# AR1B030 1

**AR1AE015 WORKSHOP 1: Curved based design**

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### Theory NURBS Curves and Geometry

## Creating Curves

**To create a curve we use the command Create:**

- Create - CV Curve Tool
- Create - EP Curve Tool For accurate drawing we will use the EP curve, for it will let you define the points the line has to go through.
- Select the option box. Define the degree.
- Click in the correct viewport to draw the curve. The curve will be placed on the grid of the viewport.

**Accuracy:**

- Optional - accuracy - Activate the grid snap option to snap to grid points.
- Optional - accuracy - Activate the curve snap option to snap to a curve( activate snap, press mouse button and hold whilst dragging along the curve).
- Optional - accuracy - Activate the point snap option to snap to a corner of a curve( first activate the display of the corner points - Display - Nurbs - Edit Points , activate snap, press mouse button and click on corner of curve).
- Optional - accuracy - Type in the coordinate or distance of next point of the curve. ( activate the curve command and define the first point, type in the absolute or relative coordinate of the next point )

** To create an Arc we use the command Create:**

- Create - | create arcs There are two options. The options define how you can create the curve.

### Editing curves

#### component mode

Further alteration of a created curve is possible on component level. By selecting the component filter, Edit Points and Control Vertices of the line itself can be moved by using the move tool.

For more information about selecting on component level, and the different type of NURBS components see selection masks.

The commands we use to edit curves in different ways then through moving the components are found in the surfaces menuset, under the edit curves menu.

#### open/close curves

When creating lines, sometimes lines don't form a closed curve. This could be a problem when wanting to create a loft or make a planar surface. Under Curves > open/close curves you find the option to close any gap in the curve.

#### attach curves

To connect different lines with similar or different degrees, the EDIT CURVES ( adjust curve) - attach curves command can be used. This will connect or blend the end of one curve to the beginning of the other curve. The Option Box contains the setting how to connect the line, if it should blend them together or connect them retaining their original shape. The begin and end of a curve is defined by the drawing order. If a connected curve loops around and connects to de wrong end of the line, the end point of that line is not correct due to the drawing order. If the EDIT CURVES - reverse curve direction command is used the direction of the line will be altered which means that the end point becomes start point and vise versa. The curve will now attach correctly.

The difference between blend and connect is that the blend option will make a smooth transition between both curve ends, whilst the connect option just makes a straight connection.

More advanced options and problem solving of the attach curves command

#### align curves

There is another way to connect two lines together. This is the align curves option. This option will give you more control on how the curves are attached. The way a curve is attached is defined by the continuity of the curvature of the connecting points of both of the lines.

- If there has to be no change in curvature of the connecting points the option connect can be used , also called a C0 connection.The position option causes the two points to meet exactly.
- Tangent causes the tangency at the two points to match, which is called C1.
- Curvature causes the two points to meet with the same arch in curvature. When this option is selected, the curvature scale sliders are available. These can be interactively adjusted in the Attribute Editor and the Channel Box.

Using options for generating continuity of the geometry is crucial if the geometry has to have a fluid continuity of form. Geometry based on curves will be affected by the continuity of the curves themselves. With the option of interactively altering the connection settings the geometry can be adjusted to alter the geometries continuity.

#### detach curves

The option to detach curves is based on edit points, which become the cutting points. The cutting point can be placed anywhere along the curve. First go to component mode and select the Edit Point option. Select the location of the cut and then give the Detach command.

In the optionbox of the detach curves command you can choose whether you want to keep the originals or not.

#### cut curve

Another option to cut a curve at a certain point is the Cut curve tool. Curves overlapping each other will behave as knives and will cut the curves at the point of intersection.

More advanced options can be found in the optionbox.

#### offset curves

When wanting to create a copy of a curve, where every side has the same distance from the original, the regular scale option does not work satisfactory. Thus we use the offset curve command.

#### extend

After a curve is drawn, it can be extended by using the extend curve command.

#### add points

The extend curves option mentioned above only lets you add one point with a certain distance, the add points tool will let you click your own points that make the extension of the curve.

#### insert knot

The geometry of the curve can be adjusted by adding extra vertices into the curve manually by inserting a knot by using the insert knot command. This will make it possible to locally adjust the vertex density of a curve. Which may be use full for local deformation of the curve.

#### rebuild curve

Another option to change the number and placement of the certices is the complete rebuild of the curve by using the rebuild curve option. This will enable the change of the amount of vertices of the curve to the change of Degree of the curve.

#### smooth curve

The smooth curve option is another way to adjust the curvature of your curve. The smoothing option works on the whole curve or the selected vertices of the curve.

#### curve fillet

Another option of smoothing is the curve fillet option. This option will create a smooth fillet of corners of two different curves.

**Curved based geometry**

There are several methods to create geometry in a digital environment. The method depends on the geometry type, complexity of geometry, the possibilities to adjust the geometry and the use of the geometry within the design process. It is important to haven an idea what and how to model the geometry before you start. Devise a model strategy to accommodate the flexibility of uses of the 3D model in the design process. Most important decision before beginning is the choice of the geometry type. Each type has its own properties and therefore possibilities of constructing and adjusting the geometry. The properties of the geometry are also of importance when the geometry has to be converted to transport the geometry to third party software.

In Maya we can use three types of geometry.

- Polygons
- NURBS
- Subdivision Surfaces

In this workshop we will use NURBS geometry.

### Creating NURBS geometry

**When we create a NURBS surface we can use two methods**.

- Generating geometry by using Primitives
- Construct geometry based on curves - curved based modeling

NURBS primitives can be selected by the:

- Create- NURBS Primitives command. The settings of the geometry can be adjusted in the option box or after creation in the channel box.

**The second method of generating 3D geometry supports the generation of very complex forms. It uses the curves as a basis for the generation of 3D. Curve based modeling is based on the principle of adding a third dimension to a curve or set of curves. There are basically only 4 options of generating 3D geometry. With these 4 options you can create almost any shape.**

**1** The first option is a simple extrude of the curve.

**SURFACE**–**EXTRUDE**:The extrude option is used for both options to create NURBS geometry. One setting in the tool is used to extrude a single curve in a certain direction, a DISTANCE, creating a surface. This option of extrude in direction uses only one curve.

The revolve option is similar to the extrude option, the difference is that the extrusion is not in one direction but in a circle

**SURFACE**–**REVOLVE**: With the revolve option a curve is created , defining one direction, and this curve is revolved around an axis. Settings of the option will influence the amount of rotation, the location of the axis, selection of the axis geometry output and degree of the rotated direction.

**2** The second option is a more complex form of the first and it gives an additional parameter which can be adjusted to generate more complex geometry.

**SURFACE**–**EXTRUDE**. : Extrusion along a path has the advantage that the direction of the extrusion precisely can , with some limits, be controlled. There is however a disadvantage of generating a surface like this. The profile ( section ) of the surface generated isn’t constant if the curve along which it is extruded curves to much. To generate this geometry select all the settings on the right of the option box of the command. The section will be centered with its pivot point at the beginning of the curve.

**SURFACE**–**BI RAIL**: The bi rail option divides the construction of the surface in two parts. The profile ( section ) and the rails. The profile is extruded along the rails en scaled to maintain contact with the rails. Birail1 uses 1 profile birail2 uses 2 and so on. The profiles have to connect at the edges to the rails otherwise the birail won’t work. Because it is possible to adjust the continuity of the surface of the birail to a curvature of a connecting surface of the profile, the option is effective in creating smooth transitions.

**3** The third option gives a large amount of freedom in generating complex geometry.

**SURFACE**–**LOFT**:With the loft option one direction is defined by a minimum of two curves. The geometry is created between the curves. The second direction is only influenced by the adjustable degree of the surface direction. This limitation is often compensated by adding more curves into the loft to get more control over the surface.

**4** The last option is the creating of a surface between a closed set of curves.

**SURFACE**–**PLANAR**Surfaces > planar creates a planar (flat) surface enclosed by one or more curves, isoparms or trim edges. Two conditions have to be met in order to create a planar surface successfully:

- the lines need to connect or intersect (no gaps between them)
- the lines need to be planar (flat).

more information and problem solving on the planar command

**SURFACE**–**BOUNDARY**. The boundary option will create a surface between an minimum of 3 curves connected to or intersecting each other.. Here the “rectangular” properties of the NURBS surface are clear to see with the isoparms squeezed at one point to accommodate the triangular shape of the geometry.

**SURFACE**–**SQUARE**The square option looks a lot like the boundary option however it is limited to four intersecting or connecting curves. The continuity of the square can be influenced by connecting surfaces. This will result in a smooth transition between the surface and the square.

Another option is the Curve Range setting. This option will make it possible to alter the length of the curves used for generating the geometry after the geometry is made and alter thereby the geometry itself. One can alter the length of the curve in the Channel box by selecting the SubCurve and alter the min and max settings of the curve or by using the Show Modifier tool in the toolbox. Moving the gizmo’s will alter the length of the curve.

**SURFACE**–**BEVEL**. The bevel option is a fast way of rounding of open edges. The settings are limited, however it can be an effective method to create more detail in an object.