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