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author | Mattias Andrée <maandree@operamail.com> | 2014-04-06 00:02:09 +0200 |
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committer | Mattias Andrée <maandree@operamail.com> | 2014-04-06 00:02:09 +0200 |
commit | ec31ebe99eb656b78e9dee3d9e3575e4ee5e6a46 (patch) | |
tree | 56cf8c48c71d43a577337a5b8625600beb1d4824 /test/cubic_interpolation | |
parent | add test of linear interpolation (diff) | |
download | blueshift-ec31ebe99eb656b78e9dee3d9e3575e4ee5e6a46.tar.gz blueshift-ec31ebe99eb656b78e9dee3d9e3575e4ee5e6a46.tar.bz2 blueshift-ec31ebe99eb656b78e9dee3d9e3575e4ee5e6a46.tar.xz |
add cubic interpolation test, did not work out too well
Signed-off-by: Mattias Andrée <maandree@operamail.com>
Diffstat (limited to '')
-rwxr-xr-x | test/cubic_interpolation | 90 |
1 files changed, 90 insertions, 0 deletions
diff --git a/test/cubic_interpolation b/test/cubic_interpolation new file mode 100755 index 0000000..249aa89 --- /dev/null +++ b/test/cubic_interpolation @@ -0,0 +1,90 @@ +#!/usr/bin/env python3 +# -*- python -*- + + +# Test of cubic interpolation. + + +# Load matplotlib.pyplot, +# it can take some time so +# print information about it. +print('Loading matplotlib.pyplot...') +import matplotlib.pyplot as plot +print('Done loading matplotlib.pyplot') + + +def main(): + # Create a page with graphs + fig = plot.figure() + + # Add graphs + add_graph(fig, 111, [i / 15 for i in range(16)]) + + # Show graphs + plot.show() + +def add_graph(fig, graph_pos, input_values): + ''' + Add a graph + + @param fig:Figure The page to which to add the graph + @param graph_pos:int Where to place the graph + @param input_values:list<float> The input values for each point + ''' + # Interpolate data + output_values = interpolate(input_values) + # Number of input points + n = len(input_values) + # Number of output points + m = len(output_values) + # Create graph + graph = fig.add_subplot(graph_pos) + # Plot interpolated data + graph.plot([i / (m - 1) for i in range(m)], output_values, 'b-') + # Plot input data + graph.plot([i / (n - 1) for i in range(n)], input_values, 'ro') + + +def interpolate(small): + ''' + Interpolate data + + @param small:list<float> The input values for each point + @return :list<float> The values for each point in a scaled up version + ''' + large = [None] * len(small) ** 2 + small_, large_ = len(small) - 1, len(large) - 1 + # Basis functions + h00 = lambda t : (1 + 2 * t) * (1 - t) ** 2 + h01 = lambda t : t * (1 - t) ** 2 + h10 = lambda t : t ** 2 * (3 - 2 * t) + h11 = lambda t : t ** 2 * (t - 1) + def tangent(values, index, last): + ''' + Calculate the tangent at a point + + @param values:list<float> Mapping from points to values + @param index:int The point + @param last:int The last point + @return :float The tangent at the point `index` + ''' + if last == 0: return 0 + if index == 0: return values[1] - values[0] + if index == last: return values[last] - values[last - 1] + return (values[index + 1] - values[index - 1]) / 2 + for i in range(len(large)): + # Scaling + j = i * small_ / large_ + # Floor, weight, ceiling + j, w, k = int(j), j % 1, min(int(j) + 1, small_) + # Points + pj, pk = small[j], small[k] + # Tangents + mj, mk = tangent(small, j, small_), tangent(small, k, small_) + # Interpolation + large[i] = h00(w) * pj + h10(w) * mj + h01(w) * pk + h11(w) * mk + return large + +# Plot interpolation +main() + |