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From: <wobsta@us...>  20131011 22:13:42

Revision: 3532 https://sourceforge.net/p/pyx/code/3532/ Author: wobsta Date: 20131011 22:13:38 +0000 (Fri, 11 Oct 2013) Log Message:  make intersection of two normline robust to colinearity Modified Paths:  trunk/pyx/CHANGES trunk/pyx/pyx/normpath.py Modified: trunk/pyx/CHANGES ===================================================================  trunk/pyx/CHANGES 20131011 11:07:37 UTC (rev 3531) +++ trunk/pyx/CHANGES 20131011 22:13:38 UTC (rev 3532) @@ 7,6 +7,8 @@  path module:  fix internal name clash when generating a normpath from an empty path (reported by Brendon Higgins) +  normpath module: +  several stability and precision improvements and bugfixes  deco module:  apply text trafos to each character in curvedtext (reported by Hans L)  properly apply all textattrs in curvedtext (for example colors or scalings) Modified: trunk/pyx/pyx/normpath.py ===================================================================  trunk/pyx/pyx/normpath.py 20131011 11:07:37 UTC (rev 3531) +++ trunk/pyx/pyx/normpath.py 20131011 22:13:38 UTC (rev 3532) @@ 256,16 +256,91 @@ b_deltax_pt = other.x1_pt  other.x0_pt b_deltay_pt = other.y1_pt  other.y0_pt  try:  det = 1.0 / (b_deltax_pt * a_deltay_pt  b_deltay_pt * a_deltax_pt)  except ArithmeticError:  # a unique (within epsilon) solution is possible even for colinear lines  if math.hypot(self.x1_pt  other.x0_pt, self.y1_pt  other.y0_pt) < epsilon:  return [(1, 0)]  if math.hypot(self.x0_pt  other.x1_pt, self.y0_pt  other.y1_pt) < epsilon:  return [(0, 1)] + + invdet = b_deltax_pt * a_deltay_pt  b_deltay_pt * a_deltax_pt + + if invdet < epsilon * epsilon: + # At least one of the lines is either very short or the lines + # are almost parallel. In both cases, a proper colinear check + # is adequate, already. Let's first check for short lines. + short_self = math.hypot(self.x1_pt  self.x0_pt, + self.y1_pt  self.y0_pt) < epsilon + short_other = math.hypot(other.x1_pt  other.x0_pt, + other.y1_pt  other.y0_pt) < epsilon + + # For short lines we will only take their middle point into + # account. + if short_self: + sx_pt = 0.5*(self.x0_pt + self.x1_pt) + sy_pt = 0.5*(self.y0_pt + self.x1_pt) + if short_other: + ox_pt = 0.5*(other.x0_pt + other.x1_pt) + oy_pt = 0.5*(other.y0_pt + other.y1_pt) + + # We define two helper functions returning a valid parameter of + # a point on a line given a point close to this line. + def closepoint(x_pt, y_pt, + x0_pt, y0_pt, x1_pt, y1_pt): + """Returns the line parameter p in range [0, 1] for which + the point (x_pt, y_pt) is closest to the line defined by + ((x0_pt, y0_pt), (x1_pt, y1_pt)). The distance of (x0_pt, + y0_pt) and (x1_pt, y1_pt) must be larger than epsilon. If + the point has a greater distance than epsilon, None is + returned.""" + p = (((x0_pt  x_pt)*(x0_pt  x1_pt) + + (y0_pt  y_pt)*(y0_pt  y1_pt))/ + ((x1_pt  x0_pt)**2 + (y1_pt  y0_pt)**2)) + p = min(1, max(0, p)) + xs_pt = x0_pt + p*(x1_pt  x0_pt) + xs_pt = x0_pt + p*(x1_pt  x0_pt) + return p + + def closepoint2(x_pt, y_pt, + x0_pt, y0_pt, x1_pt, y1_pt, + X0_pt, Y0_pt, X1_pt, Y1_pt): + """Same as closepoint but for two lines ((x0_pt, y0_pt), + (x1_pt, y1_pt) and ((X0_pt, Y0_pt), (X1_pt, Y1_pt)) + returning a tuple of parameters.""" + p = closepoint(x_pt, y_pt, x0_pt, y0_pt, x1_pt, y1_pt) + if p is None: + return None, None + P = closepoint(x_pt, y_pt, X0_pt, Y0_pt, X1_pt, Y1_pt) + return p, P + + if short_self and short_other: + # If both lines are short, we just measure the distance of + # the middle points. + if math.hypot(ox_pt  sx_pt, oy_pt  sy_pt) < epsilon: + return [(0.5, 0.5)] + elif short_self: + p = closepoint(sx_pt, sy_pt, + other.x0_pt, other.y0_pt, other.x1_pt, other.y1_pt) + if p is not None: + return [(0.5, p)] + elif short_other: + p = closepoint(ox_pt, oy_pt, + self.x0_pt, self.y0_pt, self.x1_pt, self.y1_pt) + if p is not None: + return [(p, 0.5)] + else: + # For two long colinear lines, we need to test the middle + # points constructed from a beginning and an end point of + # the two lines, in both combinations. We return just one + # solution even when the lines intersect for a whole range. + sp, so = closepoint2(0.5*(self.x0_pt + other.x1_pt), 0.5*(self.y0_pt + other.y1_pt), + self.x0_pt, self.y0_pt, self.x1_pt, self.y1_pt, + other.x0_pt, other.y0_pt, other.x1_pt, other.y1_pt) + if sp is not None and so is not None: + return [(sp, so)] + sp, so = closepoint2(0.5*(self.x1_pt + other.x0_pt), 0.5*(self.y1_pt + other.y0_pt), + self.x0_pt, self.y0_pt, self.x1_pt, self.y1_pt, + other.x0_pt, other.y0_pt, other.x1_pt, other.y1_pt) + if sp is not None and so is not None: + return [(sp, so)] return [] + det = 1.0 / det + ba_deltax0_pt = other.x0_pt  self.x0_pt ba_deltay0_pt = other.y0_pt  self.y0_pt 