def is_coplanar(pyptlist): """ This function checks if the list of points are coplanar. Parameters ---------- pyptlist : a list of tuples The list of points to be checked. List of points to be converted. A pypt is a tuple that documents the xyz coordinates of a pt e.g. (x,y,z), thus a pyptlist is a list of tuples e.g. [(x1,y1,z1), (x2,y2,z2), ...] Returns ------- True or False : bool If True the list of points are coplanar. """ from sympy import Point3D sympt_list = [] for pypt in pyptlist: sympt = Point3D(pypt[0], pypt[1], pypt[2]) sympt_list.append(sympt) coplanar = Point3D.are_coplanar(*sympt_list) return coplanar
prtemp = Psp.projection(pointL1sp) prpointL1P = vector( [prtemp.x._sage_(), prtemp.y._sage_(), prtemp.z._sage_()]) prL1Pparam = (solve([ x - prM2P[_sage_const_0] == (prpointL1P[_sage_const_0] - prM2P[_sage_const_0]) * t, y - prM2P[_sage_const_1] == (prpointL1P[_sage_const_1] - prM2P[_sage_const_1]) * t, z - prM2P[_sage_const_2] == (prpointL1P[_sage_const_2] - prM2P[_sage_const_2]) * t ], x, y, z))[_sage_const_0] L2sp = Line3D(Point3D(M2), Point3D(M3)) # проверка на компланарность (=, пересекаются или параллельны) w = Point3D.are_coplanar(Point3D(pointL), Point3D(point2L), Point3D(M2), Point3D(M3)) sL2 = M3 - M2 sLL2 = M2 - pointL if w: if Line3D.is_parallel(Lsp, L2sp): strLL2 = r"параллельны" dLL2 = Lsp.distance(M2) else: if Line3D.is_similar(Lsp, L2sp): strLL2 = r"совпадают" dLL2 = _sage_const_0 else: strLL2 = r"пересекаются" dLL2 = _sage_const_0 else: strLL2 = r"скрещиваются"