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Abstract: Morphing is an interpolation technique that changes one form into another through a seamless transition, producing, in the process, an infinite number of ‘intermediate’ forms between the original and the target. This paper examines the possibility of using the morphing technique for generating a large number of hull forms rapidly based on a number of target forms, existing or newly generated. The paper discusses the technique developed for applying morphing technique to hull form definition. The algorithm first projects the vertices of the original and target 3D surfaces onto 2D planes. After ‘regularising’ the vertices on 2D, they are projected back on the 3D surfaces. The corresponding vertices of the two surfaces are then used for interpolation. It has been found that the interpolated hull forms can be generated almost instantaneously, allowing the whole algorithm to be embedded in an optimisation program. [Copyright &y& Elsevier]

This paper presents an approach to the interpolation of angular feedrate for bi-parameter curve paths in multi-axis machining. A bi-parameter curve is the intersection of a parametric surface and an implicit surface. A tool path is identified by a position curve and an orientation curve, both of which are generated based on the bi-parameter curve. The angular feedrate interpolator calculates the tool position and orientation at each sampling cycle according to the specified angular feedrates and the given tool path. The paper analytically relates the angular arc-length derivatives to the time derivatives of the parameters along the path making use of both angular feedrates and angular feed acceleration. The results are then used to interpolate the parameters of the bi-parameter curve leading to an accurate calculation of the position and orientation of the cutting tool. A general parametric surface has been used to verify the effectiveness of the algorithm. The bi-parameter curves of the surface have been computed for arbitrarily selected intersecting cylinders. [Copyright &y& Elsevier]

In this paper, we present a new approach of-spline curve fitting to a set of ordered points, which is motivated by an insight that properly selected points called dominant points can play an important role in producing better curve approximation. The proposed approach takes four main steps: parameterization, dominant point selection, knot placement, and least-squares minimization. The approach is substantially different from the conventional approaches in knot placement and dominant point selection. In the knot placement, the knots are determined by averaging the parameter values of the dominant points, which basically transforms-spline curve fitting into the problem of dominant point selection. We describe the properties of the knot placement including the property of local modification useful for adaptive curve refinement. We also present an algorithm for dominant point selection based on the adaptive refinement paradigm. The approach adaptively refines a-spline curve by selecting fewer dominant points at flat regions but more at complex regions. For the same number of control points, the proposed approach can generate a-spline curve with less deviation than the conventional approaches. When adopted in error-bounded curve approximation, it can generate a-spline curve with far fewer control points while satisfying the desired shape fidelity. Some experimental results demonstrate its usefulness and quality. [Copyright &y& Elsevier]