Minimum Curvature

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This method generates a smooth surface by interpolation. It aims to generate a surface with continuous second derivatives and minimal total squared curvature. The method will overshoot and undershoot the point values. To control this, it allows you to introduce tension to the elastic-plate flexure equation. The method generates a solution iteratively and there are user-defined parameters that control the interpolation and that control the computing procedure that iterates towards a solution. 

When using this method, you will want to Pad and Feather the tiles. Without padding, the edge of the tiles will be clearly visible in the output grid. Padding improves this (at the cost of performance). Padding includes point data outside of the tile and so the solutions generated at the edge of adjacent tiles are likely to match well. However, because this method produces a very smooth grid, any inconsistencies in the grid will be readily visible. For that reason, you can also employ feathering. Feathering combines data in the pad with coincident data in the adjacent tiles using a weighted average. 

The Spline tension is used to control overshoots and undershoots, although it will not eliminate these effects altogether. The tension parameter ranges from 0 to 1, where a value of 0 indicates there is no additional tensions, and a value of 1 indicates you wish to apply maximum tension. A value of 0.25 is typical for gridding data like terrain. You can specify the tension in the interior of the tile and on the exterior (the interior is the primary parameter of interest). 

The Directional Bias can bias the minimum curvature spatial operator in the North-South or East-West direction. It is designed to compensate for grids with a cell size that is not square. A value of 1 indicates there is no bias. You need to have a very good reason to change this setting. 

The Relaxation value is used when combining values from the previous iteration with values from the current iteration. A value greater than 1 may help accelerate convergence. Typically, a value slightly higher than 1 is used (try 1.2 to 1.4). 

The Convergence value controls the termination of iterations. If the maximum change in a cell value is less than the convergence, then iteration terminates. Use a higher value for higher performance and lower smoothness. Use a lower value for lower performance and higher smoothness. Set convergence to zero if you want to run all iterations for maximum smoothness. 

The Coincident Distance value is used to test whether a cell centre is coincident with a source point. It is expressed as a percentage of a cell width. If a cell centre is considered coincident with an input point, then the cell value is equal to the point value. 

The Iterations value is the maximum number of iterations that will be performed to grid a tile. Use a higher value for lower performance and higher smoothness. Use a lower value for higher performance and lower smoothness. Note that you can use zero iterations and it will still generate a grid (of poorer quality and with no trend reinforcement). 

Check the “Transform the input data by Scale and Planar Offset” option to transform and normalise all input data prior to gridding a tile. In this case, the Convergence value is a percentage of the data range. Otherwise, convergence will be proportional to the band data value range. 

Check the “Collapse the number of input points in a grid cell to unity” option to average the values of all input points that lie within a cell. If not checked, the method will only use the closest point to the cell centre.