*To*: visad-list@xxxxxxxxxxxxx*Subject*: Re: Program to visualize layers*From*: "William L. Hibbard" <WHIBBARD@xxxxxxxxxxxxx>*Date*: Mon, 15 Mar 1999 05:10 CST

Hi Ugo, > . . . When one thinks of surfaces at some Z value, it doesn't > necessarily have to be a mapping like ((X, Y) -> Z). In fact, > strictly spreaking it isn't, because we eventualy have some, say, > surface attribute A that's is a mapping ((X, Y, Z) -> A). Well, if your data describe a topographical surface, such as the Earth's surface, then you have a unique Z value as a function of X and Y and the MathType is ((X, Y) -> Z) to reflect that function dependency. If you add a surface attribute A, the MathType becomes ((X, Y) -> (Z, A)) where both Z and A are functions of X and Y. > . . . That is, in our examples surface water run-off is a > function of space. That's why I tried doing it with a Linear3DSet. > And as I said, I left it with a 2D set because it worked. Another possibility is a surface where Z is not a unique function of X and Y. Such a surface can be defined with by a Set with domain dimension = 3 and manifold dimension = 2. This is supported for both GriddedSets and IrregularSets. You can use such Sets as the domain sets of Fields, in order to have dependent values on the surfaces. For example, the Field could have MathType ((X, Y, Z) -> A) and have a domain Set that defines a surface embedded in (X, Y, Z) space. However, if Z is a function of X and Y (which is the case for the Earth's surface except in the region of over-hanging cliffs) then you are much better off using the MathType ((X, Y) -> (Z, A)) because it expresses all the functional dependencies in the data. > We also have quite a few missing points, which break the > continuous surface when we set them to NaN. Unfortunately our > domain is far from being rectangular. We are basically dealing > with river catchments. If your domain at least has rectangular topology (and non-rectangular geometry) then you should use GriddedSets. If you have non-rectangular topology, then you should use IrregularSets. Perhaps this can eliminate or reduce the need for missing points (using a Linear3DSet and filling with missing values will generate lots of missing points and data that are difficult to depict). Please let me know if there is a reason why you cannot use the MathType ((X, Y) -> (Z, A)) [or ((X, Y) -> (Z, A1, A2, ...)) ] with a Gridded or Irregular domain set. By the way, I want to clarify my statement in response to Mohamad that 'In a sense, the Set is the iterator'. A Set describes a finite set of values in R^N (i.e., N-dimensional real space where N = domain dimension). The Set method: public float[][] indexToValue(int[] index) takes an array of indices into that set and returns the corresponding array of locations in R^N. It can be used as an iterator as follows: for (int i=0; i<set.getLength(); i++) { float[][] value = set.indexToValue(new int[] {i}); // value[0][0], value[1][0], value[2][0], ..., value[N-1][0] // describe the location of the i-th sample in R^N } Note that the index argument to indexToValue may contain only a single value, may contain each index from 0 to set.getLength()-1, or may contain the same value repeated (this commonly occurs during remapping operations, when multiple destination samples come from the same source sample). Cheers, Bill ---------------------------------------------------------- Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI 53706 whibbard@xxxxxxxxxxxxx 608-263-4427 fax: 608-263-6738 http://www.ssec.wisc.edu/~billh/vis.html

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