python - Finding intersection between ellipse and a line -

i trying find intersection points between elipse , line, seem unable so. have tried 2 approaches, 1 shapely trying find intersection between linestring , linearring in code bellow, did not usable values out of it. 1 of problems, elipse off center , @ small or high angle

  # -*- coding: utf-8 -*- """ created on mon aug 19 17:38:55 2013  @author: adudchenko """ pylab import * import numpy np shapely.geometry.polygon import linearring shapely.geometry import linestring def ellipse_polyline(ellipses, n=100):     t = np.linspace(0, 2*np.pi, n, endpoint=false)     st = np.sin(t)     ct = np.cos(t)     result = []     x0, y0, a, b, angle in ellipses:         angle = np.deg2rad(angle)         sa = np.sin(angle)         ca = np.cos(angle)         p = np.empty((n, 2))         p[:, 0] = x0 + * ca * ct - b * sa * st         p[:, 1] = y0 + * sa * ct + b * ca * st         result.append(p)     return result  def intersections(a, line):     ea = linearring(a)     eb = linearring(b)     mp = ea.intersection(eb)     print mp     x = [p.x p in mp]     y = [p.y p in mp]     return x, y  ellipses = [(1, 1, 2, 1, 45), (2, 0.5, 5, 1.5, -30)] a, b = ellipse_polyline(ellipses) line=linestring([[0,0],[4,4]]) x, y = intersections(a, line) figure() plot(x, y, "o") plot(a[:,0], a[:,1]) plot(b[:,0], b[:,1]) show() 

i tried using fsolve in example bellow, finds wrong intersect points ( or 1 wrong point.

from pylab import * scipy.optimize import fsolve import numpy np  def ellipse_polyline(ellipses, n=100):     t = np.linspace(0, 2*np.pi, n, endpoint=false)     st = np.sin(t)     ct = np.cos(t)     result = []     x0, y0, a, b, angle in ellipses:         angle = np.deg2rad(angle)         sa = np.sin(angle)         ca = np.cos(angle)         p = np.empty((n, 2))         p[:, 0] = x0 + * ca * np.cos(t) - b * sa * np.sin(t)         p[:, 1] = y0 + * sa * np.cos(t) + b * ca * np.sin(t)         result.append(p)     return result def ellipse_line(txy):     t,x,y=txy     x0, y0, a, b, angle,m,lb=1, 1, 2, 1, 45,0.5,0     sa = np.sin(angle)     ca = np.cos(angle)     return (x0 + * ca * np.cos(t) - b * sa * np.sin(t)-x,y0 + * sa * np.cos(t) + b * ca * np.sin(t)-y,m*x+lb-y)  a,b= ellipse_polyline([(1, 1, 2, 1, 45), (2, 0.5, 5, 1.5, -30)]) t,y,x=fsolve(ellipse_line,(0,0,0)) print t,y,x #print a[:,0] m=0.5 bl=0 xl,yl=[],[] in range(10):     xl.append(i)     yl.append(m*i+bl) figure() plot(x, y, "o") plot(a[:,0], a[:,1]) plot(xl,yl) 

any appriceated?

with shapely part, def intersections(a, line) can fixed. first, there error, references global b instead of using line parameter, ignored. comparison between 2 ellipses a , b, , not between each ellipse line, think intended.

also, intersection between 2 lines can 1 of several outcomes: empty set, point (1 intersection) multipoint (more 1 intersection), linestring (if part(s) of linestrings overlap , parallel each other), or collection of points , lines. assuming first 3 outcomes:

def intersections(a, line):     ea = linearring(a)     mp = ea.intersection(line)     if mp.is_empty:         print('geometries not intersect')         return [], []     elif mp.geom_type == 'point':         return [mp.x], [mp.y]     elif mp.geom_type == 'multipoint':         return [p.x p in mp], [p.y p in mp]     else:         raise valueerror('something unexpected: ' + mp.geom_type) 

so these correct:

>>> intersections(a, line) ([2.414213562373095], [2.414213562373095]) >>> intersections(b, line) ([0.0006681263405436677, 2.135895843256409], [0.0006681263405436642, 2.135895843256409])