N-side Filling

■Muraki, Y., Konno, K., Tokuyama, Y., Curve Mesh Modeling Method of Trimmed Surfaces for Direct Modeling,   The Journal of the Society for Art and Science, Vol.10, No.1, pp. 12-27,(2010).

In the shape modeling with 3D CAD systems, the trimmed surface is quite popular. For instance, Japanese Industrial Standards (JIS) models contain a lot of notches, expressed using trimmed surfaces. Since trimmed surfaces are directly modified in direct modeling, it has a big restriction in the shape modification. It is effective to apply a new free-form surface to a closed region composed of the modified edges because the consistency of a trimmed surface can be maintained. This paper proposes the method of fitting a free-form surface by using the offset curve. To be more concrete, an offset curve is generated according to the tangent planes and a point cloud is generated. After that, a B-spline surface is generated using the generated point clouds and the boundary curves, so that a new trimmed surface is generated. Our method is effective for direct modeling that directly modifies the boundary edges of the trimmed surface representing a notch shape.

■Tokuyama, Y., Konno, K., Filling n-sided region with a B-spline surface, IPSJ Journal, Vol.43, No.10, pp. 3209-3218,(2002).

To fill an n-sided region with surfaces by keeping some level of continuity with surrounding surfaces, the conventional methods use n four-sided patches joining with some level of continuity. However, if the lengthes of boundary curves are quitely unbalanced, the generated inner curves may undulate or intersect, and so may the generated surfaces. To solve this problem, this paper presents an approach to fill an n-sided region with a bi-cubic B-spline surface. The boundary curves of the n-sided region trim the generated B-spline surface and lie on the surface within user-specified tolerance.