INTERPOLATE Convenience function providing a simple interphase to the
different interpolation methods in the Heightmap Interpolation Toolbox
Input:
- x, y, z: the known function values of the bivariate function f(x,y)=z
- xi, yi: locations to interpolate
- method: the method to use. Available:
- 'Nearest': Nearest Neighbor.
- 'Delaunay': Delaunay triangulation (linear interpolation).
- 'Natural': Natural neighbors.
- 'IDW': Inverse Distance Weighted.
- 'Kriging': Kriging interpolation.
- 'MLS': Moving Least Squares.
- 'RBF.<rbf_type>': Radial Basis Functions.
- 'QTPURBF.<rbf_type>': QuadTree Partition of Unity BRF.
For the last two cases, you need to indicate in <rbf_type>
the type of the Radial Basis Function to use. Available:
- 'linear'
- 'cubic'
- 'quintic'
- 'multiquadric'
- 'thinplate'
- 'green'
- 'tensionspline'
- 'regularizedspline'
- 'gaussian'
- 'wendland'
For more information on each RBF, please check their
individual documentation in their corresponding functions on
the "rbf" folder of this toolbox.
- options: Options data structure. Each algorithm has its own set of
options that may be tunned according to the data. In case this
structure is not provided, a set of default values will be
generated using the hmitDefaultOptions function. The values
returned by this function may not fit your data at all. We
encourage the user to read the documentation of the individual
methods in order to set the options properly. The parameters
structure should follow that returned by the hmitDefaultOptions
function, so a good way of setting parameters is to generate this
structure using the hmitDefaultOptions function, and then change
some of them as required. Note: 'Nearest', 'Delaunay' and 'Natural'
methods do not require any parameters, so you can skip this parameter.
Output:
- zi: the interpolated z values0001 function zi = interpolate(x, y, z, xi, yi, method, options) 0002 %INTERPOLATE Convenience function providing a simple interphase to the 0003 %different interpolation methods in the Heightmap Interpolation Toolbox 0004 % 0005 % Input: 0006 % - x, y, z: the known function values of the bivariate function f(x,y)=z 0007 % - xi, yi: locations to interpolate 0008 % - method: the method to use. Available: 0009 % - 'Nearest': Nearest Neighbor. 0010 % - 'Delaunay': Delaunay triangulation (linear interpolation). 0011 % - 'Natural': Natural neighbors. 0012 % - 'IDW': Inverse Distance Weighted. 0013 % - 'Kriging': Kriging interpolation. 0014 % - 'MLS': Moving Least Squares. 0015 % - 'RBF.<rbf_type>': Radial Basis Functions. 0016 % - 'QTPURBF.<rbf_type>': QuadTree Partition of Unity BRF. 0017 % For the last two cases, you need to indicate in <rbf_type> 0018 % the type of the Radial Basis Function to use. Available: 0019 % - 'linear' 0020 % - 'cubic' 0021 % - 'quintic' 0022 % - 'multiquadric' 0023 % - 'thinplate' 0024 % - 'green' 0025 % - 'tensionspline' 0026 % - 'regularizedspline' 0027 % - 'gaussian' 0028 % - 'wendland' 0029 % For more information on each RBF, please check their 0030 % individual documentation in their corresponding functions on 0031 % the "rbf" folder of this toolbox. 0032 % - options: Options data structure. Each algorithm has its own set of 0033 % options that may be tunned according to the data. In case this 0034 % structure is not provided, a set of default values will be 0035 % generated using the hmitDefaultOptions function. The values 0036 % returned by this function may not fit your data at all. We 0037 % encourage the user to read the documentation of the individual 0038 % methods in order to set the options properly. The parameters 0039 % structure should follow that returned by the hmitDefaultOptions 0040 % function, so a good way of setting parameters is to generate this 0041 % structure using the hmitDefaultOptions function, and then change 0042 % some of them as required. Note: 'Nearest', 'Delaunay' and 'Natural' 0043 % methods do not require any parameters, so you can skip this parameter. 0044 % 0045 % Output: 0046 % - zi: the interpolated z values 0047 % 0048 0049 % Parameters' check 0050 if nargin < 7 && ~strcmpi(method, 'Nearest') && ~strcmpi(method, 'Delaunay') && ~strcmpi(method, 'Natural') 0051 options = hmitDefaultOptions(x, y, z, xi, yi); 0052 end 0053 0054 C = strsplit(method, '.'); 0055 method = C{1}; 0056 if numel(C) > 1 0057 rbfType = lower(C{2}); 0058 end 0059 0060 switch lower(method) 0061 case 'nearest' 0062 nearNeighInterp = NearestNeighborInterpolant(x, y, z); 0063 zi = nearNeighInterp.interpolate(xi, yi); 0064 case 'delaunay' 0065 dtInterp = DelaunayTINInterpolant(x, y, z); 0066 zi = dtInterp.interpolate(xi, yi); 0067 case 'natural' 0068 naturNeighInterp = NaturalNeighborsInterpolant(x, y, z); 0069 zi = naturNeighInterp.interpolate(xi, yi); 0070 case 'idw' 0071 idwInterp = IDWInterpolant(x, y, z, 'DistanceType', options.DistanceType, ... 0072 'SearchType', options.IDW.SearchType, ... 0073 'k', options.IDW.K, ... 0074 'Radius', options.IDW.Radius, ... 0075 'Power', options.IDW.Power); 0076 zi = idwInterp.interpolate(xi, yi); 0077 case 'kriging' 0078 % Create the experimental variogram from the samples 0079 vg = Variogram(x, y, z, 'model', options.Kriging.Variogram.Type, ... 0080 'DistanceType', options.DistanceType, ... 0081 'NumBins', options.Kriging.Variogram.NumSamples, ... 0082 'OptimNugget', options.Kriging.Variogram.OptimNugget); 0083 0084 % Use it in the Kriging 0085 krigInterp = KrigingInterpolant(x, y, z, vg, 'DistanceType', options.DistanceType, ... 0086 'PolynomialDegree', options.Kriging.PolynomialDegree, ... 0087 'Smooth', options.Kriging.Smooth, ... 0088 'Regularization', options.Kriging.Regularization); 0089 zi = krigInterp.interpolate(xi, yi); 0090 case 'mls' 0091 mlsInterp = MLSInterpolant(x, y, z, 'DistanceType', options.DistanceType, ... 0092 'PolynomialDegree', options.MLS.PolynomialDegree, ... 0093 'RBF', options.MLS.RBF, ... 0094 'RBFEpsilon', options.MLS.RBFEpsilon, ... 0095 'MinSamples', options.MLS.MinSamples); 0096 zi = mlsInterp.interpolate(xi, yi); 0097 case 'rbf' 0098 rbfInterp = RBFInterpolant(x, y, z, 'DistanceType', options.DistanceType, ... 0099 'PolynomialDegree', options.RBF.(rbfType).PolynomialDegree, ... 0100 'RBF', rbfType, ... 0101 'RBFEpsilon', options.RBF.(rbfType).RBFEpsilon, ... 0102 'Smooth', options.RBF.(rbfType).Smooth, ... 0103 'Regularization', options.RBF.(rbfType).Regularization); 0104 zi = rbfInterp.interpolate(xi, yi); 0105 case 'qtpurbf' 0106 rbfInterp = QuadTreePURBFInterpolant(x, y, z, 'MinPointsInCell', options.PURBF.MinPointsInCell, ... 0107 'Overlap', options.PURBF.Overlap, ... 0108 'Domain', options.PURBF.Domain, ... 0109 'DistanceType', options.DistanceType, ... 0110 'PolynomialDegree', options.RBF.(rbfType).PolynomialDegree, ... 0111 'RBF', rbfType, ... 0112 'RBFEpsilon', options.RBF.(rbfType).RBFEpsilon, ... 0113 'Smooth', options.RBF.(rbfType).Smooth, ... 0114 'Regularization', options.RBF.(rbfType).Regularization); 0115 zi = rbfInterp.interpolate(xi, yi); 0116 otherwise 0117 error('Unknown interpolation method'); 0118 end 0119 0120 end