Merge with the worst possible conflicts: png and xml. Think i didnt yet integrate Simons latest png changes.

flame_solver.py

@@ -0,0 +1,41 @@
+#!/usr/bin/env python3
+
+from math import pi, sin, cos, exp
+from numpy import arange
+
+# f(x) = p1 * sin(p2 * x)
+
+parameter_sin_1=3
+parameter_sin_2=0.3
+
+transition_point = (1/parameter_sin_2) * pi * 0.75
+
+sin_value = parameter_sin_1 * sin(parameter_sin_2 * transition_point) 
+
+derived_sin_value = parameter_sin_1 * parameter_sin_2 * cos(parameter_sin_2 * transition_point)
+
+#g(x) = e^(p1 - p2 * x)
+parameter_ex_p1 = list(arange(0,10, 0.01))
+parameter_ex_p2 = list(arange(0, 1, 0.00001))
+
+best_parameter_ex_p1 = -1
+best_parameter_ex_p2 = -1
+value = exp(parameter_ex_p1[0] - parameter_ex_p2[0] * transition_point)
+derived_value = - parameter_ex_p2[0] * exp(parameter_ex_p1[0] - parameter_ex_p2[0] * transition_point)
+value_error = abs(value - sin_value)
+derived_value_error = abs(derived_value - derived_sin_value)
+
+for p1 in parameter_ex_p1:
+    for p2 in parameter_ex_p2:
+            value = exp(p1 - p2 * transition_point)
+            derived_value = - p2 * exp(p1 - p2 * transition_point)
+            if abs(value - sin_value) < value_error and abs(derived_value - derived_sin_value) < derived_value_error:
+                value_error = abs(value -sin_value)
+                derived_value_error = abs(derived_value - derived_sin_value)
+                best_parameter_ex_p1 = p1
+                best_parameter_ex_p2 = p2
+
+print("p1: " + str(best_parameter_ex_p1))
+print("p2: " + str(best_parameter_ex_p2))
+print("value error: " + str(value_error))
+print("derived value error: " + str(derived_value_error))