The design of a roller coaster begins with its geometry. A suitable layout must be designed that will appeal visually to the riders, as well as fitting into the space the amusement park has available for it. Once the initial layout has been planned, a dynamic analysis can be performed to determine if it will produce an acceptable ride. If not, the geometry will need to be modified accordingly.
In order to geometrically design a track, a set of elements has been created. These elements include straight sections, curves, loops, corkscrews, and joints, which are used to connect the other elements. The element types were chosen such that the way one designs a coaster will be similar to the way one thinks about riding a coaster. Reading publications from the American Coaster Enthusiasts (ACE), it is clear that they commonly view coasters as being composed of several elements, many of which are included in this element set. The designer can first think about a track consisting of a lift hill (straight element), a drop (straight element), a loop, and a corkscrew, much as a passenger would describe the ride. The details of the elements are then specified by the designer, resulting in the unique characteristics of each roller coaster.
Tenaglia[12] presents an alternate method of defining elements. The element set he presents is analytically complete, including eight elements which allow the designer to create any angular rotations desired. Each element type produces an angular rotation about a different axis or combination of axes.1.6 While this method does provide analytical completeness, it was felt that his elements were less intuitive than those presented in this research, requiring the designer to think more about angular rotations than simply which element type to specify. The intention here was to allow a designer to think about roller coasters more as a passenger would, than as an engineer would, at least in the initial specification of which element types to use.
Another difference between Tenaglia's elements and those presented here is the method of specifying banking. In his research, banking is a geometrically defined parameter, while it is determined dynamically in this research. Ideally, a combination of the two would be better, allowing the designer to determine when to specify the banking geometrically and when to calculate it dynamically. Yet another difference is the curvature variation throughout the elements. In his research, the curvature remains constant through each element, but discontinuities occur when they are connected. In this research, the curvature varies continuously through each element, and this continuity continues through the junction between elements as well.
The design methodology used in this research can be summarized as follows.
axis to line up the 
axis with the azimuth angle at the end of the previous track element.