2246.sagews

pts_idaho=[(-117.0319,	48.9996), 
(-117.0394,	46.9451), 
(-117.0408,	46.4270), 
(-117.0511,	46.3446), 
(-117.0209,	46.3152), 
(-116.9920,	46.2782), 
(-116.9591,	46.2435), 
(-116.9646,	46.2007), 
(-116.9268,	46.1727), 
(-116.9344,	46.1385), 
(-116.9838,	46.0932), 
(-116.9302,	46.0218), 
(-116.8925,	45.9769), 
(-116.8739,	45.9545), 
(-116.8595,	45.9053), 
(-116.8046,	45.8642), 
(-116.7908,	45.8341), 
(-116.7586,	45.8159), 
(-116.7105,	45.8259), 
(-116.6597,	45.7805), 
(-116.5965,	45.7781), 
(-116.6357,	45.7843), 
(-116.5594,	45.7541), 
(-116.5354,	45.7340), 
(-116.5354,	45.6904), 
(-116.4640,	45.6140), 
(-116.5334,	45.5371), 
(-116.5553,	45.4630), 
(-116.5883,	45.4433), 
(-116.6185,	45.3984), 
(-116.6741,	45.3213), 
(-116.7105,	45.2178), 
(-116.7229,	45.1627), 
(-116.7819,	45.0968), 
(-116.8417,	45.0313), 
(-116.8554,	44.9896), 
(-116.8513,	44.9624), 
(-116.8327,	44.9356), 
(-116.8980,	44.8568), 
(-116.9316,	44.7921), 
(-117.0442,	44.7423), 
(-117.1458,	44.5376), 
(-117.1836,	44.5234), 
(-117.2269,	44.4769), 
(-117.2372,	44.3813), 
(-117.1994,	44.3445), 
(-117.2255,	44.2973), 
(-117.1541,	44.2590), 
(-117.1122,	44.2806), 
(-117.0895,	44.2585), 
(-117.0525,	44.2304), 
(-117.0339,	44.2486), 
(-116.9810,	44.2442), 
(-116.9714,	44.1965), 
(-116.8945,	44.1561), 
(-116.9330,	44.1014), 
(-116.9735,	44.0491), 
(-116.9302,	44.0244), 
(-116.9776,	43.9073), 
(-117.0030,	43.8632), 
(-117.0325,	43.8330), 
(-117.0277,	43.7820), 
(-117.0264,	42.0013), 
(-117.0140,	41.9962), 
(-115.9126,	41.9973), 
(-114.8222,	42.0013), 
(-114.0422,	41.9942), 
(-113.8458,	41.9871), 
(-112.1663,	41.9962), 
(-111.0471,	42.0013), 
(-111.0471,	43.8623), 
(-111.0539,	44.4759), 
(-111.3684,	44.7292), 
(-111.5057,	44.6198), 
(-111.4645,	44.5396), 
(-111.8271,	44.5132), 
(-111.8848,	44.5582), 
(-112.1127,	44.5220), 
(-112.3270,	44.5347), 
(-112.3901,	44.4504), 
(-112.7266,	44.4887), 
(-112.8310,	44.4151), 
(-112.8502,	44.3592), 
(-113.0246,	44.4887), 
(-113.1180,	44.7350), 
(-113.2471,	44.8062), 
(-113.3459,	44.7887), 
(-113.4998,	44.9405), 
(-113.4256,	45.0260), 
(-113.7085,	45.2720), 
(-113.7978,	45.4409), 
(-113.8403,	45.6102), 
(-113.9708,	45.6889), 
(-114.1342,	45.5631), 
(-114.2441,	45.5468), 
(-114.3375,	45.4601), 
(-114.4666,	45.5439), 
(-114.5654,	45.5621), 
(-114.5229,	45.6745), 
(-114.5654,	45.7742), 
(-114.4418,	45.8585), 
(-114.5105,	46.1227), 
(-114.4611,	46.2682), 
(-114.4144,	46.3488), 
(-114.3896,	46.4530), 
(-114.3430,	46.5135), 
(-114.3279,	46.6466), 
(-114.4638,	46.6325), 
(-114.5874,	46.6325), 
(-114.7549,	46.6984), 
(-114.7865,	46.7201), 
(-114.9472,	46.8677), 
(-115.0433,	46.9728), 
(-115.2493,	47.1542), 
(-115.2878,	47.1888), 
(-115.3235,	47.2606), 
(-115.5350,	47.3109), 
(-115.7595,	47.4239), 
(-115.7574,	47.5487), 
(-115.6915,	47.5765), 
(-116.0445,	47.9752), 
(-116.0486,	49.0018), 
(-117.0319,	49.0000)]

list_plot(pts_idaho)

ps = polygon_spline(pts_idaho)
f = lambda t: ps.value(t)  
fprime = lambda t: ps.derivative(t)  
m = Riemann_Map([f], [fprime], (44-115*I),N=4000,)

m.plot_colored(plot_points=400) +m.plot_boundaries()