“Two aspects of domain designing: C@@@@ curve rendering and blended map projections” by Rockwood and Jensen
Conference:
Type:
Title:
- Two aspects of domain designing: C@@@@ curve rendering and blended map projections
Presenter(s)/Author(s):
Abstract:
In 1965, Shepard introduced a general interpolation formula for arbitrarily spaced data over any finite dimensional Euclidean space. The deficiencies in his initial results have been corrected and later derivations have been widely applied to surface fitting problems in aviation design and geology. This paper describes a new research direction in Shepard’s method and a new application to computer graphics. In the first, the convex weighting functions are generalized by the creation of a user-defined mathematical domain which is independent of the surface. In the second, the original formula is applied to blend mapping projections for aviation visual simulation and an algorithm for rapid evaluation is presented.
References:
1. R. K. Adler and P. Richardus, Map Projections, North-Holland Publishing, 1972.
2. R. E. Barnhill (1977), Representation and Approximation of Surfaces, Mathematical Software III, edited by J.R. Rice, 69-118, Academic Press, Inc., New York.
3. C. Caratheodory (1911), Über den Variabilitatsbereich det Fourierschen Konstanten von Positiven harmonischen Furktionen. Ren, Circ. Mat. Palermo, No. 32, 193-217.
4. N. Draper and H. Smith (1966), Applied Regression Analysis, John Wiley and Sons, New York.
5. G.M. Neilson (1974), Some Piecewise Polynomial Alternatives to Splines under Tension. Computer Aided Geometric Design edited by R. Barnhill and R. Riesenfeld, 209-235, Academic Pass, Inc., New York.
6. D.T. Pilcher (1974), Smooth Parametric Surfaces, Ibid, 237-253.
7. D. Shepard (1965), A Two Dimensional Interpolation Function for Irregularly Spaced Data, Proc. 23rd Nat. Conf. ACM, 517-523.
