Let a family of curves or surfaces be given in parametric form via the model equation x =J‘(s, /I), where x E R”, p E KY’, and s E S c [wd. d < n. We present an algorithm for solving the problem: Find a shape cec’tor p* such that the manlfold M* = (f(s, /I*): s E S) is a best fir to scattered data :z, j ,‘= , c R” in the Sense that, jbr some is* )y=, , the sum of the squared least distances )-y...

Recent years have seen an increasing interest in algebraic curves and surfaces of high degree as geometric models or shape descriptors for model-based computer vision tasks such as object recognition and position estimation. Although their invariant-theoretic properties them a natural choice for these tasks, fitting algebraic curves and surfaces to data sets is difficult, and fitting algorithms...

A hyperbolic curve is an algebraic curve obtained by removing r points from a smooth, proper curve of genus g, where g and r are nonnegative integers such that 2g−2+r > 0. If X is a hyperbolic curve over the field of complex numbers C, then X gives rise in a natural way to a Riemann surface X . As one knows from complex analysis, the most fundamental fact concerning such a Riemann surface (due ...

The shoulder of a packaging machine is a developable surface that guides the packing material without stretching or tearing. The shoulder is traditionally manufactured by bending a flexible plate along a given bending curve, also without stretching ortearing. In this paper, the shoulder geometry isdescribed mathematically b methods from classical differential geometry. For a given bending curve...

Deformation of 3D shapes usually requires the use of a deformation tool. The freeform deformation technique requires the use of a lattice of control point for deforming an object. This may require a synchronized movement of the lattice control points in order to obtain the desired effects. The axial deformation technique allows an object to be deformed by manipulating an axial curve. However, u...

In Nitella the action curve has two peaks, apparently because both protoplasmic surfaces (inner and outer) are sensitive to K(+). Leaching in distilled water makes the outer surface insensitive to K(+). We may therefore expect the action curve to have only one peak. This expectation is realized. The action curve thus obtained resembles that of Chara which has an outer protoplasmic surface that ...