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# GEOMETRY

All available geometrical operations, generating or deleting entities and performing particular options are included in this chapter.

## View geometry

This command changes from mesh visualization to geometry visualization. If mesh doesn't exist, the user is asked to generate it.

## Create

Generation of all the different possible geometrical entities. Usually, the new entities are created inside the current layer (see section Layers).

### Point creation

Individual points are created by entering each point in the usual way (see section Point definition). The point can later be used to join lines to it.

Caution: It is impossible to create new points joining old ones.

Option `Number` Lets the user choose the label that will be assigned to the next created point. If a point with this number already exists, the old point changes its number.

### Line creation

To create a straight line it is only necessary to enter two points (see section Point definition) and continue entering points in order to create more lines from the first one. Every part of the total line created is an independent line.

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

Option `Close` joins the first point and the last point created with a straight line and finishes.

Option `Undo` undoes the creation of the last point (if new) and the last line. It is possible to continue undoing back until the first point.

Option `Number` Lets the user choose the label that will be assigned to the next created line. If a line with this number already exists, the old line changes its number.

If `Join` is chosen, it is maintained for all points until `No join` is selected.

### Arc creation

To create an arc it is necessary to enter 3 points (see section Point definition) or enter a radius and the two tangent lines at the arc ends.

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

An arc that begins and ends on one of the first or third points defined is always created. The arc will always contain the second point. This one is only used as a reference and, if non-existent, it is automatically erased when the arc is created.

Option `Undo` undoes the creation of the last point (if new). It is possible to continue undoing back until the first point.

Option `By tangents` lets the user input a radius and select two lines that share one common point. An arc will be then created and the two lines will be modified to be tangent and continuous with this new arc. This function is the same than the one defined in (see section Arc tangents).

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

### Arc tangents

This option lets the user input a radius and select two lines that share one common point. An arc will be then created and the two lines will be modified to be tangent and continuous with this new arc.

### NURBS line creation

NURBS are non-uniform rational B-splines. They are a type of curves 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.

This command can be used to create a NURBS line in the following two ways.

To create a NURBS, user enters either some interpolated points or enters the points that form the control polygon (see section Point definition).

Option `Undo` undoes the creation of the last point. It is possible to continue undoing back until the first point.

By default, NURBS will be a cubic polynomial passing through all the points. However, this option can be changed by calling `ByControlPts`, 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, user chooses the degree of the curve that will be the degree of the connected polynomials that define the NURBS.

When defining interpolating curves, user can choose to define the tangents to one or both ends (option `Tangents`). These tangents are customizable, in the sense 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 (option `ByLine`). The option `Next` 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 end one, choosing option 'tangent', 'next', and 'ByLine'.

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

Option `Number` Lets the user choose the label that will be assigned to the next created line. If a line with this number already exists, the old line changes its number.

To enter rational weights to the curve, command See section Edit NURBS line, can be used.

### Polyline creation

Polylines are a set of other lines (two, at least) 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 (see section Entities selection). 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.

Polylines are drawn in green to show the difference between the other lines which are drawn in blue.

Polylines are widely used when creating 4-sided surfaces (see section 4-sided surface creation) and automatic 4-sided surfaces (see section 4-sided surface automatic creation).

When deleting a polyline, all its lines are also deleted. When exploding (see section Explode polyline), 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 not the new one.

Option `Number` Lets the user choose the label that will be assigned to the next created line. If a line with this number already exists, the old line changes its number.

### Parametric line

The required input datas are the mathematical formulas of the coordinates X(t), Y(t), Z(t), where 't' is the parameter of the curve, and its value belongs at the interval [ t0-t1 ] The curve is created by approximation. That curve is a NURB (Non Uniform Rational B-Spline) which is created with N points. In GiD these kind of curves are created with degree 3 (cubical).
EXAMPLE

We fill the formulas with the expression of a conic helix. That helix starts with radius R0=4 and finishes with radius R1=1, performing N=3 turns from t=0.0 to t=1.0, the height also changes from 0 to H=5.

Example of conic helix with a unique curve or with only points

### Planar surface creation

Note: Entity planar surface has been substituted by entity NURBS surface (see section NURBS surface creation). This entity automatically detects if boundary lines lie in a plane and create a planar NURBS.

Note: It is possible to access to this deprecated function with the Right buttons (see section Graphical).

Planar surface is an entity formed by a closed set of lines, all of them lying on the same plane. Lines must share endpoints between them.

To create a planar surface, some lines must be selected (see section Entities selection). 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. If all lines are not in the same plane the surface is not created.

It is possible to add holes to a planar surface. To do so, it is first necessary to create the outside planar surface. After this, press `Hole` button and select the created surface. Then, select lines that form every hole, one by one. Finish with `escape` (see section Escape). It is also possible to define the surface and holes at the same time, selecting all the curves.

If the surfaces lie on the plane `z=0`, the orientation of the surfaces will be anti-clockwise in this plane (the normal vector points towards `z` positive). Otherwise, orientation will be arbitrary. This can be checked with the DrawNormals command (see section Draw surface normals).

### 4-sided surface creation

Note: Entity 4-sided surface has been substituted by entity NURBS surface (see section NURBS surface creation). This new entity has all the functionality of the old one.

Note: It is possible to access to this deprecated function with the Right buttons (see section Graphical).

A 4-sided surface is an entity formed by a closed set of four lines in the space. Its mathematical definition is a bilinear Coon's surface. The surface is totally defined by the shape of the lines, with no information about the interior. This means that, sometimes, it will be necessary to use more surfaces to obtain a good shape definition.

To create a 4-sided surface defined by three lines, it is necessary to divide one of the lines in two pieces (see section Divide). Then, the creation of a 4-sided surface is possible.

To create a 4-sided surface, several lines must be selected (see section Entities selection). The order of selection is not important, but all of them must join each other by sharing common points and they must form a closed contour. If the creation is not possible, information about the endpoints is displayed in one window.

In order to make one or more lines form parts of a polyline (see section Polyline creation), select the entire polyline as one of the lines and GiD will automatically select the piece or pieces of the polyline that are required. Using this facility, non-conforming surfaces can be created. This means creating a surface by using the entire line on one side of the polyline, and creating more than one 4-sided surface by using parts of it on the other side.

When selecting more than four lines, GiD will automatically search for all the possible 4-sided surfaces that can be created with these lines. This allows the creation of many surfaces at the same time.

The button `Automatic` is equivalent to `4-sided surface automatic creation` (see section 4-sided surface automatic creation).

If the surfaces lie on the `z=0` plane, the orientation of the surfaces will be anti-clockwise in this plane (normal vector points towards `z` positive). Otherwise, the orientation will be arbitrary. This can be checked with the DrawNormals command (see section Draw surface normals).

Option `Number` Lets the user choose the label that will be assigned to the next created surface. If a surface with this number already exists, the old surface changes its number.

Caution: When creating some surfaces at the same time, it is possible that some undesired surfaces may also be created. It is necessary to check the surfaces after creation and erase the undesired ones.

### 4-sided surface automatic creation

Inside this option, GiD creates as many 4-sided surfaces as it can find. Every new surface will be created either in the current layer.

Caution: When creating some surfaces at the same time, it is possible that some undesired surfaces may also be created. It is necessary to check the surfaces after creation and erase the undesired ones.

### NURBS surface creation

NURBS are non-uniform rational B-splines. They are a type of surfaces defined by their control polygon (one set of points that the surface approximates smoothly); one set of knots for the two senses 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 `Surface drawing type` (see section Preferences).

- `By contour:` creates a NURBS by their contour lines. GiD calculates automatically the interior information of the surface so as to interpolate the boundaries smoothly.
  To create a NURBS surface, some lines must be selected (see section Entities selection). 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. Number of lines must be equal or bigger than one and shape must be topologically similar to a triangle or a quadrilateral in the space, for the algorithm 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 problems about 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.
  Note: Option `No try planar` (this option is found in the Contextal mouse menu) avoid the creation of a trimmed NURBS surface when lines are coplanar.
  Note: To enter rational weights to the surface, use command `Edit NURBS surface` (see section Edit NURBS surface).
- `Automatic:` creates automatically all possible surfaces with a number of sides given by the user. Every new surface will be created in the current layer.
  Caution: When creating some surfaces at the same time, it is possible that some undesired surfaces may also be created. It is necessary to check the surfaces after creation and erase the undesired ones.
- `Trimmed:` this option let the user select one existing NURBS surface and a set of closed lines that are inside the surface. Some of this lines may belong already 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:

  Option `Untrimm` (inside the Contextual mouse menu after selecting a Nurbs surface), constructs one new surface with the selected surface as base and as contours, the natural contours of the NURBS surface. The resulting surface is not trimmed.

- `Parallel lines:` permit to create one surface given a set of parallel lines in the space. The new surface will interpolate all the selected lines.
- `Search:` lets the user select one line and creates one surface that contains this line.
- `By points/By line points:` these two options are avalaible 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. This two functions are very useful to create reliefs and terrains. In the image below, a NURBS surface created from level curves:

  Note: This surface only is an approximation to the selected points/lines, but there's no interpolation.

### Volume creation

A volume is an entity formed by a closed set of surfaces that share their lines between them.

To create a volume, some surfaces must be selected (see section Entities selection). The order of selection is not important but all of them must join each other by sharing common lines and they must form a closed contour.

If there is an error and the volume is not created, helpful information is displayed in one window.

It is possible to add holes to a volume. To do so, it is first necessary to create the outside and the interior volumes as independent volumes. After this, push `Hole` button and select the outside volume. Then, select the interior volumes that form every hole, one by one. Finish with `escape` (see section Escape).

Orientation of volumes and their surfaces is automatically set to facilitate a correct meshing.

An additional feature allows the selection of surfaces that form the outer part of the volume as well as the ones that form the holes at the same time. In this case, GiD automatically recognizes the holes.

Option `Search` lets the user select one surface and create one of the volumes that contains this surface.

#### Automatic 6-sided volumes

This option creates all possible volumes that have 6 sides. It can be applied several times over the geometry and volumes are not repeated.

It can be useful for structured meshing (see section Structured mesh).

### Contact creation

Contact surfaces or contact volumes are defined between two lines or two surfaces that are physically in the same place but with different entities as surfaces, lines and points. From a contact surface, it is possible to generate contact elements or algorithms that define special contact between two bodies.

Those surfaces that have been generated from another one, although not physically in contact, or simply, identical surfaces separated by a movement, can obtain equal meshes from this option, ensuring a one-to-one relationship between nodes.

It is necessary to choose `contact surface` or `contact volume` to create contact surfaces. The first one is between lines and the second one is between surfaces. After this, it is necessary to choose lines in the first case and surfaces in the second. GiD automatically searches possible contacts combining selected surfaces in pairs.

Contact elements are, by default, 4-node planar quadrilaterals for surfaces and 8-node hexahedra or 6-node prisms (depending on the geometry) for contact volumes.

However, the user can select 2-node lines for all cases (see section Element type).

The 4-node planar quadrilaterals can be converted to the 8-node or 9-node for the quadratic case.

The user can also select `no mesh` for the contact entity. This makes it possible to have exactly the same mesh in both lines or both surfaces but without any additional element.

When creating the contact volumes, GiD internally checks what surfaces occupy the same location in the space and creates the contact, therefore there is no need to specify what surfaces have to be in contact. For this reason, several surfaces can be selected at once and GiD performs the contact automatically, indicating the number of contact volumes that have been generated.

For contact surfaces, however, the two lines in contact have to be specified.

A feature in GiD is the option of creating `contact separated volumes` for surfaces that are not physically in contact.

For these separated volumes, GiD internally checks whether there exists a unique solid-rigid movement between two surfaces and creates the contact between both. There is the possibility of the existence of more than one solid-rigid movement between two of them. In this situation, GiD asks for the point image of a particular original point to define the movement and, consequently, applies the right contact.

The same considerations about element type for `contact volumes` are used.

### Intersection

#### Intersection line-line

With command `Intersect lines`, two lines must be selected. GiD searches the closest points between the two lines. If the lines do not intersect, GiD determines the distance between the two closest points, draws both points and asks for confirmation. Otherwise, the new point will be the intersection point. If confirmed, the two lines are converted into four and the second point is moved to the one in the first line and converted into a unique point (if interior points of one or two of the lines coincide with endpoints, only two or three new lines are created). Polylines cannot accept this option.

Option `No divide lines` creates the intersection point but do not modify the lines.

`Note:` This option can be used to extend one line until reaching the other line.

Caution: Second selected line can have higher entities only if it is not necessary the extension of this line.

#### Intersection multiple lines

This option lets the user select several lines. Then, it tries to find as many intersection points between them as possible. Lines are divided when applicable.

Option `No divide lines` creates the intersection point but do not modify the lines.

#### Intersection Surface 2 points

User must select one surface and two points that lie approximately over the surface. GiD calculates the line intersection between the surface and a plane defined by the two given points and the average normal to the surface in these points.

`Note:` Planar surfaces can not be used with this option.

`Note:` See section Option point in line, or See section Option point in surface, can be used to define the points.

#### Intersection Surface lines

User must select one NURBS surface and several lines. GiD calculates the intersection between the surface and the lines. Lines will be divided in the intersection point.

Option `No divide lines` creates the intersection point but do not modify the lines.

Option `Extend` Divide lines and also extends lines until they reach the surface.

#### Intersection Surface surface

This command creates the intersection lines between two surfaces. If these lines intersect surfaces contour lines, these are divided.

Option `No divide lines` creates the intersection point but do not modify the contour lines.

Option `No divide surface`. By default the surfaces are divided, unless this option is selected.

#### Intersection Multiple surfaces

This command creates the intersection lines between surfaces.

### Volume boolean operations

The GiD Volume Boolean Modeler has been designed to accomplish geometric feats as physically punching a hole trough 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 two volumes wherever they intersect to create a single, more complex volume.
- `intersection`: creates a volume based on the intersecting points of two separate volumes.
- `substraction`: negates a specific portion of a volume to create a hole or indentation.

User must select the two volumes (order is important in substraction).

### Surface boolean operations

User must select the two 2D surfaces located in the XY plane (order is important in substraction).

The valid surface boolean operations are:

- `union`: fuses two surfaces wherever they intersect to create a single, more complex volume.
- `intersection`: creates a surface based on the intersecting points of two separate volumes.
- `substraction`: negates a specific portion of a surface to create a hole or indentation.

### Object

With this command it is possible to create several objects which are:

- Rectangle
- Circle
- polygon
- sphere
- cilynder
- cone
- prism
- thorus

When creating an object, GiD asks for a center and a normal. To enter the coordinates of the center you can click on the screen or select an existing point (see section Point definition). To enter the normal, GiD displays a window where you can choose one of the three axes or enter the coordinates of a point.

The button In screen of the `Enter normal` window, lets you manually enter the coordinates of the point which defines the normal: you can directly click on the screen or pick an existing point using the option Join C-a of the Contextual mouse menu.

When using the commands `sphere`, `cilynder`, `cone`, `prism` or `torus` the volume of the object is also created.

## Delete

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 (see section Entities selection) in both cases. After pressing `escape` (see section Escape), the entities are erased.

To avoid erasing the selected entities, press `Clear selection`.

Entities which depend on 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.

## Edit

There are some particular editing options for geometrical entities:

- Move point
- Explode polyline
- Edit polyline
- Edit NURBS line
- Edit NURBS surface
- Hole NURBS surface
- Divide
- Join lines end points
- Swap arcs
- Edit SurfMesh
- Convert to NURBS line
- Convert to NURBS surface

### Move point

By using this command, an existing point is selected and moved. The new position is entered in the usual way (see section Point definition). If the new position is an existing point (when using `join`), GiD will determine the distance between the points and ask if they should be joined. If answered `yes`, both points are converted into one. Lines and surfaces joined to the point are also moved and deformed to maintain their links.

### Explode polyline

This command lets the user select lines. Lines that are not polylines or have higher entities or conditions are rejected. After confirmation, the polylines are exploded and converted into their original lines. Polylines then disappear (see section Polyline creation).

### Edit polyline

The command `Edit Polyline` allows the user select lines. 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 4-sided surface over a part of a polyline (see section 4-sided surface automatic creation).
- Only points: When meshing this polyline, the nodes will only be placed where the geometry points are.

`Note:` If one condition is assigned to one interior point of a polyline (see section Conditions), one node of the mesh will be placed over that point.

### Edit NURBS line

Once a NURBS line is selected (use the Pick button of the `Edit NURBS Line` window), it is possible to interactively edit its control points (see section NURBS line creation). Select the control points as if they were regular points and enter their new positions in the usual way (see section Point definition).

The `Influence factor` affects the movement propagation of the neighboring control points.

Options:

- Fix boundary Check olption `fix boundary`, if you don't want to move the boundary control points of the untrimmed surface.
- Insert knot: User is asked by a knot value between 0.0 and 1.0 and this is inserted. Program checks that knot multiplicity is not bigger than order (order=degree+1). As the number of knots increase, the number of control points also increase. So, this option can be used to have more points defining the same curve.
- Degree elevate: With this option degree of the curve is elevated by one. The new curve will have the same shape but with more control points and knots.
- Change Weight: A new positive weight can be introduced for any control point, except the end points.
- Cancel weights: All weights of the NURBS are converted to 1.0 and the curve is no more rational.
- Reparametrize: With the same control points a new curve is calculated to get a better curve with a more uniform parametrization.
- Simplify: This option converts the curve to a simplified curve, which is an approximation of the original one.

### Edit NURBS surface

Once one NURBS surface is selected (use the Pick button of the `Edit NURBS Surface` window), it is possible to interactively edit its control points (see section NURBS surface creation). Select the control points as if they were regular points and enter their new positions in the usual way (see section Point definition).

Options:

- Insert knot: User is asked by a knot value between 0.0 and 1.0 and it is inserted. Program checks that knot multiplicity is not bigger than order. This option can be used to have more points defining the same surface.
- Degree elevate: With this option degree of the surface is elevated by one. The new surface will have the same shape but with more control points and knots.
- Change Weight: A new positive weight can be introduced for any control point, except the extremes.
- Cancel weights: Converts the weights of all the control points to 1.0
- Simplify: Simplifies the surface (if possible) removing the less significant knots.
- Reparametrize: Reparametrizes the surface obtaining an optimized surface. When a Nurbs surface is not well parametrized, the mesh has a worse quality.

The Movement type menu of the `Edit NURBS Surface` window, determines the kind of movement of the selected knots. This movement can be along an axis (X-Axis, Y-Axis, Z-Axis), describing the Normal of the surface (Normal), following the screen movement of the mouse (Screen) or the new location of the knot can be defined introducing the coordinates of a point (Point).

`Note:` Options `Insert knot` and `Degree elevate` can be chosen for the `u` or the `v` parameters direction.

### Hole NURBS surface

This option let the user select one existing NURBS surface and a set of closed lines that are inside the surface and that form a hole inside it. The lines may be created with an intersection with another surface. The hole will be added to the existing surface.

### Divide

Command `Divide`, can be applied either to lines that are not polylines or to surfaces (trimmed surfaces included). After selecting the entity, the division can be given in several ways:

- Number of divisions: line will be converted in equally spaced pieces.
- Near point: With this option one point must be selected near the line. (See section Option point in line, or See section Option point in surface, can be used). The line will be divided into two entities near that point.
- Parameter: One factor is given between 0.0 and 1.0 and entity will be divided where the parametric variable takes that value.
- Relative length: 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 curve was arc length parameterized).
  If the line is a polyline, the user must choose an existing interior point. The polyline will be converted into two lines that may or not be polylines. Polyline division have an option `Angle` that permits to divide the polyline in all the points where the angle between the sublines before and after is bigger than the given one.
  Caution: An interior point must belong to level one of a polyline (see section Polyline creation).
- Surfaces
  - Num divisions: surface will be converted in equally spaced pieces.
  - Near point: With this option one point must be selected near the surface. The surface will be divided into two entities near that point.
  - Parameter: One factor is given between 0.0 and 1.0 and the surface will be divide into two where the parametric variable takes that value.
  - Split: surface will be divided following the divide lines. These lines must intersect the surface contour. (command: `Geometry Edit SplitSurf`)

  In the case of surfaces it is necessary to give the division sense that can be `u` or `v`. This sense can be previously checked with the command Edit NURBS Surface. (see section Edit NURBS surface)

Note: After the division, the entity disappears and new entities are created.

### Join lines end points

With command `Join lines end points`, two lines must be selected. GiD determines the distance between the two closest endpoints, 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 deformed. The new point will then take the place of the first line's point.

See section Move point, for another method of converting two points into one.

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

### Swap arcs

This command lets the user select and alter arcs. Lines that are not arcs are rejected. After confirmation, 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 supplementary to the angle of the old arc.

Caution: Arcs with higher entities cannot be swapped.

### Edit SurfMesh

User must select one or several surface meshes (see section Surface mesh). Options are:

- Draw mesh: Surface will be drawn as a mesh.
- No draw mesh: Surface will be drawn as a regular surface. With magenta lines close to the boundary lines.

### Convert to NURBS line

This option converts the selected lines or surfaces to NURBS lines or NURBS surfaces.
Note: Some algorithms only work with NURBS entities.

### Simplify NURBS

This option converts the selected NURBS lines or surfaces to other ones very similar to the originals but with and easier definition. It can be useful for imported data that is defined with a too complex control polygon and displays or is meshed too slow.

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