Template:Nurbstheory CAD1
Certain properties of NURBS geometry make the NURBS perfectly suitable for designing complex 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. To 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).
The use of NURBS in architecture. Smooth double curved surfaces.
There are similarities between the properties of the Bezier curve and the NURBS geometry.
NURBS Curves
Lines Created in Maya are called CURVES, that are based on Bezier Curves and are used as the basis for NURBS and Polygon modeling within Maya. The way the lines are defined make is possible to draw rectangular and smooth curves. The concept of the structure of the lines where inspired on techniques used in the shipbuilding industry at the beginning of the 19th century. The wooden planks of the ships hull where bend by adding weights at different points on the plank. The amount of bend of shape of the bend could be adjusted by increasing the weight or the position of the weights.
Curves themselves are often used as a basis for geometry.
The concept of deformation was digitally implemented in to the Bezier curves definition. With the effect that the curve in not only defined by the start and end point of the line but also by the weights between the two. These weights will determine the amount of bending of the curve. The amount of weights between the start and end point are defined by the Degree . Degree 1 will mean that there are only the start and the end point. This will generate a straight line. Degree 3 will contain next to the start and end points two weights to define the curve. By increasing the degree more weights are added and the possibility to deform the line will increase.
To create a curve we use the command Create - CV Curve Tool or the command Create - EP Curve Tool
The degree can be adjusted by clicking on the rectangular box next to the command. An option box will open where adjustments can be made regarding the activated command. When a CV (control vertex) curve is selected the mouse clicks will define the location of the weight point or Control Vertices. However this isn’t the same location, except for the starting and end point, as the curve itself. There is less direct control over the curvature of the line when a CV curve is drawn. If there has to be more direct control of the curvature of the line an EP ( Edit Point) curve can be used. The Edit Points which are defined by the mouse clicks will intersect with the curve itself. This will make drawing the curvature of the line more intuitive.
For accurate drawing we will use the EP curve, for it will let you decide the points the line has to go through.
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 itself 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 found 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, but are part of the surface itself.
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 parameterization 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.
