NURBS Curves

Adjusting Curves

To adjust a curve we can use the EDIT CURVES pull-down menu. We already have seen how curves can be attached and aligned to create continuity of the attached curves. There are other options to adjust the curve which can be divided basically into four categories.

• Detaching parts of the curve.
• Extending a curve.
• Changing the geometry of the curve
• Smoothing the curve or the corners.

There are two methods of detaching a curve into several parts. One which is makes use of the component settings is the EDIT CURVES – DETACH CURVES option. Because the cutting point is defined by an Edit Point. The cutting edge can be places 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.

The other option is the Cut Curve tool. Curves overlapping each other will behave as knives and will cut the curves at the point of intersection.

After a curve is drawn the length of the curve can be adjusted by the EDIT CURVES – EXTEND CURVES option. The length of the curve will be extended with an amount which is defined in the Option Box.

Or an curve can be extended by adding point to the curve. This option is especially use full when 3d geometry is constructed with use of the curve. By using the history of the geometry, the adding of the point to the curve will take effect on the 3d geometry itself.

The geometry of the curve can be adjusted by adding extra vertices into the curve manually by inserting a knot (Insert Knot). 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.

Another option is the complete rebuild of the curve. Rebuild Curve. This will enable the change of the amount of vertices of the curve to the change of Degree of the curve.

The smoothing of curves and 3d geometry is a method to blend the different curvature of the geometry into a smoother object. With the align option it was possible to create a smooth transition between different curves. The option of smoothing of the curve is less well to tweak. The smoothing option works on the whole curve or the selected vertices of the curve. To use the smooth option select Smooth curve.

Another option of smoothing is the Curve Fillet option. This option will create a smooth fillet of corners of two different curves. If applied to a single curve the beginning and end of the curve will be blended together. The direction of the blended curve depends on the direction the extended curves would intersect.Adjusting the options in the Option Box will give added control of the fillet.

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.

NURBS geometry

Certain properties of NURBS geometry make the NURBS perfectly suitable for designing geometries like double curves surfaces. The form freedom which NURBS supports and the possibilities to adjust them give the designer a wide range of 3 dimensional forms to explore. The be able to make the right decision a designer will need a basic understanding of the topology of the geometry which will be used in the design process. NURBS geometry are widely used in computer aided design CAD, computer aided manufacturing CAM and computer aided engineering CAE software. It supports industry standards like IGES, STEP and ACIS. The ability to intuitively and predictable adjust the curves and surfaces make it an power full geometry suitable for design.The NURBS are a generalized derivative of the Bezier curve. ( Pierre Bezier worked as engineer for Renault , development started in the 1950’s to find a method to represent curved lines and surfaces for car design.)

There are similarities between the properties of the Bezier curve and the NURBS geometry. Parts of the geometries topology is comparable with the Bezier curve. The surface supports the same use of weighted vertices to define the curvature and shape of the geometry. The geometry it self can be seen as a combination of two sets of "parallel" curves placed at a crosswise angle, with the mesh defined between the curves. Resulting effect is that the surface can support two different Degrees, one in each direction. These curves on the surface are called ISOPARMS. The ISOPARM will behave almost the same as a Bezier curve. Selecting and moving a vertex on a surface will basically deform the ISOPARM causing the surface to deform. The more ISOPARMS on a surface the more vertices are generated to deform the surface OR the higher the degree of the curves the more vertices will be generated per ISOPARM and surface as a whole.

The NURBS surface contains several different components. We have already find out that the NURBS surface contains ISOPARMS.

The ISOPARMS are the sets of crosswise angled curves on the surface. They are in fact the curves where the surface is based on. Although they are a part of the surface, the Isoparms can be copied as a curve with the EDIT CURVES – Duplicate Surface Curve. The Isoparms are placed in two directions, the U and V direction. If two surfaces are attached or aligned, the connection can be twisted due to the wrong direction of the surfaces. By Reverse Surface Direction, the surface directions can be aligned, causing the twist to disappear and make a smooth connection.

The vertices shape the Isoparms connected to them. The degree of the surface defines how much vertices will be necessary to define the Isoprams. Vertices can be directly edited

This construction of surfaces has an important limitation. Unlike a Polygon a single NURBS surface can never define a closed object. NURBS surfaces always have a "rectangular" topology. This can be illustrated with the analogy of the two sets of curves which define the geometry. The organization of vertices and the parametrization of the geometry are basically crosswise organized to each other to create basically a surface with four edges. Forms like spheres and tubes are basically deformed rectangular surfaces. By welding (closing) the connection of one of the directions of the isoparms the surface can be closed in one direction creating a tube like structure. However the other direction can’s be welded or closed. The surface remains open.