Path: utzoo!utgpu!watserv1!watmath!att!bellcore!rutgers!apple!vsi1!zorch!xanthian From: xanthian@zorch.SF-Bay.ORG (Kent Paul Dolan) Newsgroups: comp.graphics Subject: Re: Scattered Data -> Regular Grid Data Keywords: Scattered , Data , Regular Message-ID: <1990Jun16.004234.17224@zorch.SF-Bay.ORG> Date: 16 Jun 90 00:42:34 GMT References: <1990Jun15.122858.1197@jarvis.csri.toronto.edu> Organization: SF Bay Public-Access Unix Lines: 29 In article <1990Jun15.122858.1197@jarvis.csri.toronto.edu> corkum@csri.toronto.edu (Brent Thomas Corkum) writes: >I'm looking for some references or comments concerning the conversion >of scattered data in two dimensions to data on a regular grid. I would >alos like to be able to handle holes in the data, meaning areas in which >no interpolation or extrapolation will occur or cross. But this last >requirement is not mandatory. > > >Brent >corkum@csri.toronto.edu This problem is regularly encountered in the digital cartography field, where it is a preprocessing step to several contouring packages. Make sure that it is the only way to solve your problem before you select this approach, however, as it is fraught with special cases, numerical instabilities, and numerical artifacts. A superior method for many uses is to triangulate the data points with a method that replaces the edge between two skinny triangles with a common long border with the edge connecting the two uninvolved points of the two triangles (where this edge is internal to the quadrilateral formed by the two triangles) to make them more nearly equilateral, until no further such cases exist, and then either doing linear interpolation from the corner values to get interior values for whatever your problem needs, or doing a higher order interpolation using points from surrounding triangles to get second order continuity at the edges. Kent, the man from xanth.