Abstract

Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computer-aided design, curves have been sought which maximize "smoothness". The curve discussed here is the one arising in this way from a commonly used measure of smoothness. The human visual system may use such a curve when it constructs a subjective contour.

Citations

818	A Practical Guide to Splines - Boor - 1978
70	Computational Geometry for Design and Manufacture - Faux, Pratt
63	Filling-in the gaps: the shape of subjective contours and a model for their generation - Ullman - 1976
62	Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review, Second Edition - Korn, Korn - 2003
45	Calculus and Analytic Geometry - THOMAS - 1968
39	Principle of Interactive Computer Graphics - Newman, Sproull - 1979
25	A Catalog of Special Plane Curves - Lawrence - 1972
17	Introduction to Elliptic Functions with applications - Bowman - 1953
12	Methods of Applied Mathematics - Hildebrand - 1965
7	Shape encoding and subjective contours - Bradly, Grimson, et al. - 1980
4	Advanced strength of materials - HARTOG - 1949
3	Curve and surface fitting based on variational criteriae for smoothness - Mehlum - 1969
2	Calculus of Variation - Forsyth - 1960
2	I.A.Stegun, Handbook ofMathematical Functions: with Formulas - Abramowitz - 1972
1	Interactive Computer Graphics: Data Structures, Algorithms, Languages - GILOI - 1978
1	Shape Encoding and Subjectiv e Contours - L, Langridge - 1980
1	Slrength of Materials, l)over - Hartog - 1949
1	Interactive Compuler Graphics: Data Structures, Algorithms - Giloi - 1978
1	Curve and Surface Fitting Based on Varialional Criteriae for Smoothness - Mehlum - 1969
1	lnlroduclion to Elliptic Functions with ,4pplications - Bowman - 1961
1	4 Catalog of Special Plane - Lawrence - 1972