# Template:Nurbstheory

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 1960’s to find a method to represent curved lines and surfaces for car design).

Bend lines created in Maya and Rhino are called CURVES, that are based on Bezier Curves and are used as the basis for NURBS and Polygon modeling within Maya or only as basis for NURBS modelling in Rhino. The way the curves are defined makes is possible to draw straight lines 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.

The concept of deformation was digitally implemented in to the 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 position and strength of the 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.

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.