added math minimal distance example

documents/math-minimal-distance-to-cubic-function/calcMinDist.py

@@ -0,0 +1,35 @@
+#!/usr/bin/env python
+
+import numpy
+
+class Point:
+    def __init__(self, x, y):
+        self.x = x
+        self.y = y
+
+def euclideanDist(p1, p2):
+    from math import sqrt
+    return sqrt((p1.x-p2.x)**2 + (p1.y-p2.y)**2)
+
+def getMinDist(y, precision=0.001, startX=0, endX=3):
+    """Get x of point on (x,x^2) that has minimal distance to given Point."""
+    minDist = -1
+    p1 = Point(0, y)
+    for x in numpy.arange(startX, endX, precision):
+        p2 = Point(x, x**2)
+        dist = euclideanDist(p1, p2)
+        if minDist == -1 or dist < minDist:
+            minDist = dist
+            #print(dist)
+        else:
+            if abs(i-minDist) <0.005:
+                print("x: %s" % str(x))
+            break
+    return minDist
+
+for i in numpy.arange(0, 3, 0.01):
+    minDist = getMinDist(i)
+    if abs(i-minDist) < 0.005:
+        print(i, minDist)
+
+#print(getMinDist(5, 0.00001, 2, 3))