine of arg, measured in radians.

cosh (arg): Returns the hyperbolic cosine of arg. If the result would cause an overflow, an error is returned.

double (arg): The argument may be any numeric value. If arg is a floating-point value, the function returns arg; otherwise, it converts arg to a floating-point and returns the converted value. May return Inf or –Inf when the argument is a numeric value that exceeds the floating-point range.

exp (arg): Returns the exponential of arg, defined as e**(arg). If the result would cause an overflow, an error is returned.

floor (arg): Returns the largest integral floating-point value (i.e., with a zero fractional part) not greater than arg. The argument may be any numeric value.

fmod (x, y): Returns the floating-point remainder of the division of x by y. If y is 0, an error is returned.

hypot (x, y): Computes the length of the hypotenuse of a right-angled triangle “sqrt [x × x + y × y]”

int (arg): The argument may be any numeric value. The integer part of arg is determined, and then the low-order bits of that integer value, up to the machine word size, are returned as an integer value.

log (arg): Returns the natural logarithm of arg. Arg must be a positive value.

log10 (arg): Returns the base 10 logarithm of arg. Arg must be a positive value.

pow (x, y): Computes the value of x raised to the power y. If x is negative, y must be an integer value.

rand : Returns a pseudo-random floating-point value in the range (0, 1). The generator algorithm is a simple linear congruential generator that is not cryptographically secure. Each result from rand completely determines all future results from subsequent calls to rand, so rand should not be used to generate a sequence of secrets, such as one-time passwords. The seed of the generator is initialized from the internal clock of the machine or may be set with the srand function.

round (arg): If arg is an integer value, the function returns arg; otherwise it converts arg to an integer by rounding, and returns the converted value.

sin (arg): Returns the sine of arg, measured in radians.

sinh (arg): Returns the hyperbolic sine of arg. If the result would cause an overflow, an error is returned.

sqrt (arg): The argument may be any non-negative numeric value. Returns a floating-point value that is the square root of arg. May return Inf when the argument is a numeric value that exceeds the square of the maximum value of the floating-point range.

srand (arg): The arg, which must be an integer, is used to reset the seed for the random number generator of rand. Returns the first random number (see rand) from that seed. Each interpreter has its own seed.

tan (arg): Returns the tangent of arg, measured in radians.

tanh (arg): Returns the hyperbolic tangent of arg.

2. One can edit the mathematical formulas of the parametric surfaces in the list.

• Parametric Equations (X, Y, Z): select the edit field of X/Y/Z in the Parametric Equations column by using the left mouse button, and edit the formula. Press the Enter key and the parametric surface changes accordingly.
• U: its value belongs to the interval [U0, U1]. The number in the POINTS field denotes the number of points in the u direction, which are used to create the surface. One can select the edit field of U0/U1/POINTS in the U column by using the left mouse button and then editing the value. Press the Enter key and the parametric surface changes accordingly.
• V: its value belongs to the interval [V0, V1]. The number in the POINTS field denotes the number of points in the v direction, which are used to create the surface. One can select the edit field of V0/V1/POINTS in the V column by using the left mouse button and editing the value. Press the Enter key and the parametric surface changes accordingly.

Delete a parametric surface

1. Click the left mouse button on the box in front of a parametric surface ID to select the surface.

2. Click the left mouse button on the Delete icon in the Parametric Surfaces tab, and the selected surface will be removed from the list.

Figure 4.53. Generation of a parametric surface: (a) a selected parametric surface, (b) a parametric surface displayed in transparent green color.

Highlight parametric surfaces

Click the icon in the Parametric Surfaces tab to highlight all surfaces with a transparent green color {Figure 4.54 (a)}, and click it again to cancel the highlight {Figure 4.54 (b)}. The parametric formulas of the paraboloid surface in Figure 4.54 are given by:

where −1.5 ≤ u ≤ 1.5, −1.0 ≤ v ≤ 1.0.

Figure 4.54. A reflector: (a) displaying the highlight, (b) hiding the highlight.

Other commands

The commands , , , , and in the Parametric Surfaces tab have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

4.1.6.6 Parametric Lines

The Parametric Lines tab is shown in Figure 4.55. Each row of the list defines one parametric line, which includes two parameters: Parametric Equations and t.

Figure 4.55. Parametric surface window.

Add a parametric line

1. Click the left mouse button on the Add icon in the Parametric lines tab and an information window appears (Figure 4.56). The required input data are the mathematical formulas of the coordinates X(t), Y(t), and Z(t), where t is the parameter of the line, and its value belongs to the intervals set in t from…to…. The line is created by approximation and is a NURBS line, which is created with N points. In HOBBIES, these kinds of curves are cubic (third-order). By default, the interval is [0, 1] and the number of points is 10.

Figure 4.56. A window to input the mathematical formula for the creation of a parametric line.

2. Click Ok in the Parametric Lines window when finished entering the mathematical formulas, and a parametric line is created and added in the Object list (or, click Cancel to close the window).

3. One can edit the mathematical formulas of the parametric lines in the list.

• Parametric Equations (X, Y, Z): select the edit field of X/Y/Z in the Parametric Equations column by using the left mouse button and editing the formula. Press the Enter key and the parametric line changes accordingly.
• t: its value belongs to the interval [T0, T1]. The number in the POINTS field denotes the number of points for t sampling, which is used to create the line. One can select the edit field of T0/T1/POINTS in the t column by using the left mouse button and editing the value. Press the Enter key and the parametric line changes accordingly.

4. If the parametric line acts as an antenna or a feeding pin, open the Wire list window (Section 4.1.2) and enter Radius for the wire. One can also edit Dom, Nds and Ncs for the wire.

The valid mathematical operators and functions are (see Section 4.1.6.5): +, −, *, /, %, **, abs, acos, as in, atan, atan2, ceil, cos, cosh, double, exp, floor, fmod, hypot, int, log, log10, pow, rand, round, sin, sinh, sqrt, srand, tan, tanh.

Example

We fill the formula bars with the expression of a helix. That helix starts with radius R₀ = 4 and finishes with a radius R₀ = 4, performing N = 3 turns per unit length. Therefore, for t = 0.0 to t = 2.0 , it will constitute six turns of the helix. The height also changes from 0 to H = 10. The mathematical formulas are given below.

The parameters for the helix are shown in Figure 4.57, and the outline of the helix is shown in Figure 4.58.

Figure 4.57. Parameters for a helix in the Parametric Lines window.

Figure 4.58. Example of a helix with a unique curve.

Delete a parametric line

1. Click the left mouse button on the box in front of a parametric line ID to select the line.

2. Click the left mouse button on the Delete icon in the Parametric Lines tab, and the selected line will be removed from the list.

Figure 4.59. A selected parametric line: (a) object list, (b) its display with a dark red color.

Highlight parametric lines

Click the icon in the Parametric Lines tab to highlight all lines with a dark red color {Figure 4.60 (a)}, and click it again to cancel the highlight {Figure 4.60 (b)}.

Figure 4.60. A parabola: (a) showing the highlight, (b) hiding the highlight.

The parametric formulas of the parabolic curve in Figure 4.60 are as follows:

where, −5.0 ≤ t ≤ 5.0.

Other commands

The commands , , , , and in the Parametric Lines tab have the same functions as those in the Node list window (Section 4.1.1), and thus the description is omitted.

4.1.7 Symbols

The node coordinates, wire radii, object parameters, etc., can be defined not only by numeric values but also through symbolic names. A combination of a minus sign and symbolic name is also allowed (for example, a symbolic name a can be used with a minus sign as −a). Symbols are defined in the Symbol list, as shown in Figure 4.61.

Figure 4.61. Symbol list.

The symbol value is defined by a numeric value or by a symbolic expression. Symbolic expressions can use brackets, arithmetic operations (+, −, *, /, %, **) and functions (abs, acos, asin, atan, atan2, ceil, cos, cosh, double, exp, floor, fmod, hypot, int, log, log10, pow, rand, round, sin, sinh, sqrt, srand, tan, tanh).

One can also perform the following in the Symbol list:

Add a symbol

1. Click the Add icon (Figure 4.61) in the Symbol list window and then a window opens as shown in Figure 4.62.

Figure 4.62. Symbol definition window.

2. Enter the new symbol in the blank field. It consists of the symbol name, followed by the equal sign and the symbol value. For example, symbol a with the value of 1 can be defined as a = 1.0, as shown in Figure 4.63.

Figure 4.63. Definition of a symbol.

The symbol value can be defined by a symbolic expression of the existing symbols, as depicted in Figure 4.64, where the value of symbol b is defined as a/2 and the value of symbol c is defined as a function of symbol a and symbol b as c = a*sin(b).

Figure 4.64. Symbols defined by symbolic expressions: (a) symbol b is a function of symbol a, (b) symbol c defined using the function of symbols a and b.

3. Click Ok in the Enter the New Symbol window in Step 2, and the new symbol is added in the Symbol list window. Each row of the Symbol list defines one symbol, which includes Real Value and Symbol Value, as shown in Figure 4.65.

Figure 4.65. Symbol list containing three symbols.

Modify a symbol

The symbol value can be modified by double clicking the left mouse button on the row of an existing symbol. For example, when one double left clicks the first row of the symbol list as depicted in Figure 4.65, the modify the symbol window appears, as shown in Figure 4.66.

Figure 4.66. Modify a symbol.

Delete a symbol

1. Click the left mouse button on the box in front of a symbol number to select the symbol (Figure 4.67).

2. Click the left mouse button on the Delete icon in the Symbol list window, and the selected symbol will be removed from the list.

Figure 4.67. Delete the selected symbol.

Figure 4.68. Error window when a symbol is used to define other symbols.

Other commands

The commands , , , , and in the Symbol list window have the same functions as those in the Node list window (Section 4.1.1), and thus, the description is omitted.

4.2 CREATING AN ARBITRARILY SHAPED MODEL USING THE GEOMETRY MENU

The GeometryCreate menu is for the generation of all the different possible geometric entities. By default, new entities are created inside the current layer (see Layers in Appendix A).

4.2.1 Point

Individual points are created by entering each point in any of the following ways:

1. Placing them in the graphical window with the mouse.
2. Entering points by coordinates.

The points can then be joined together to form lines.

4.2.1.1 Placing Points in the Graphical Window

Points are placed in the HOBBIES graphical window in the plane z = 0 according to the coordinates viewed in the window. Depending on the activated preferences (see Preferences in Appendix A), if one selects a region located in the vicinity of an existing point, HOBBIES asks whether it should create a new point or use the existing one.

4.2.1.2 Entering Points by Coordinates

HOBBIES offers the command line (Section 3.4.4) for entering points in order to create geometries easily, defining coordinates in the Cartesian coordinate system.

The coordinates of a point can be entered in the command line by following one of two possible formats, with or without the commas:

Coordinate z can be omitted in both cases.

The following are valid examples of point definitions:

The basic steps for creating points are:

1. Select the GeometryCreatePoint menu, or click the icon in the Toolbar.

2. Enter coordinates of a point in one of the valid formats in the command line, press the Enter key, and a point is created.

3. Create other points one by one by following the process in Step 1.

4. Press the ESC key to finish the entering process and to add all points created in the Node list window. You can edit the nodes in the Node list window, as described in Section 4.1.1.

The Number option in the Contextual menu (Section 3.4.2) lets one choose the label that will be assigned to the next point created. If a point with this number already exists, the old point changes its number.

4.2.2 Line

4.2.2.1 Straight Line

The steps for creating lines are:

1. Select the GeometryCreateStraight line menu, or click the icon in the Toolbar.

2. Enter two points to create a straight line, and then continue entering points in order to create more lines from the first one. Every part of the total line created is an independent line.

3. Press the ESC key to finish the line creation process and to add all lines created in the Wire list window.

4. If the wires act as antennas or feeding pins, open the Wire list window (Section 4.1.2) and enter the Radius for each wire. One can also edit Dom, Nds, and Ncs for each wire.

If two points already exist, one can connect the two points by following these steps:

1. Select the GeometryCreateStraight line menu, or click the icon in the Toolbar.

2. Click the right mouse button while the cursor is over the HOBBIES screen, select the ContextualJoin menu (keyboard shortcut: Ctrl-a), and the cursor becomes . Select the first point and the second point by clicking the left mouse button; press the ESC key to finish the line creation process and to add the line in the Wire list window.

3. If the wire acts as an antenna or a feeding pin, open the Wire list window (Section 4.1.2) and enter the Radius for the wire. One can also edit Dom, Nds, and Ncs for the wire.

4.2.2.2 NURBS Line

NURBS are Non-Uniform Rational B-Splines. They are a type of curve that can interpolate a set of points. NURBS can also be defined by their control polygon, another set of points that the curve approximates smoothly. There are two ways of creating a NURBS line using this command; either by entering some interpolated points or by entering the points that form the control polygon, or selecting the existing points by the mouse.

By default, a NURBS line is created by entering interpolated points, which is called Interpolant mode. The steps are as follows:

1. Select the GeometryCreate NURBS line menu, or click the icon in the Toolbar.

2. Enter two or more points to create a NURBS line that is a cubic polynomial passing through all the points.

3. Press the ESC key to finish the line creation process and to add the NURBS line created in the Wire list window.

4. If the NURBS line acts as an antenna or a feeding pin, open the Wire list window (Section 4.1.2) and enter the Radius for the wire. One can also edit Dom, Nds, and Ncs for the wire.

An example of a NURBS line is given in Figure 4.69.

Figure 4.69. A NURBS line.

The Interpolant option can be changed by calling the ContextualBy Control Pnts option, which defines NURBS by their control polygon. This polygon is a set of points where the first and the last points match the first and last points of the curve. The rest of the points do not lie on the curve. It can be assumed that the curve approximates the points of the polygon in a smooth way. In this case, the user needs first to choose the degree of the curve, which will be the degree of the connected polynomials that define the NURBS.

Instead of entering interpolated points, the ContextualFitting option lets you approximate a line using a minimum squared criterion. One has also to select the degree of approximation for this curve.

When defining interpolating curves, one can choose to define the tangents to one or both ends (using the ContextualTangents option). These tangents can be customized, in that they can either be defined by picking their direction on the screen or by considering an existing line as a tangent to the NURBS if it follows a previous curve (the option ContextualByLine). The ContextualNext option allows only one tangent to be defined. In this way, it is possible to create a closed NURBS by selecting the initial point as the endpoint and choosing one of the options ContextualTangent, Next, or ByLine.

When a NURBS has been created, all the interior points (exclude the first and last) are not really entity points unless they previously existed.

The ContextualUndo option undoes the creation of the last point; this can be done all the way back to the first point.

The ContextualNumber option lets one choose the label that will be assigned to the next created line. If a line with this number already exists, its number is changed.

To enter rational weights on the curve, select the GeometryEditEdit NURBSLine/Surface menu (see Edit NURBS line/surface in Section 4.3.7).

4.2.2.3 Parametric Line

The user can refer to Section 4.1.6.6 for a detailed description.

4.2.2.4 Polyline

A polyline is a set of at least two other lines of any type (including polylines themselves). Every line must share one or two of its endpoints with the endpoints of other lines.

There are two possible ways to create a polyline; either by selecting one line and searching the rest until a corner or end is reached, or by selecting several lines. In the case of the latter, the order of selection is not important, but all of them must join each other by sharing common points. By default a polyline line is created by selecting several lines. The basic steps for creating a polyline are as follows:

1. Select the GeometryCreatePolyline menu.

2. Select two or more lines by clicking the left mouse button.

3. Press the ESC key and a polyline is created. The Wire list window is updated.

4. If the polyline acts as an antenna or a feeding pin, open the Wire list window (Section 4.1.2) and enter the radius of the wire. One can also edit Dom, Nds, and Ncs for the wire.

Polylines are drawn in green to show the difference from the other lines, which are drawn in blue, as show in Figure 4.70.

Instead of selecting several lines, the ContextualSearch option lets one create a polyline by selecting one line and searching the rest until a corner or end is reached.

Polylines are widely used when creating NURBS surfaces (see NURBS surface creation in Section 4.2.3.1). When deleting a polyline, all its lines are deleted. When exploding it (see Polyline in Section 4.3.6), the polyline will disappear and its individual lines will appear. It is not possible to create third-level polylines: One former polyline can be included inside another, but this is the limit and these two cannot be included within a further polyline.

The ContextualNumber option lets one choose the label that will be assigned to the next created line. If a line with this number already exists, its number is changed.

Figure 4.70. Example of a polyline: (a) four lines, (b) a polyline created by four lines.

4.2.2.5 Arc

To create an arc, one can either enter three points or enter a radius and the two tangent lines at the arc's ends (Fillet curves).

The steps for creating an arc by using three points are as follows:

1. Select the GeometryCreateArcBy 3 points menu, or click the icon in the Toolbar.

2. Enter three points to create an arc line. One can also select existing points (see Straight line creation in Section 4.2.2.1) to create arcs.

3. Press the ESC key to finish the line creation process and to add the arc created in the Wire list window.

4. If the arc acts as an antenna or a feeding pin, open the Wire list window (Section 4.1.2) and enter the radius of the wire. One can also edit Dom, Nds, and Ncs for the wire.

It is important to note that when creating an arc, new points are also being created (if existing ones are not being used).

The basic steps for creating an arc by using a radius and the two tangent lines at the arc's ends are as follows:

1. Select the GeometryCreateArcFillet curves menu.

2. Enter the radius in the command line, and then select two lines that share one common point to create two tangent lines.

3. Press the ESC key to finish the line creation process. An arc is created and the two lines are modified to be tangent and continuous with this new arc (Figure 4.71), which is added in the Wire list window.

4. If the arc acts as an antenna or a feeding pin, open the Wire list window (Section 4.1.2) and enter the radius of the wire. One can also edit Dom, Nds, and Ncs for the wire.

An example of a fillet curve is given in Figure 4.71.

An arc that begins and ends at the same point (i.e. where the first and third points are the same) will be created as a circle. An arc will always include the second point that is entered, although this point is only used as a reference and, if it is not an existing point, is automatically erased when the arc is created.

Figure 4.71. Example of a fillet curve: (a) two lines, (b) an arc created by the two lines.

The ContextualUndo option undoes the creation of the last point (if it is a new one). It is possible to continue undoing all the way back to the first point.

To convert one arc to another one with the same center and in the same plane but with a complementary angle, the Swap arc command can be used (see Swap arc in Section 4.3.5).

4.2.3 Surface

4.2.3.1 NURBS surface

NURBS are Non-Uniform Rational B-Splines. They are a type of surface that is defined by its control polygon (one set of points that the surface approximates smoothly), one set of knots for the two directions u and v (a non-decreasing list of real numbers between 0 and 1), and optionally, one set of rational weights.

To draw the isoparametric lines in u, v = 0.5, check the Surface drawing type option in the UtilitiesPreferencesGraphical window as shown in Figure 4.72.

HOBBIES provides several ways in the GeometryCreateNURBS surface menu to create NURBS surfaces:

• By contour: this creates a NURBS according to its contour lines. HOBBIES automatically calculates the interior information of the surface so as to interpolate the boundaries smoothly. To create a NURBS surface, some lines must be selected. The order of selection is not important, but all of them must join each other by sharing common points and must form a closed contour. The number of lines must be equal to or greater than one, and their shape must be topologically similar to a triangle or a quadrilateral in the space if the algorithm is to work correctly. This last argument is not necessary if all the lines lie in one plane. In this case, the surface is created as a trimmed one and any problems with the shape are avoided. It is possible to select the boundary lines and the boundary lines of interior holes at the same time, if all the lines belong to a plane. A NURBS surface by contour is given in Figure 4.73.

Figure 4.72. Preferences for window settings and a NURBS surface with isoparametric lines: (a) Preferences window (b) NURBS surface with marked isoparametric lines in u, v = 0.5.

Figure 4.73. Creation of a NURBS surface by contour.

• Automatic: this automatically creates all possible surfaces with the number of sides given by the user. Every new surface will be created in the current layer. NURBS surfaces created by the command Automatic are given in Figure 4.74.

Figure 4.74. Creation of NURBS surfaces in an automatic fashion.

• Trimmed: this option lets one select one existing NURBS surface and a set of closed lines that are inside the surface. Some of these lines may already belong to the contour of the existing surface. Some other lines may be created with an intersection with another surface. Another new surface will be created without changing the old one. It is possible to select the boundary lines and the boundary lines of interior holes at the same time, if all the lines belong to the surface. An example of a trimmed surface with a hole is given in Figure 4.75.
• Untrimmed: this constructs one new surface with the selected surface as its base and with the natural contours of the NURBS surface as its contours. The resulting surface is not trimmed. An example of an untrimmed surface from a trimmed surface (see Figure 4.75) is given in Figure 4.76.
• Parallel lines: this lets one create one surface given a set of parallel lines in the space. The new surface will interpolate all the selected lines. An example is shown in Figure 4.77.

  

  Figure 4.75. Creation of a new trimmed surface with half a cylinder surface.

  

  Figure 4.76. Creation of a new untrimmed surface with a quarter of a cylinder surface.

  

  Figure 4.77. Creation of a NURBS surface by parallel lines.

• By points/By line points: these two options are available in the Contextual mouse menu after the NURBS surface creation tool is selected. By points creates a NURBS surface from a cloud of points, and By line points creates a NURBS surface from level curves. These two functions are very useful for creating relief and terrains. In Figure 4.78, there is a NURBS surface created from level curves.

Figure 4.78. Creation of a NURBS surface by points.

• Search: this lets one select one line and then creates one surface that contains that line. An example of creation of a NURBS surface by searching lines is given in Figure 4.79.

Figure 4.79. Creation of a NURBS surface by searching lines.

When NURBS surfaces are created, they are added in the Surface list window (Section 4.1.3) automatically. One can edit Domains (1st, 2nd), Degrees (Ndp, Nds), and Current (Ncp, Ncs) options in the Surface list window as described in Section 4.1.3.

4.2.3.2 Parametric Surface

The user can refer to Section 4.1.6.5 for a detailed description.

4.2.3.3 Geometry Creation using a Surface Mesh

With this option, a surface can be created by selecting triangular quadrilateral mesh elements. An example is shown in Figure 4.80.

Figure 4.80. Geometry from surface mesh: (a) selected mesh, (b) geometry model after the conversion.

4.2.3.4 Geometry Creation using Geometry from a Mesh

This option converts all mesh models (only surface mesh, triangles, and quadrilaterals) to a geometry model, obtaining a NURBS surface-based definition. It creates a group of new layers called Reconstruction. Inside the Reconstruction layer, the user will see two new layers: The first “All Lines And Points” contains lines and points, and the second Reconstructed Nurbs contains the surfaces. If some surfaces could not be reconstructed, a third layer will appear, called SurfMeshes Not Reconstructed, containing the remaining parts. An example is shown in Figure 4.81.

Figure 4.81. Geometry from mesh: (a) a structure in 3DS format (a format used by Discreet Software's 3D Studio max), (b) geometry model after the conversion.

4.2.3.5 Geometry Creation using Geometry from Elements

By using this option, the user can import meshes into HOBBIES and use them to create geometry models.

Here is an example using this option to create a geometry model from the 3DStudio mesh. The basic steps are as follows:

1. Import the mesh of a missile-shaped model by selecting FilesImport3DStudio mesh, as shown in Figure 4.82.

2. Click GeometryCreateGeometry from elements, a model will appear, as shown in Figure 4.83(a).

3. Create a new layer (e.g., Layer1), and send the points that can describe the shape of the geometric model to this layer (see Layers in Appendix A), as shown in Figure 4.83 (b). Keep this layer on and the rest layers off, and use these points to create NURBS lines, as shown in Figure 4.83 (c).

4. Create another layer (e.g., Layer2), and send the NURBS lines in Layer1 to it {Figure 4.83 (d)}. Create more lines that will be needed for surfaces by connecting the points, and create the NURBS surfaces using these lines, as shown in Figure 4.83 (e). To view the geometric model clearly, keep Layer2 on and the rest layers off, and display it in the Flat or Smooth render mode {Figure 4.83 (f)}. Note that in this example, only part of the full model is taken from the whole 3DS model for demonstration in Figures 4.83 (b)–(f).

Figure 4.82. Imported model in 3DS format.

Figure 4.83. Steps for creating a model using Convert mesh to geometry: (a) 3DS geometric model with selected points marked, (b) points sent to Layer1, (c) NURBS lines created by selected points, (d) NURBS lines sent to Layer2, (e) NURBS surfaces generated, (f) NURBS surfaces in Flat render mode.

4.2.4 Volume

A volume is an entity formed by a closed set of surfaces that share the lines between them. As described in Section 4.1.5, the purpose of introducing volumes is to utilize the volume Boolean operations for geometric modeling.

HOBBIES provides three ways to create a volume in the GeometryCreateVolume menu: By contour, Search, and Automatic 6-sided volumes.

The basic steps to create a volume by contour are as follows:

1. Choose the GeometryCreateVolumeBy contour menu, or click the icon in the Toolbar.

2. Select some surfaces by clicking the left mouse button. The order of selection is not important, but all surfaces must join each other by sharing common lines and they must form a closed contour.

3. Press the ESC key to create the volume and to add it in the Volume list (Section 4.1.5).

If there is an error and the volume is not created, a window appears with some useful information.

An example of a volume creation is shown in Figure 4.84.

Figure 4.84. Creation of a cylinder volume.

The Search option lets one select one surface and create one of the volumes that contains this surface.

The Automatic 6-sided volumes option creates all possible volumes that have six sides (contour surfaces). It can be applied several times over the geometry and volumes will not be repeated. Every new volume will be created in the current layer. This can be useful for structured meshing (see Structured Mesh in Section 5.2).

4.2.5 Object

With this command, it is possible to create the following kinds of objects:

• Rectangle
• Polygon
• Circle
• Sphere
• Cylinder
• Cone
• Prism
• Torus

When creating an object, HOBBIES requires information about the definition of a center and a normal as shown in the area of the command line. To enter the coordinates of the center, one can click on the screen or select an existing point (see Point creation in Section 4.2.1). To enter the normal, HOBBIES displays a window (Figure 4.85) where one can choose one of the three axes or enter the coordinates of a point.

Figure 4.85. Window to define the direction of the normal to the plane.

The In screen button in the Enter normal window lets one manually enter the coordinates of the point that defines the normal: One can directly click on the screen or pick an existing point using the Join option in the Contextual mouse menu.

When using the command, the volume of the object is also created. The user needs to delete the volume before meshing.

Example

The objects that can be created by the GeometryCreateObject menu are demonstrated in Figure 4.86.

4.3 OPERATIONS ON A MODEL

These operations are the HOBBIES editing options for geometrical entities:

• Move points
• Divide lines, polylines, surfaces, or volumes
• Join surfaces

  

  Figure 4.86. Examples of objects: (a) a rectangle, (b) a polygon, (c) a circle, (d) a sphere, (e) a cylinder, (f) a cone, (g) a prism, (h) a torus.

• Join endpoints of two lines
• Force lines to be tangent
• Swap arc
• Explode or edit polylines
• Edit SurfMesh
• Edit NURBS lines or surfaces
• Convert to NURBS lines or surfaces
• Simplify NURBS lines or surfaces
• Hole NURBS surface or volumes
• Collapse or Uncollapse entities or models
• Intersections between entities
• Surface or volume Boolean operations

4.3.1 Move Point

By using this command, an existing point is selected and moved. The new position is entered in the usual way (see Point definition in Section 4.2.1). If the new position is an existing point (when using join), HOBBIES will determine the distance between the points, and ask whether they should be joined. If the answer is yes, both points are converted into one. Any lines of surfaces that include the point in question will be moved accordingly so that the links are maintained. This may lead to these lines or surfaces being distorted, as shown in Figure 4.87.

Figure 4.87. Movement of point/node 3.

4.3.2 Divide

The Divide command can be applied either to lines, polylines, surfaces (including trimmed surfaces), or volumes.

Polylines:

In the case of polylines, an existing interior point must be chosen. The polyline will be converted into two lines that may or may not be polylines.

Polyline division has the ContextualBy Angle option, which allows one to divide the polyline at all the points where the angle between the sub-lines is greater than a given value (Figure 4.88).

Figure 4.88. One polyline is divided into four lines by the angle option.

Lines, Surfaces, and Volumes:

In the case of lines, surfaces, and volumes, once the entity has been selected, the division can be done in several ways:

• Number of divisions (lines or surfaces): The line or surface will be converted into equally spaced pieces (Figure 4.89). In the case of surfaces, it is necessary to give the division direction as u or v.

  

  Figure 4.89. One surface is divided into six surfaces (number of divisions in u-direction is 2 and that in v-direction is 3).

• Near point (lines or surfaces): With this option, one point must be selected near the line or the surface. Points inside the entities can be selected by the Point in line or Point in surface option in the Contextual mouse menu. The line or the surface will be divided into two entities near that point. In the case of surfaces, it is necessary to give the division direction as u or v (Figure 4.90).

  

  Figure 4.90. One surface is divided into four surfaces by a near point.

• Parameter (lines or surfaces): One factor is given between 0.0 and 1.0, and the entity will be divided where the parametric variable u or v takes that value. In the case of surfaces, it is necessary to give the division direction as u or v (Figure 4.91).

  

  Figure 4.91. One surface is divided into four surfaces by a parameter 0.4 in u-direction and 0.6 in v-direction.

• Relative length (lines only): One factor is given between 0.0 and 1.0 to divide the line with relative arc length ratio equal to the selected factor. (Same concept as Parameter if the line was arc length parameterized.) An example is shown in Figure 4.92.

  

  Figure 4.92. One line is divided into two lines by a relative length 0.3.

• Length (lines only): The length of the resulting divided lines is given, and HOBBIES divides the line into as many lines as it can. If the length given is bigger than the length of the selected line, no division is made.

  An example is given in Figure 4.93.

  

  Figure 4.93. One line is divided into three lines by the length option.

• Split (surfaces or volumes): The surface/volume will be divided following the divide lines/surfaces. These lines/surfaces must share points/lines with the surface to be split. As shown in Figure 4.94, one surface is split into two surfaces.

Figure 4.94. One surface is split into two surfaces.

4.3.3 Join

This option is utilized to join surfaces with common boundary lines to create one single and complex surface.

Rebuild by boundary:

An example of three NURBS surfaces joined into one by using this command is shown in Figure 4.95.

Join only coplanars:

This command is similar to the Rebuild by boundary option, but it is only valid for coplanar surfaces.

Figure 4.95. Three NURBS surfaces are joined into one.

4.3.4 Line Operations

With this option, one can edit groups of lines with respect to their topology and shape.

Join lines end points:

With the command Join lines end points, two lines must be selected. HOBBIES determines the distance between the two closest end-points, draws both points, and asks for confirmation. If one of the lines is a polyline, interior points are also considered. If accepted, the points are converted into one and the lines are distorted. The new point will then take the place of the first line's point. See Move point in Section 4.3.1 for another method of converting two points to one. Figure 4.96 shows that two end-points from two lines are joined.

Caution: The second selected line cannot have higher entities (the second point is moved to the first).

Force to be tangent:

With the command Force to be tangent, two lines (which share at least one point) must be selected. They must be NURBS line; otherwise they will be rejected. You are asked to enter the maximum angle between tangents of lines to accept the operation, and HOBBIES will modify the selected NURBS lines and force them to be tangents at their common point. Figure 4.97 shows that two NURBS lines are forced to be tangent at point 2.

Figure 4.96. Two end-points from two lines are joined.

Figure 4.97. Two NURBS lines are forced to be tangent at point 2.

4.3.5 Swap Arc

This command lets you select and alter arcs. Lines that are not arcs are rejected. When you confirm the operation, the arc is converted to a new arc with the same center and in the same plane but opposite the old one. The old arc disappears, and the angle of the new arc will be complementary to the angle of the old arc. Figure 4.98 shows that an arc is swapped.

Caution: Arcs belonging to higher entities cannot be swapped.

Figure 4.98. An arc is swapped.

4.3.6 Polyline

Explode polyline:

This command lets you select which polylines you wish to explode. Lines that are not polylines or have higher entities or conditions are rejected. After confirmation, the polylines are exploded and converted back to their original lines. Polylines then disappear (see polyline creation in Section 4.2.2.4). Figure 4.99 shows that a polyline is exploded into two lines.

Edit polyline:

The command Edit Polyline allows you to select which polylines you wish to edit; lines that are not polylines are rejected. It is possible to choose several options for the polylines:

• Use points: When meshing this polyline, there will be at least one node at every point location that defines the polyline. These will be the endpoints of interior lines.
• Not use points: When meshing this polyline, the mesh generator ignores the points and, therefore, the nodes will be placed anywhere. This is the default option. Nodes will only be put in the position of a point if there is a four-sided surface over part of a polyline.
• Only points: When meshing this polyline, the nodes will only be placed where the geometry points are.

  

  Figure 4.99. A polyline is exploded into two lines.

4.3.7 Edit NURBS Line/Surface

Edit NURBS line:

This option is a tool to modify some NURBS geometric properties, like control points, degree, and so on.

Once a NURBS line is selected (use the Pick button in the Edit NURBS Line window as shown in Figure 4.100 (a), you can edit its control points (see NURBS line creation in Section 4.2.2.2). Select the control points as if they were regular points and enter their new positions in the usual way (see Point definition in Section 4.2.1).

The Influence factor (Figure 4.100 (b)) affects the movement propagation of the neighboring control points.

Available options in the Edit NURBS Line window:

• Fix boundary: Check the fix boundary option if you do not want to move the boundary control points of the line.
• Insert knot: You are asked for a knot value between 0.0 and 1.0, and this is then inserted. The program checks that the knot multiplicity is not greater than the order (order = degree + 1). As the number of knots increases, the number of control points also increases, so this option can be used to have more points defining the same curve.
• Knot removal: The inverse of knot insertion. Remove knots, if possible, without changing the shape with a given tolerance in the interest of saving memory.
• Elevate degree: With this option, the degree of the curve is raised by one. The new curve will have the same shape but with more control points and knots.
• Reduce degree: The inverse of degree elevation. Decrease the polynomial degree, if possible, without changing the shape with a given tolerance.
• Change weight: A new positive weight can be introduced for any control point, with the exception of the end points.
• Cancel weights: All weights of the NURBS are converted to 1.0, and the curve is no longer rational.
• Reparameterize: With the same control points, a new curve is calculated to get a better curve with a more uniform parameterization.
• Similar cubic: This option converts the curve to a simplified one with degree = 3, which is only an approximation of the original one.

Figure 4.100. Edit NURBS line windows: (a) the window before picking a NURBS line, (b) the window after picking a NURBS line.

Edit NURBS surface:

Once a NURBS surface is selected (use the Pick button of the Edit NURBS Surface window as shown in Figure 4.101 (a)), you can edit its control points interactively (see NURBS surface creation in Section 4.2.3). Select the control points as if they were regular points, and enter their new positions in the usual way (see Point definition in Section 4.2.1).

Available options in the Edit NURBS surface window {Figure 4.101 (b)}:

• Insert knot: You are asked for a knot value between 0.0 and 1.0, and it is then inserted. The program checks that the knot multiplicity is not greater than the order. This option can be used to have more points defining the same surface.
• Knot removal: The inverse of knot insertion. Remove knots, if possible, without changing the shape with a given tolerance in the interest of saving memory.
• Elevate degree: With this option, the degree of the surface is raised by one. The new surface will have the same shape but with more control points and knots.
• Reduce degree: The inverse of degree elevation. Decrease the polynomial degree, if possible, without changing the shape with a given tolerance.
• Change weight: A new positive weight can be introduced for any control point, with the exception of the end points, which must have weight = 1 (to force the surface to pass over the corner control points).
• Cancel weights: This makes the weights of all the control points equal to 1.0.
• Reparametrize: This reparameterizes the surface obtaining an optimized surface. When a NURBS surface is not well parameterized, the mesh is of a lower quality.
• Similar cubic: This option converts the surface to a simplified one with degree = 3 in both parametric directions, which is only an approximation of the original one.

Figure 4.101. Edit NURBS surface windows: (a) the window before picking a NURBS surface, (b) the window after picking a NURBS surface.

The control polygon of a NURBS surface is depicted in Figure 4.102.

The Movement type menu of the Edit NURBS Surface window determines the way the selected knots will move. This movement can be along an axis (x-axis, y-axis, z-axis), can describe the Normal of the surface (Normal), can follow the screen movement of the mouse (Screen), or the new location of the knot can be defined by introducing the coordinates of a point (Point).

Figure 4.102. Control polygon of a NURBS surface of a cylinder.

4.3.8 Convert to NURBS Line/Surface

This option converts the selected lines or surfaces to NURBS lines or NURBS surfaces.

4.3.9 Simplify NURBS Line/Surface

This option converts the selected NURBS lines or surfaces to other ones very similar to the originals but with a less complicated definition. It can be useful when importing data where a control polygon is too complex for HOBBIES to display or mesh quickly.

The Model option performs the operation over all the geometrical entities in the model.

4.3.10 Hole NURBS Surface

With this option, one can select one existing NURBS surface and a set of closed lines that are inside of it and which form a hole. The lines may be created by an intersection with another surface. The hole will be added to the existing surface, as illustrated in Figure 4.103.

Figure 4.103. Hole made of two arcs inside a NURBS surface.

4.3.11 Hole Volume

It is possible to add holes to a volume. To do so, start by creating the interior volumes as independent volumes. After this, click the Hole volume and select the outside volume. Then, select the interior volumes that form every hole, one by one. Finish with the ESC key.

It is possible to specify ContextualNo delete holes to not delete the volumes used to create the holes (or ContextualDelete holes to delete them).

4.3.12 Collapse

The Collapse function converts coincident entities (i.e., entities that are very close to each other) into one.

The UtilitiesPreferencesExchangeImport tolerance variable determines which entities will be collapsed. When the distance between two points is less than the tolerance, they will be converted into one. With lines and surfaces, the maximum distance between both entities is calculated, and if it is less than the Import tolerance, they are converted into one.

Select the type of entities—point, line, surface, or volume—when in geometry mode. All of the lower entities that belong to the selected entities will automatically be computed. Upon pressing the ESC key, the collapse operation will be performed.

The Model option performs the operation over all the geometrical entities in the model.

4.3.13 Uncollapse

The Uncollapse function lets one select lines, surfaces, or volumes and duplicate all common lower entities. Typically, if two surfaces share one line as an edge, after applying this function to both surfaces, that line and its shared points will be duplicated and every line will belong to a different surface. This feature is useful, for example, if you want to disconnect joined bodies or generate a non-conformal mesh with fewer elements than a conformal one.

4.3.14 Intersection

By using this option, the intersection of many geometrical entities can be performed.

Intersection: Lines

This option lets one select several lines for which HOBBIES then tries to find as many intersection points as possible. Lines are divided where applicable.

The ContextualNo Divide Lines option creates an intersection point but does not modify the lines. The intersection of two straight lines is illustrated in Figure 4.104.

Figure 4.104. Intersection of two straight lines.

Intersection: Surface–2 pc nts

One surface and two points that lie approximately over it need to be selected. HOBBIES then calculates the line generated by the intersection between the surface and a plane defined by the two given points and the average normal to the surface of these points. Figure 4.105 shows the intersection of one surface with two points.

Figure 4.105. Intersection of one surface with two points (nodes 2 and 3).

Intersection: Surface–lines

One NURBS surface and several lines need to be selected. HOBBIES then calculates the intersection between the surface and the lines. Lines will be divided at the intersection point with ContextualDivide lines as the default option.

The ContextualNo Divide Lines option creates the intersection point but does not divide the lines.

Figure 4.106 shows the intersection of one surface with one line.

Figure 4.106. Intersection of one surface with one line.

Intersection: Surfaces

This command creates the intersection lines between two surfaces.

The ContextualNo Divide Lines option creates the intersection point but does not split the contour lines. By default, the surfaces are divided, unless the ContextualNo divide surface option is selected.

Figure 4.107 shows the intersection of two surfaces.

Figure 4.107. Intersection of two surfaces.

4.3.15 Surface Boolean Operations

Two 2D surfaces located in the XY plane need to be selected (order is important when dealing with subtraction).

The valid surface Boolean operations are:

• Union: Fuses two surfaces, wherever they intersect, to create a single, more complex surface. Figure 4.108 shows the Union of two surfaces as one.
• Intersection: Creates a surface based on the intersecting points of two separate surfaces. Figure 4.109 shows the intersection of two surfaces into one.
• Subtraction: Negates a specific portion of a surface to create a hole or indentation. Figure 4.110 shows the subtraction of the rectangle from the circle.
• Subtract and intersect: This is the combination of Subtraction and Intersection as described above. The subtraction and intersection of a rectangle and a circle are shown in Figure 4.111.

Figure 4.108. Union of two surfaces as one.

Figure 4.109. Intersection of two surfaces into one.

Figure 4.110. Subtraction of the rectangle from the circle.

Figure 4.111. Subtraction and intersection of a rectangle and a circle.

4.3.16 Volume Boolean Operations

The HOBBIES Volume Boolean Modeler has been designed to accomplish geometric feats, such as physically punching a hole through a volume, combining two volumes into one, and creating a new volume from the intersecting points of two separate volumes.

The valid volume Boolean operations are:

• Union: Fuses several volumes, wherever they intersect, to create a single, more complex volume, as illustrated in Figure 4.112.
• Intersection: Creates a volume based on the intersecting points of several separate volumes, as illustrated in Figure 4.113.
• Subtraction: Negates a specific portion of a volume to create a hole or indentation, as illustrated in Figure 4.114. Order is important when dealing with subtraction.
• Subtract and intersect: This is the combination of Subtraction and Intersection as described above, and illustrated in Figure 4.115.

Figure 4.112. Union of two volumes as one.

Figure 4.113. Intersection of two volumes into one.

Figure 4.114. Subtraction of the smaller volume from the larger one.

Figure 4.115. Subtraction and intersection of a smaller volume and a larger one.

4.4 MANIPULATIONS ON A MODEL

4.4.1 Copy

Copy is a general function that allows one to select a group of entities and copy them with a movement operation performed; either translation, rotation, mirror, scale, offset, sweep, or align. The entity types include points, lines, surfaces, and volumes.

The copy window is shown in Figure 4.116 (a), while the drop-down menu showing the entities is given in Figure 4.116 (b) and the drop-down menu for the transformation performed is illustrated in Figure 4.116 (c).

Figure 4.116. Copy windows: (a) copy window, (b) entities in copy window, (c) transformations in copy window.

Select the type of entities to copy

In geometry mode (ViewModeGeometry), choose between point, line, surface, and volume; and in mesh mode (ViewModeMesh), choose between nodes and elements. All of the lower entities belonging to the selected one will automatically be computed. Next, the type of movement needs to be chosen and its parameters defined. The options are as follows:

• Translation: Two points are defined. Relative movements can be obtained by defining the first point as 0,0,0 and considering the second point as the translation vector (see Point Creation in Section 4.2.1). The copy manipulation with a translation transformation is illustrated in Figure 4.117.
• Rotation: It is necessary to enter two points in 3D, or one point in 2D. These two points define the axis of rotation and its orientation. In 2D, the axis goes from the defined point towards z positive. Enter the angle of rotation in degrees; it can be positive or negative. The direction is defined by the right hand rule. In 2D, the direction is counter-clockwise. The copy manipulation with a rotation transformation is illustrated in Figure 4.118.

  

  Figure 4.117. Translation of two rings.

  

  Figure 4.118. Rotation of two half rings by 180°.

• Mirror: Three points are defined (they cannot be in a line). These points form the mirror plane. In 2D, the mirror line is defined by two points. The copy manipulation with a mirror transformation is illustrated in Figure 4.119.

  

  Figure 4.119. Mirror of a volume about a horizontal plane.

• Scale: This is defined by a manipulation center point and a vector scale factor for x, y, z axes. A scale factor greater than one increases the size, while a scale factor less than one decreases the size. The scale factor may also be negative, which changes the sign of the corresponding coordinates. The copy manipulation with a scale transformation is illustrated in Figure 4.120.

  

  Figure 4.120. Scale of the inner ring by half.

• Offset: This is defined by one positive or negative scalar magnitude. Each entity will be moved in the direction of its normal, by the magnitude given. In 2D, the normal is considered to lie in the plane z = 0. This option works either for lines, surfaces, or mesh elements. The copy manipulation with an offset transformation is illustrated in Figure 4.121.
• Sweep: This is an option for copying figures along a line (path line). One can simply copy the figures (and then specify a number of copies) or extrude them. Both methods basically have the same options. The copy manipulation with a sweep transformation is illustrated in Figure 4.122.

Figure 4.121. Offset of a circle.

Figure 4.122. Demonstration of a shape figure and path line.

The End scale factor determines how the figure is scaled along the path curve (the scale value starts at 1.0 and varies in a linear way until the End scale value). This scale value must be greater than zero. The extrusion (and the copy) always starts on the start point of the path line. If you select Twist modes to be on, then the relative position of the figure to copy, with respect to the start of the path line, is conserved along the line. This is illustrated in Figure 4.123.

Figure 4.123. Demonstration of the twist mode (Natural Twist option): (a) off, (b) on.

In a non-planar curve, there is not only curvature, but also torsion. This may cause some unexpected behavior because the figure also has a rotation along the tangent direction of the path. Figure 4.124 shows the extruded surfaces with a natural twist option in twist mode for a non-planar structure.

Figure 4.124. Surface generated with natural twist option in twist modes.

Next, the XY plane option in Twist modes is used, which makes certain that the initial vector will remain in this plane during extrusion. In the example given in Figure 4.125, the axis is oriented along the z-direction.

Figure 4.125. Surface generated with an XY plane option.

The option ByDer2 in Twist modes uses the second derivate of the path line as a normal to the plane in which that initial vector has to remain. A rotation along the path line can be forced using the Angle parameter (degrees), as illustrated in Figure 4.126.

Finally, if the path line is a polyline, then the extrusion will be divided into several parts. The generation of a coaxial line by twist along a polyline is shown in Figure 4.127.

• Align: This is an option to move figures from a generic position to the desired one. Set the new location specifying three source points and three destination points: The first point defines the exact destination of the source point; the second point is not necessarily the exact destination, but a point over the destination straight line; and the third point is not necessarily the exact destination, but a point over the destination plane. The operation is illustrated in Figure 4.128.

Figure 4.126. Twist of a polygon with the ByDer2 option: (a) angle is 90°, (b) angle is 360°.

Figure 4.127. Generation of a coaxial line by twist along a polyline.

Figure 4.128. Align surfaces.

Other available options are as follows:

• Extrude: This option can be set to either lines, surfaces, or volumes. When a movement is selected, a copy is made and lines connecting the old and new points are created. These lines will either be straight lines or arcs depending on the movement type. If extrude Surfaces is chosen, NURBS surfaces connecting old and new lines will also be created. If extrude Volumes is chosen, the volume contained between old and new surfaces is also created. This option is not allowed when copying volumes.
• Multiple copies: By selecting this option and giving the number of repetitions, the selected operation is performed this number of times. This option is not available for mirroring.
• Create contacts: Creates separated contact volumes for every copied surface. This option is only available when copying surfaces.
• Duplicate entities: If this option is not set and after the copy operation, an entity occupies the same position as an existing one that does not belong to a frozen layer, both entities are converted into one.
• Maintain layers: If this option is not set, the new entities created will be placed in the layer to use; otherwise, the new entities are copied to the same layers as their originals.

4.4.2 Move

Move is a general function that allows you to select a group of entities and move them with a movement operation, either translation, rotation, mirror, scale, offset, and align. The entity types include points, lines, surfaces, volumes, and all types.

The Move window is shown in Figure 4.129 (a), while the drop-down menu showing the entities is given in Figure 4.129 (b) and the drop-down menu for the transformation performed is illustrated in Figure 4.129 (c).

This command works like Copy but moves the entities instead of copying them. The program automatically checks to see whether any of the entities must be copied instead of being moved (for example, if they also belong to other higher level entities) and performs the appropriate operation.

Options like Extrude, Multiple copies, and Create contacts are disabled for movements.

Figure 4.129. Move windows: (a) move window, (b) entities in move window, (c) transformations in move window.

4.5 DELETE A MODEL

The deletion of entities can be done in two ways: at one level (point, line, surface, or volume) or erasing all entities at once. A selection is made in both cases. After pressing the ESC key, the entities are erased.

To undo the selection of entities, press Clear Selection in the Contextual mouse menu.

Entities that form the basis of higher entities cannot be erased. For example, if a surface is created over some lines, it is necessary to erase the surface before erasing the lines.

4.6 CONCLUSION

In this chapter, how to create the geometry model for a structure in HOBBIES is explained in detail. The reader can use the submenus in the HOBBIES Structure menu to create simple-shaped models. The reader can also use commands in the toolbar and HOBBIES main menu to create complicated models. With these two flexible modeling methods, users can create HOBBIES geometry models for the structures to be simulated. Since NURBS modeling technology is used, HOBBIES can deal with structures associated with any real-world industrial production of today.

REFERENCES

[1] http://gid.cimne.upc.es/support/manuals.