From c5b296096e78839d53c72e7023934ea3aa56187d Mon Sep 17 00:00:00 2001
From: Florian Mounier <florian.mounier@kozea.fr>
Date: Fri, 14 Jun 2013 17:31:28 +0200
Subject: [PATCH] Start adding hermite interpolation

---
 demo/moulinrouge/tests.py |  2 +-
 pygal/graph/graph.py      |  4 +++-
 pygal/interpolate.py      | 32 ++++++++++++++++++++++++++++++++
 3 files changed, 36 insertions(+), 2 deletions(-)

diff --git a/demo/moulinrouge/tests.py b/demo/moulinrouge/tests.py
index e53c47c..7934656 100644
--- a/demo/moulinrouge/tests.py
+++ b/demo/moulinrouge/tests.py
@@ -159,7 +159,7 @@ def get_test_routes(app):
 
     @app.route('/test/interpolate/<chart>')
     def test_interpolate_for(chart):
-        graph = CHARTS_BY_NAME[chart](interpolate='cubic')
+        graph = CHARTS_BY_NAME[chart](interpolate='hermite')
         graph.add('1', [1, 3, 12, 3, 4])
         graph.add('2', [7, -4, 10, None, 8, 3, 1])
         return graph.render_response()
diff --git a/pygal/graph/graph.py b/pygal/graph/graph.py
index 13d05f0..18f23d6 100644
--- a/pygal/graph/graph.py
+++ b/pygal/graph/graph.py
@@ -23,7 +23,7 @@ Commmon graphing functions
 
 from __future__ import division
 from pygal.interpolate import (
-    quadratic_interpolate, cubic_interpolate)
+    quadratic_interpolate, cubic_interpolate, hermite_interpolate)
 from pygal.graph.base import BaseGraph
 from pygal.view import View, LogView, XYLogView
 from pygal.util import (
@@ -388,6 +388,8 @@ class Graph(BaseGraph):
         interpolate = cubic_interpolate
         if self.interpolate == 'quadratic':
             interpolate = quadratic_interpolate
+        elif self.interpolate == 'hermite':
+            interpolate = hermite_interpolate
 
         return list(interpolate(x, y, self.interpolation_precision))
 
diff --git a/pygal/interpolate.py b/pygal/interpolate.py
index f0a627e..00483b8 100644
--- a/pygal/interpolate.py
+++ b/pygal/interpolate.py
@@ -92,6 +92,38 @@ def cubic_interpolate(x, y, precision=250):
             yield x[i] + X, a[i] + b[i] * X + c[i] * X2 + d[i] * X3
 
 
+def hermite_interpolate(x, y, precision=250):
+    n = len(x) - 1
+    m = [1] * (n + 1)
+    c = 0
+    delta_x = [x2 - x1 for x1, x2 in zip(x, x[1:])]
+
+    for i in range(1, n):
+        m[i] = (1 - c) * (y[i + 1] - y[i - 1]) / (x[i + 1] - x[i - 1])
+
+    def p(i, x_):
+        t = (x_ - x[i]) / delta_x[i]
+        t2 = t * t
+        t3 = t2 * t
+
+        h00 = 2 * t3 - 3 * t2 + 1
+        h10 = t3 - 2 * t2 + t
+        h01 = - 2 * t3 + 3 * t2
+        h11 = t3 - t2
+
+        return (h00 * y[i] +
+                h10 * m[i] * delta_x[i] +
+                h01 * y[i + 1] +
+                h11 * m[i + 1] * delta_x[i])
+
+    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
+            yield X, p(i, X)
+
 if __name__ == '__main__':
     from pygal import XY
     points = [(.1, 7), (.3, -4), (.6, 10), (.9, 8), (1.4, 3), (1.7, 1)]