Donald Shepard
ABSTRACT
In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface. These irregularly-spaced locations, hence referred to as “data points,” may have diverse meanings: in meterology, weather observation stations; in geography, surveyed locations; in city and regional planning, centers of data-collection zones; in biology, observation locations. It is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
In order to display these data in some type of contour map or perspective view, to compare them with data for the same region based on other data points, or to analyze them for extremes, gradients, or other purposes, it is extremely useful, if not essential, to define a continuous function fitting the given values exactly. Interpolated values over a fine grid may then be evaluated. In using such a function it is assumed that the original data are without error, or that compensation for error will be made after interpolation.
- 1.P SWITZER C M MOHR R E HEITMAN Statistical analyses of ocean terrain and contour plotting procedures Project Trident Report 1440464 Arthur D Little Inc April 1964Google Scholar
- 2.J F STEFFENSEN Interpolation Williams and Wilkins Baltimore 1927 Chap 19Google Scholar
- 3.I S BEREZIN N P ZHIDKOV Computing methods Addison-Wesley Publishing Company Inc Reading Mass 1965 Vol I Chap 2Google Scholar
- 4.C deBOOR Bicubic spline interpolation J Math and Phys 41 212-218 1962Google ScholarCross Ref
- 5.A DOWNING The automatic construction of contour plots with applications to numerical analysis research Defense Documentation Center Report AD 649811 January 1966Google Scholar
- 6.W R TOBLER An interpolation algorithm for geographical data University of Michigan undatedGoogle Scholar
- 7.W C KRUMBEIN Trend surface analysis of contour-type maps with irregular control point spacing J Geophys Re 64 823-834 1959Google ScholarCross Ref
- 8.B E BENGTSSON S NORDBECK Construction of isarithms and isarithmic maps by computers University of Lund Sweden BIT 4 87-105 1964Google Scholar
- 9.A H SCHMIDT SYMAP A user's manual Tri-County Regional Planning Commission Lansing Michigan May 1966Google Scholar
- 10.User's reference manual for synagraphic computer mapping 'SYMAP' version V Laboratory for Computer Graphics Harvard Univ June 1968Google Scholar
Recommendations
Interpolation of two-dimensional curves with Euler spirals
We propose an algorithm for the interpolation of two-dimensional curves using Euler spirals. The method uses a lower order reconstruction to approximate solution derivatives at each sample point. The computed tangents are then used to connect ...
G1 Surface Interpolation for Irregularly Located Data
GMP '02: Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)The purpose of this research is to construct a surface 1) passing through all unorganized data points, 2) with G1 -continuity and 3) with the minimum square-sum of theprincipal curvatures \kappa_1^2 + \kappa_2^2 over the surface. In order to construct ...
Two interpolation operators on irregularly distributed data in inner product spaces
Two interpolation operators in inner product spaces for irregularly distributed data are compared. The first is a well-known polynomial operator, which in a certain sense generalizes the classical Lagrange interpolation polynomial. The second can be ...
Comments