Hi Gregoire, A TIN offers a number of advantages over grid data; first a TIN minimizes data storage requirements by allowing the density of triangles to vary over the surface to reflect its variability. The data structure also allows surface derivatives such as slope and aspect, or surface normal information to be calculated and stored for each triangle, edge or node, thereby improving performance of subsequent surface analysis. However, it requires that your samples are located appropriately — peaks and troughs are sampled at an appropriate interval, and triangle edges are forced to follow breaklines within the surface.
With respect to interpolation of the surface, it largely depends on what sort of surface you are willing to accept. Both grids and TINs can easily provide continuous surfaces, but the algorithm used to estimate a surface value away from a sampled point will determine if the surface is smooth or not. Most linear interpolation techniques, that I am aware of, result in discontinuities across triangle or grid edges. To maintain a smooth surface more complex algorithms such as the Qunitic patch, or the Clough-Tocher triangle patch, are required for TINS. For a grid surface the bi-cubic Bézier will produce a smooth surface. The point I’m trying to get at is that a TIN, or a Grid, is really a data storage mechanism for a surface within a computer — each have their advantages. It is the model that you overlay on top of the data that will allow you to estimate your surface in a manner that is appropriate to your application, and it is the model that will determine if it is possible to estimate uncertainty, or what ever else you require. Most exact interpolators have zero degrees of freedom (dof); hence, estimates of uncertainty are not possible. If uncertainty of estimation is what you are interested in, then Kriging will provide you with a solution. If you are not really concerned with smoothness, a simple linear interpolator will likely sufice, but to determine uncertainty of your estimates you will need to increase your dof, which will likely result in the interpolator nolonger being exact. Regards Andrew Hunter ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~ Andrew Hunter PhD Candidate Mobile Multi-Sensor Research Group Department of Geomatics Engineering, The University of Calgary 2500 University Dr. N.W. Calgary, Alberta, Canada T2N 1N4 Tel: (403) 220 8785, Fax: (403) 284 1980 E-mail: [EMAIL PROTECTED] -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Sent: Wednesday, January 19, 2005 1:55 AM To: Gregoire Dubois Cc: ai-geostats@unil.ch Subject: Re: [ai-geostats] TIN, monitoring netwoks and density Maybe, in order to have a quick and "safe" interpolation, the natural neighbor method of Dave Watson could perfom better than TIN. Sebastiano Trevisani Quoting Gregoire Dubois <[EMAIL PROTECTED]>: > Dear list, > > I would appreciate feedback on an issue that is closely related to > SIC2004 > > Let us consider a variable (air pollutants, radioactivity) that is > measured at regular time intervals by an automatic monitoring network > that is structured like a regular grid. In the case one needs maps to > be generated on a regular basis, I was wondering what arguments would > be against the use of Triangulated Irregular Networks (or any simple > linear interpolation algorithm)? As a matter of fact, if TIN cannot > be used to assess uncertainties, it can be easily automated and it is > an exact interpolator (no risk to smooth out critical values). I thus > understand TIN is the most reasonable approach in the case one has a > network that is dense enough. Obviously, the "dense enough" obviously > needs to be defined properly as I expect it to be the main parameter > that will define the need for more advanced interpolation techniques. > But with the exception of density, are there any non obvious issues I > am missing here? > > Thank you in advance for any feedback. > > Best regards, > > Gregoire > > ------------------------------------------------- This mail sent through IMP: webmail.unipd.it
BEGIN:VCARD VERSION:2.1 N:Hunter;Andrew FN:Andrew Hunter ([EMAIL PROTECTED]) ORG:University of Calgary;Geomatics Engineering TITLE:PhD Student TEL;WORK;VOICE:(403) 220-8785 TEL;HOME;VOICE:(403) 251-9230 TEL;WORK;FAX:(403) 284-1980 TEL;HOME;FAX:(403) 251-9236 ADR;WORK;ENCODING=QUOTED-PRINTABLE:;F 124;c/- University of Calgary=0D=0ADepartment of Geomatics Engineering= =0D=0A2500 University Drive N.W.;;;T2N 1N4 LABEL;WORK;ENCODING=QUOTED-PRINTABLE:F 124=0D=0Ac/- University of Calgary=0D=0ADepartment of Geomatics Engineerin= g=0D=0A2500 University Drive N.W.=0D=0AT2N 1N4 ADR;HOME:;;616 Woodbine Boulevard S.W.;Calgary;Alberta;T2W 4Z9;Canada LABEL;HOME;ENCODING=QUOTED-PRINTABLE:616 Woodbine Boulevard S.W.=0D=0ACalgary, Alberta T2W 4Z9=0D=0ACanada URL;WORK:http://www.ucalgary.ca/~ahunter EMAIL;PREF;INTERNET:[EMAIL PROTECTED] REV:20040107T175029Z END:VCARD
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