Overview
This tool will interpolate the heights of undefined (null) sample points.
After defining a representative sample of points, for example along contour
lines, this facility enables heights to be derived for the remaining undefined
points. This version of GenesisII offers two interpolation algorithms,
an implementation of the Natural Neighbour algorithm (nngridr), which
should be used to interpolate the majority of missing heights, and a trend
analysis/smoothing transform, which should be used for filling in the
last few points once the majority of heights have been interpolated.
The Interpolation Process
You should broadly follow the steps outlined below:
Define a representative set of points, for example using the spot height
and contour line tools. See the item on interpolation considerations below
for more information.
- Select the interpolation tool from the button bar and click and drag
to define an area to be interpolated. After the mouse button is released
a dialog box will be displayed to confirm that interpolation is to be
started. Fill in the appropriate parameters for nearest neighbour interpolation
(see below, but these will be the defaults when using the interpolation
tool for the first time) and press OK to commence. Whilst calculating
a dialog box will be displayed showing progress and allowing cancellation
of the calculation.
- If possible it is best to interpolate all points in one calculation.
GenesisII has no practical limit on the number of grid points that may
be interpolated. However in cases where interpolation is to be used
to 'fill in' missing areas from a map (for example, to recalculate heights
after altering an area of a landscape) smaller areas can be processed
individually. In all cases however you should aim to fill in 95% or
more of all points using Nearest Neighbour interpolation. Nearest
neighbour interpolation should always be used except for final 'point
filling' as trend analysis often produces artifactes when used other
than with small groups of points.
- Finally, if there are any missing points, or you wish to smooth the
surface, click the mouse anywhere on the canvas to start interpolation
again. Select the Trend Analysis/Smoothing radio button, set the check
boxes as required to apply trend analysis and/or smoothing, then click
on OK. Both trend analysis and smoothing always apply to all grid points.
The Interpolate Heights Dialog
The following parameters may be set:
- Use Nearest Neighbour/Trend Analysis. This pair of radio
buttons determines which of the interpolation algorithms will be used.
Controls not used by the selected algorithm will be disabled.
Nearest Neighbour Interpolation.
- Use calculated gradients. Used by Nearest Neighbour interpolation.
Defaults to ON. With this option checked the algorithm uses gradients
to estimate the trends in the data when checked. For example, a rounded
hilltop will be deduced if points are available around a hill, but not
on top. If turned off gradients will not be used and a flat top will
be deduced.
- Optimise for speed. Used by Nearest Neighbour interpolation.
Defaults to ON. Calculates faster by making more generous usage of memory.
When turned off requires less memory but is significantly slower. With
modern computers memory is unlikely to be limiting unless interpolating
extremely large areas.
- Extrapolate. Used by Nearest Neighbour interpolation. Defaults
to OFF. Enables extrapolation when checked. This is by its nature a
tenuous proposition, and should be used with caution after the majority
of the map heights have been defined directly or by interpolation. Note
that it is advisable to define as many grid points as possible on the
edges of the map, and particularly at the corners, as this reduces the
amount of extrapolation required.
- Tautness Parameters #1 and #2. Used by Nearest Neighbour
interpolation. These two parameters control the 'taughtness' of the
generated surface around the points already defined. Increasing the
value of parameter 1 increases the influence of the gradient, increasing
the value of parameter 2 increases the area over which the influence
of the gradient is felt. Reasonable ranges are 1 to 3 for parameter
#1, and 5 - 12 for parameter #2. In practice
- Minimum Height. Used by both interpolation methods. The
minimum height setting is available to help when defining sea coasts
and other areas of water. For example, to define an island draw the
appropriate contour lines and spot heights for the island and an area
of sea at zero height for two or more sample points around the coast
before applying interpolation.
Trend Analysis Interpolation
- Trend Analysis. Used by Trend Analysis interpolation. Defaults
to ON. Applies a trend analysis to the whole grid to fill in any undefined
points.
- Smoothing Transform. Used by Trend Analysis interpolation.
Defaults to ON. Applies a smoothing algorithm to the whole grid to correct
any anomalous points.
Common Items
- Minimum Height: A minimum height for interpolation, useful if interpolating
coastline as by default interpolation would set values near the shoreline
as negative.
Interpolation Considerations
The proportion of defined to undefined sample points required depends
on the kind of landscape being defined. For smooth, rounded hills or plains
reasonable results may be obtained with 1 point in 40 or less. For more
complex structures 1 in 20 or less is recommended. Interpolation is most
accurate where the surface has few discontinuities - so for a valley with
steep sides and a flat bottom placing defined points along the sides will
be sufficient to derive the shape of the sides. However, without further
information the interpolation function will assume a continuation of the
sides to form an over-deepened 'V', so you will need to define some of
the valley floor.
Nearest neighbour interpolation should
always be used except for final 'point filling',
usually around extrapolated edges where trend analysis can be useful.
In most circumstances however nearest neighbour gives vastly better results
than trend analysis, which often produces artifacts when interpolating
groups of points.
In some circumstances the nearest neighbour interpolation algorithm will
be unable to proceed and an error message will be displayed: for example
if the height to width ration of the selected area is too extreme. Re-select
and try again.
nngridr and Calculation Efficiency
The implementation of the nearest neighbour algorithm used in GenesisIV
was developed by Dave Watson (contact PO Box 734 Claremont, WA 6010, Australia).
This is probably one of the most effective algorithms of it's type available.
However, although yielding excellent results, the time required to calculate
interpolated values varies approximately with the square of the number
of points. We found that in practice on a Pentium-4 an area of up to about
10,000 points could be calculated with a delay of only a few seconds,
and calculations on up to 500,000 points or more are certainly feasible
if you are willing to allow for the time required.
Calculation times can be improved by dividing a large area into several
smaller ones and interpolating in a stepwise manner, but in practise this
is not recommended as artefacts may be produced around the edges of these
areas (although these can be minimised by ensuring a good overlap).
|
|
