The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions

Miniature sonar fish tag

Self-powered sonar device may be implanted in body of fish. It transmits signal that can be detected with portable tracking gear or by automatic detection-and-tracking system. Operating life of over 4000 hours may be expected. Device itself may be used almost indefinitely

Evaluation of the advance/anticipatory care planning (ACP) facilitators training programme

This report presents an overview of the findings of the three phases of the study and assesses the degree to which the Facilitator Training Programme and Resource Pack have prepared the cohort of facilitators with the knowledge, skills and tools to deliver training initiatives in ACP to address local and regional needs