Add trigonometric interpolation from redditor viscence

demo/moulinrouge/tests.py

@@ -174,7 +174,7 @@ def get_test_routes(app):
 
     @app.route('/test/interpolate/<chart>')
     def test_interpolate_for(chart):
-        graph = CHARTS_BY_NAME[chart](interpolate='hermite')
+        graph = CHARTS_BY_NAME[chart](interpolate='trigonometric')
         graph.add('1', [1, 3, 12, 3, 4])
         graph.add('2', [7, -4, 10, None, 8, 3, 1])
         return graph.render_response()

pygal/graph/graph.py

@@ -22,8 +22,7 @@ Commmon graphing functions
 """
 
 from __future__ import division
-from pygal.interpolate import (
-    quadratic_interpolate, cubic_interpolate, hermite_interpolate)
+from pygal.interpolate import INTERPOLATIONS
 from pygal.graph.base import BaseGraph
 from pygal.view import View, LogView, XYLogView
 from pygal.util import (
@@ -415,11 +414,7 @@ class Graph(BaseGraph):
                 x.append(xs[i])
                 y.append(ys[i])
 
-        interpolate = cubic_interpolate
-        if self.interpolate == 'quadratic':
-            interpolate = quadratic_interpolate
-        elif self.interpolate == 'hermite':
-            interpolate = hermite_interpolate
+        interpolate = INTERPOLATIONS[self.interpolate]
 
         return list(interpolate(x, y, self.interpolation_precision))
 

pygal/interpolate.py

@@ -23,6 +23,7 @@ TODO: Implement more interpolations (cosine, lagrange...)
 
 """
 from __future__ import division
+from math import sin
 
 
 def quadratic_interpolate(x, y, precision=250):
@@ -124,6 +125,37 @@ def hermite_interpolate(x, y, precision=250):
             X = x[i] + s * delta_x[i] / precision
             yield X, p(i, X)
 
+
+def trigonometric_interpolate(x, y, precision=250):
+    """ As per http://en.wikipedia.org/wiki/Trigonometric_interpolation"""
+    n = len(x) - 1
+    delta_x = [x2 - x1 for x1, x2 in zip(x, x[1:])]
+    for i in range(n + 1):
+        yield x[i], y[i]
+        if i == n or delta_x[i] == 0:
+            continue
+
+        for s in range(1, precision):
+            X = x[i] + s * delta_x[i] / precision
+            s = 0
+            for k in range(n + 1):
+                p = 1
+                for m in range(n + 1):
+                    if m == k:
+                        continue
+                    p *= sin(0.5 * (X - x[m])) / sin(0.5 * (x[k] - x[m]))
+                s += y[k] * p
+            yield X, s
+
+
+INTERPOLATIONS = {
+    'quadratic': quadratic_interpolate,
+    'cubic': cubic_interpolate,
+    'hermite': hermite_interpolate,
+    'trigonometric': trigonometric_interpolate
+}
+
+
 if __name__ == '__main__':
     from pygal import XY
     points = [(.1, 7), (.3, -4), (.6, 10), (.9, 8), (1.4, 3), (1.7, 1)]