From ec31ebe99eb656b78e9dee3d9e3575e4ee5e6a46 Mon Sep 17 00:00:00 2001
From: Mattias Andrée <maandree@operamail.com>
Date: Sun, 6 Apr 2014 00:02:09 +0200
Subject: add cubic interpolation test, did not work out too well
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Signed-off-by: Mattias Andrée <maandree@operamail.com>
---
test/cubic_interpolation | 90 ++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 90 insertions(+)
create mode 100755 test/cubic_interpolation
(limited to 'test/cubic_interpolation')
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()
+
--
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