To bridge the gap between form and function, this 3D modeling tool utilizes a cylindrical lattice to alter the surface contours of a surfboard. The application of a cylindrical lattice extends on free-form deformation (FFD), through which a design object is encased inside a lattice structure that can be deformed to alter the design object. FFD is an efficient and intuitive method of three-dimensional shape design and modification and many types of deformations are possible. However, the parallelepiped (box-shaped) structure of the lattice does limit the range of deformation that is possible. This limitation is resolved with extended free-form deformation (EFFD), which introduces a non-parallelepiped lattice structure, such as a cylindrical lattice.

The lattice structure serves as a geometric constraint. So the arc of the cylinder's annular axis applies varying degrees of curvature to the design model, depending on the position of the design model relative to the cylinder's central axis. The cylindrical lattice structure is shown in figure 1.

The cylinder's central axis is a key feature of the deformation tool, since its position relative to the surfboard affects the amount of curvature transferred to the surfboard. This can be visualized by focusing on the alignment of the surfboard's fins, as depicted in figure 2. Whereas the middle fin is typically aligned within the central plane of the surfboard (corresponding to the surfboard's stringer), the outer fins tilt away from this central plane and, where they are joined to the surfboard, point inward toward a point not far beyond the nose of the surfboard.

By visualizing the alignment of the outer fins in terms of the planes that they occupy, the efficacy of a cylindrical lattice becomes apparent. The intersection of these two planes corresponds to the central axis of the cylinder, which is a line extending from a point beyond the nose of the surfboard to a point located well above the deck of the surfboard; both points sitting within the central plane of the surfboard. Altering the position of the cylinder's central axis, relative to the surfboard, adjusts the angle of the side fins, which in turn adjusts the angle of penetration required before the side-fins meet resistance. So, the further the cylinder's central axis from the surfboard, the smaller the angle of tilt in the side fins and the smaller the angle of penetration required before the side fins meet resistance. Conversely, the nearer it is to the surfboard, the greater the angle of tilt in the side fins and thus the larger the angle of penetration required before the side fin meets resistance.

The same principle applies to the shape of the surfboard itself. By moving the cylinder's central axis toward the deck of the surfboard, the cross-section of the bottom surface becomes increasingly convex, as depicted in figure 3. This has the effect of decreasing the response of the surfboard during penetration, since it increases the angle of penetration required before resistance is met. Conversely, by moving the cylinder's central axis toward the underside of the surfboard, the cross-section of the bottom surface becomes increasingly concaved, as depicted in figure 4. This has the effect of increasing the response of the surfboard during penetration, since it decreases the angle of penetration required before resistance is met.

By changing the position of the cylindrical lattice relative to the surfboard model, the proposed modeling tool alters the shape of the surfboard to make it either more responsive or less responsive (i.e. more forgiving). However, the user needn't understand the nature of the tool. Instead, he would simply choose between more responsive and less responsive. So, as his surfing ability improved, he might decide to get a more responsive version of a board he is already familiar with. The beauty of the proposed geometric modeling tool is that it ensures finished designs are acceptable to the owner/manufacturer of the models, from which they have been derived. So, customers would be able to interactively adjust the design of their new surfboard, without the risk of producing a bad design.

Copyright © 2005 by Dan Webber.

## See also Edit

## References Edit

- Coquillart, S. (1993), "Extended Free-Form Deformation: A Sculpturing Tool for 3D Geometric Modeling", Computer Graphics, 24(4), 187-196.

- Francis L, Sabine C and Pierre J., "Interactive Axial Deformations", Rapport de recherche Nr. 1891.