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Merge pull request #46 from videlec/flatsurf-conversion
functions for conversion from sage-flatsurf/pyflatsurf
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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| r""" | ||
| Conversions from pyflatsurf and sage-flatsurf to veerer. | ||
| """ | ||
|
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| from array import array | ||
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| from sage.matrix.constructor import matrix | ||
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| from .features import sage_flatsurf_feature, pyflatsurf_feature | ||
| from .triangulation import Triangulation | ||
| from .veering_triangulation import VeeringTriangulation | ||
| from .linear_family import VeeringTriangulationLinearFamily | ||
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| def oriented_slope(a, rotate=1): | ||
| r""" | ||
| Return either ``(1, 1)``, ``(1, -1)``, ``(-1, 1)`` or ``(-1, -1)``. | ||
| If ``rotate`` is set to ``1`` then consider the edge as if it was rotated counterclockwise | ||
| infinitesimally (to make horizontal edges positive slopes and vertical edges negative | ||
| slopes). If it is set to ``-1`` then the rotation is in clockwise direction. If it is | ||
| set to ``0`` then return ``0`` on horizontal and vertical. | ||
| EXAMPLES:: | ||
| sage: from veerer.flatsurf_conversion import oriented_slope | ||
| sage: oriented_slope((1, 1)) | ||
| (1, 1) | ||
| sage: oriented_slope((-1, 1)) | ||
| (-1, 1) | ||
| sage: oriented_slope((-1, -1)) | ||
| (-1, -1) | ||
| sage: oriented_slope((1, -1)) | ||
| (1, -1) | ||
| sage: oriented_slope((1, 0)) | ||
| (1, 1) | ||
| sage: oriented_slope((0, 1)) | ||
| (-1, 1) | ||
| sage: oriented_slope((-1, 0)) | ||
| (-1, -1) | ||
| sage: oriented_slope((0, -1)) | ||
| (1, -1) | ||
| sage: oriented_slope((1, 0), rotate=-1) | ||
| (1, -1) | ||
| sage: oriented_slope((0, 1), rotate=-1) | ||
| (1, 1) | ||
| sage: oriented_slope((-1, 0), rotate=-1) | ||
| (-1, 1) | ||
| sage: oriented_slope((0, -1), rotate=-1) | ||
| (-1, -1) | ||
| sage: oriented_slope((1, 0), rotate=0) | ||
| 0 | ||
| sage: oriented_slope((0, 1), rotate=0) | ||
| 0 | ||
| sage: oriented_slope((-1, 0), rotate=0) | ||
| 0 | ||
| sage: oriented_slope((0, -1), rotate=0) | ||
| 0 | ||
| sage: oriented_slope((0, 0)) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: zero vector | ||
| """ | ||
| x, y = a | ||
| if not x and not y: | ||
| raise ValueError("zero vector") | ||
| if (x > 0 and y > 0): | ||
| return (1, 1) | ||
| if (x < 0 and y < 0): | ||
| return (-1, -1) | ||
| if (x > 0 and y < 0): | ||
| return (1, -1) | ||
| if (x < 0 and y > 0): | ||
| return (-1, 1) | ||
|
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| if rotate == 0: | ||
| return 0 | ||
| if rotate == 1: | ||
| if x > 0: | ||
| return (1, 1) | ||
| if y > 0: | ||
| return (-1, 1) | ||
| if x < 0: | ||
| return (-1, -1) | ||
| if y < 0 : | ||
| return (1, -1) | ||
| if rotate == -1: | ||
| if x > 0: | ||
| return (1, -1) | ||
| if y > 0: | ||
| return (1, 1) | ||
| if x < 0: | ||
| return (-1, 1) | ||
| if y < 0: | ||
| return (-1, -1) | ||
| raise ValueError("invalid argument rotate={}".format(rotate)) | ||
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| def pyflatsurf_surface_to_veerer_veering_triangulation(surface): | ||
| r""" | ||
| Convert a pyflatsurf surface in a veering triangulation. | ||
| Note that the flatstructure is lost in the process. | ||
| EXAMPLES:: | ||
| sage: from veerer.flatsurf_conversion import pyflatsurf_surface_to_veerer_veering_triangulation | ||
| sage: from flatsurf import Polygon, similarity_surfaces # optional - sage_flatsurf pyflatsurf | ||
| sage: P = Polygon(angles=(1,1,1,7), lengths=(3, 2)) # optional - sage_flatsurf pyflatsurf | ||
| sage: S1 = similarity_surfaces.billiard(P).minimal_cover("translation").erase_marked_points() # optional - sage_flatsurf pyflatsurf | ||
| sage: S2 = S1.l_infinity_delaunay_triangulation() # optional - sage_flatsurf pyflatsurf | ||
| sage: S2.is_veering_triangulated() # optional - sage_flatsurf pyflatsurf | ||
| True | ||
| sage: S3 = S2.pyflatsurf().codomain().flat_triangulation() # optional - sage_flatsurf pyflatsurf | ||
| sage: pyflatsurf_surface_to_veerer_veering_triangulation(S3) # optional - sage_flatsurf pyflatsurf | ||
| (VeeringTriangulation("(0,1,2)(3,4,~0)(5,6,~1)(7,8,~2)(9,~3,10)(11,~8,~4)(12,13,~5)(14,15,~6)(16,~11,~10)(17,18,~12)(19,20,~13)(~20,~15,~18)(~19,~16,~17)(~14,~7,~9)", "BRRRRRBRBBBRBRRRRRBBR"), [-1, -1, 1, 1, ..., -1, 1, 1]) | ||
| """ | ||
| pyflatsurf_feature.require() | ||
|
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||
| faces = surface.faces() | ||
| n = 3 * faces.size() | ||
| ep = array('i', [n - i - 1 for i in range(n)]) | ||
| fp = array('i', [-1] * n) | ||
| slopes = [None] * n | ||
| x_orientation = [None] * n | ||
| for face in faces: | ||
| a, b, c = face | ||
| va = surface.fromHalfEdge(a) | ||
| sa = oriented_slope((va.x(), va.y())) | ||
| vb = surface.fromHalfEdge(b) | ||
| sb = oriented_slope((vb.x(), vb.y())) | ||
| vc = surface.fromHalfEdge(c) | ||
| sc = oriented_slope((vc.x(), vc.y())) | ||
| a = a.id() | ||
| b = b.id() | ||
| c = c.id() | ||
| if a < 0 : | ||
| a = n + a | ||
| elif a > 0: | ||
| a = a - 1 | ||
| if b < 0: | ||
| b = n + b | ||
| elif b > 0: | ||
| b = b - 1 | ||
| if c < 0: | ||
| c = n + c | ||
| elif c > 0: | ||
| c = c - 1 | ||
| fp[a] = b | ||
| fp[b] = c | ||
| fp[c] = a | ||
| x_orientation[a] = sa[0] | ||
| slopes[a] = sa[0] * sa[1] | ||
| x_orientation[b] = sb[0] | ||
| slopes[b] = sb[0] * sb[1] | ||
| x_orientation[c] = sc[0] | ||
| slopes[c] = sc[0] * sc[1] | ||
|
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| colors = "".join("R" if x == 1 else "B" for x in slopes) | ||
| t = Triangulation.from_face_edge_perms(fp, ep) | ||
| return VeeringTriangulation(t, colors), x_orientation | ||
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| def sage_flatsurf_orbit_closure_to_veerer_linear_family(orbit_closure): | ||
| r""" | ||
| Conversion of sage-flatsurf ``GL2ROrbitClosure`` to veerer ``VeeringTriangulationLinearFamily``. | ||
| EXAMPLES:: | ||
| sage: from veerer.flatsurf_conversion import sage_flatsurf_orbit_closure_to_veerer_linear_family | ||
| sage: from flatsurf import Polygon, similarity_surfaces, GL2ROrbitClosure # optional - sage_flatsurf pyflatsurf | ||
| sage: P = Polygon(angles=(1,1,1,7), lengths=(3, 2)) # optional - sage_flatsurf pyflatsurf | ||
| sage: S1 = similarity_surfaces.billiard(P).minimal_cover("translation").erase_marked_points() # optional - sage_flatsurf pyflatsurf | ||
| sage: S2 = S1.l_infinity_delaunay_triangulation() # optional - sage_flatsurf pyflatsurf | ||
| sage: O = GL2ROrbitClosure(S2) # optional - sage_flatsurf pyflatsurf | ||
| sage: for d in O.decompositions(4): # optional - sage_flatsurf pyflatsurf | ||
| ....: O.update_tangent_space_from_flow_decomposition(d) | ||
| ....: if O.dimension() == 4: | ||
| ....: break | ||
| sage: F = sage_flatsurf_orbit_closure_to_veerer_linear_family(O) # optional - sage_flatsurf pyflatsurf | ||
| sage: F.base_ring() # optional - sage_flatsurf pyflatsurf | ||
| Number Field in c0 with defining polynomial x^2 - x - 1 with c0 = 1.618033988749895? | ||
| sage: F # optional - sage_flatsurf pyflatsurf | ||
| VeeringTriangulationLinearFamily("(0,1,2)(3,4,~0)(5,6,~1)(7,8,~2)(9,~3,10)(11,~8,~4)(12,13,~5)(14,15,~6)(16,~11,~10)(17,18,~12)(19,20,~13)(~20,~15,~18)(~19,~16,~17)(~14,~7,~9)", "BRRRRRBRBBBRBRRRRRBBR", [(1, 0, 1, 0, 1, c0, c0, 0, -1, -c0, -c0, 0, c0, 0, c0, 2*c0, c0, 0, c0, -c0, c0), (0, 1, 1, 0, 0, c0, c0 - 1, 0, -1, -1, -1, -1, 1, c0 - 1, 1, c0, 0, -c0 + 1, -c0 + 2, -c0 + 1, 2*c0 - 2), (0, 0, 0, 1, 1, 0, 0, 0, 0, -c0, -c0 + 1, 1, 0, 0, c0, c0, c0, c0 - 1, c0 - 1, -1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, c0 - 1, c0 - 1, c0 - 1, -c0 + 1)]) | ||
| """ | ||
| sage_flatsurf_feature.require() | ||
|
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| vt, x_orientation = pyflatsurf_surface_to_veerer_veering_triangulation(orbit_closure._surface) | ||
|
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| # build generators for the tangent space | ||
| phi = orbit_closure.V2.base_ring().coerce_embedding() | ||
| K = phi.codomain() | ||
| subspace = [] | ||
| for i in range(orbit_closure._U_rank): | ||
| v = orbit_closure.lift(orbit_closure._U[i]) | ||
| v = [x_orientation[j] * phi(v[j]) for j in range(len(v))] | ||
| subspace.append(v) | ||
|
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| R = orbit_closure.field_of_definition() | ||
| if orbit_closure.base_ring() != R: | ||
| subspace = matrix(orbit_closure.base_ring(), subspace).echelon_form().change_ring(R) | ||
| return VeeringTriangulationLinearFamily(vt, subspace) |
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