m + fix cubic interpolation

Signed-off-by: Mattias Andrée <maandree@operamail.com>

4 files changed, 23 insertions, 10 deletions

diff --git a/TODO b/TODO
index c5d0d16..3ed5a10 100644
--- a/TODO
+++ b/TODO
@@ -15,6 +15,8 @@ Low priority:
 	  https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
 	  https://en.wikipedia.org/wiki/Spline_interpolation
 	  https://en.wikipedia.org/wiki/Lanczos_resampling
+	  https://en.wikipedia.org/wiki/Kochanek–Bartels_spline
+	  https://en.wikipedia.org/wiki/Stairstep_interpolation
 	Use curve sizes returned from RandR/VidMode/...
 	Use Robertson's method
 
diff --git a/src/interpolation.py b/src/interpolation.py
index 0d16838..e81c93c 100644
--- a/src/interpolation.py
+++ b/src/interpolation.py
@@ -47,13 +47,14 @@ def linearly_interpolate_ramp(r, g, b):
     return (R, G, B)
 
 
-def cubicly_interpolate_ramp(r, g, b):
+def cubicly_interpolate_ramp(r, g, b, tension = 0): # TODO demo and document tension parameter
     '''
     Interpolate ramps to the size of the output axes using cubic Hermite spline
     
     @param   r:list<float>                                   The red colour curves
     @param   g:list<float>                                   The green colour curves
     @param   b:list<float>                                   The blue colour curves
+    @param   tension:float                                   A [0, 1] value of the tension
     @return  :(r:list<float>, g:list<float>, b:list<float>)  The input parameters extended to sizes of `o_size`,
                                                              or their original size, whatever is larger.
     '''
@@ -61,8 +62,8 @@ def cubicly_interpolate_ramp(r, g, b):
     R, G, B = C(r), C(g), C(b)
     # 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)
+    h10 = lambda t : t * (1 - t) ** 2
+    h01 = lambda t : t ** 2 * (3 - 2 * t)
     h11 = lambda t : t ** 2 * (t - 1)
     def tangent(values, index, last):
         '''
@@ -77,6 +78,8 @@ def cubicly_interpolate_ramp(r, g, b):
         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
+    # Tension coefficent
+    c_ = 1 - tension
     # Interpolate each curve
     for small, large in ((r, R), (g, G), (b, B)):
         small_, large_ = len(small) - 1, len(large) - 1
@@ -90,7 +93,7 @@ def cubicly_interpolate_ramp(r, g, b):
                 # Points
                 pj, pk = small[j], small[k]
                 # Tangents
-                mj, mk = tangent(small, j, small_), tangent(small, k, small_)
+                mj, mk = c_ * tangent(small, j, small_), c_ * tangent(small, k, small_)
                 # Interpolation
                 large[i] = h00(w) * pj + h10(w) * mj + h01(w) * pk + h11(w) * mk
     ## Check local monotonicity
diff --git a/test/cubic_interpolation b/test/cubic_interpolation
index 249aa89..6d2b22c 100755
--- a/test/cubic_interpolation
+++ b/test/cubic_interpolation
@@ -12,13 +12,16 @@ print('Loading matplotlib.pyplot...')
 import matplotlib.pyplot as plot
 print('Done loading matplotlib.pyplot')
 
+from math import *
+
 
 def main():
     # Create a page with graphs
     fig = plot.figure()
     
     # Add graphs
-    add_graph(fig, 111, [i / 15 for i in range(16)])
+    add_graph(fig, 211, [i / 15 for i in range(16)])
+    add_graph(fig, 212, [sin(6 * i / 15) for i in range(16)])
     
     # Show graphs
     plot.show()
@@ -45,7 +48,7 @@ def add_graph(fig, graph_pos, input_values):
     graph.plot([i / (n - 1) for i in range(n)], input_values, 'ro')
 
 
-def interpolate(small):
+def interpolate(small, tension = 0):
     '''
     Interpolate data
     
@@ -56,8 +59,8 @@ def interpolate(small):
     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)
+    h10 = lambda t : t * (1 - t) ** 2
+    h01 = lambda t : t ** 2 * (3 - 2 * t)
     h11 = lambda t : t ** 2 * (t - 1)
     def tangent(values, index, last):
         '''
@@ -72,6 +75,8 @@ def interpolate(small):
         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
+    # Tension coefficent
+    c_ = 1 - tension
     for i in range(len(large)):
         # Scaling
         j = i * small_ / large_
@@ -80,7 +85,7 @@ def interpolate(small):
         # Points
         pj, pk = small[j], small[k]
         # Tangents
-        mj, mk = tangent(small, j, small_), tangent(small, k, small_)
+        mj, mk = c_ * tangent(small, j, small_), c_ * tangent(small, k, small_)
         # Interpolation
         large[i] = h00(w) * pj + h10(w) * mj + h01(w) * pk + h11(w) * mk
     return large
diff --git a/test/linear_interpolation b/test/linear_interpolation
index ae622cc..140616c 100755
--- a/test/linear_interpolation
+++ b/test/linear_interpolation
@@ -14,13 +14,16 @@ print('Loading matplotlib.pyplot...')
 import matplotlib.pyplot as plot
 print('Done loading matplotlib.pyplot')
 
+from math import *
+
 
 def main():
     # Create a page with graphs
     fig = plot.figure()
     
     # Add graphs
-    add_graph(fig, 111, [i / 15 for i in range(16)])
+    add_graph(fig, 211, [i / 15 for i in range(16)])
+    add_graph(fig, 212, [sin(6 * i / 15) for i in range(16)])
     
     # Show graphs
     plot.show()