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import FreeCAD as App
import Part
class InterpolateF:
'''InterpolateF class interpolates an F(x) function from a set of points using BSpline interpolation'''
def __init__(self, XPoints = None, YPoints = None):
self.XPoints = XPoints
self.YPoints = YPoints
if XPoints is not None:
self.recompute()
def recompute(self):
'''call before using value(), if changing sample values via attributes'''
#compute min-max
XPoints = self.XPoints
YPoints = self.YPoints
x_max = max(XPoints)
x_min = min(XPoints)
self._x_max = x_max
self._x_min = x_min
if x_max - x_min <= (x_max + x_min)*1e-9:
raise ValueError('X range too small')
min_x_step = x_max - x_min #initialize
for i in range(0,len(self.XPoints)-1):
step = abs( XPoints[i+1] - XPoints[i] )
if step <= (x_max + x_min)*1e-9:
raise ValueError("X points "+str(i)+"-"+str(i+1)+" are too close.")
if step < min_x_step:
min_x_step = step
y_min = min(YPoints)
y_max = max(YPoints)
# we want to make sure the smallest X step is way larger than possible
# Y step, so only X points affect knotting. This is what we are using
# _y_multiplicator for - it is the scaling applied to Y coordinates of
# the interpolation points. Doing this will make u parameter of the
# spline equivalent to X coordinate.
if y_max - y_min < 1e-40:
self._y_multiplicator = 1.0
else:
self._y_multiplicator = 1e-20*min_x_step/(y_max - y_min)
self._y_demultiplicator = 1.0/self._y_multiplicator
# create the spline
if not hasattr(self,"_spline"):
self._spline = Part.BSplineCurve()
spline = self._spline
points_for_spline = [App.Vector(XPoints[i], YPoints[i]*self._y_multiplicator, 0.0) for i in range(0,len(XPoints))]
spline.interpolate(points_for_spline)
#precache some scaling values for faster calculation of value()
self._u1 = spline.FirstParameter
self._u2 = spline.LastParameter
self._x_to_u_scale = (self._u2 - self._u1) / (self._x_max - self._x_min)
def value(self, x):
return self._spline.value( self._u1 + x*self._x_to_u_scale ).y * self._y_demultiplicator
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