def render_spiral(self,
                      initial_elements,
                      sides,
                      max_height,
                      file_name,
                      initial_colors=(),
                      color_dic=None):
        """
        Create an image file depicting a flower complex.

        Note that the identification between colors and elements is not preserved across images with different
        `sides` and `max_layer` values unless a color dictionary is provided. Don't be misled by this.

        Args:
            initial_elements (tuple): The first elements to be operated on.
            sides (int): The number of sides of the original polygon.
            max_beight (int): The number of steps up from the origin to construct.
            file_name (str): The name of the file generated.
            intial_colors (tuple): Colors used to display the complex. These are used before the colors in `self.initial_colors`.
            color_dic (dict): Dictionary of colors to be used when displaying the complex. This is used before the dictionary in `self.color_dic`.
        """

        values = self.grow_spiral(initial_elements, sides, max_height)
        while color_dic is None:
            color_dic = self.color_dic
            color_dic = self.color_dictionary(values, initial_colors)
        g = 0
        loc = lambda b, c, a=1: polar_location(
            a, b, sides, height=c, dimension=3)
        for h in range(max_height):
            for n in range(sides - 1):
                p1 = loc(0, h, 0)
                p2 = loc(n, h)
                p3 = loc(n + 1, h)
                c1 = color_dic[values[0][0]]  # left input
                c2 = color_dic[values[h + 1][n]]  # right input
                c3 = color_dic[values[h + 1][n + 1]]  # output
                sub_div = barycentric_subdivision(p1, p2, p3)
                cols = (c1, c2, c3, c3)
                for i in range(4):
                    g += polygon(sub_div[i], color=cols[i])
            if h != max_height - 1:
                p1 = loc(0, h, 0)
                p2 = loc(sides - 1, h)
                p3 = loc(0, h + 1)
                c1 = color_dic[values[0][0]]  # left input
                c2 = color_dic[values[h + 1][sides - 1]]  # right input
                c3 = color_dic[values[h + 2][0]]  # output
                sub_div = barycentric_subdivision(p1, p2, p3)
                cols = (c1, c2, c3, c3)
                for i in range(4):
                    g += polygon(sub_div[i], color=cols[i])
        g.save(file_name + '.x3d', axes=False)
Exemplo n.º 2
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    def plot_n_cylinders(self, n, labels=True):
        r"""
        EXAMPLES::

            sage: from slabbe.markov_transformation import markov_transformations
            sage: T = markov_transformations.Selmer()
            sage: G = T.plot_n_cylinders(3)

        TESTS::

            sage: G = T.plot_n_cylinders(0)
        """
        from sage.plot.graphics import Graphics
        from sage.plot.polygon import polygon
        from sage.plot.text import text
        M3to2 = projection_matrix(3, 2)
        G = Graphics()
        for w, cyl in self.n_cylinders_iterator(n):
            columns = cyl.columns()
            G += polygon((M3to2 * col / col.norm(1) for col in columns),
                         fill=False)
            if labels:
                sum_cols = sum(columns)
                G += text("{}".format(w), M3to2 * sum_cols / sum_cols.norm(1))
        return G
Exemplo n.º 3
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    def plot_n_cylinders(self, n, labels=True):
        r"""
        EXAMPLES::

            sage: from slabbe.matrix_cocycle import cocycles
            sage: C = cocycles.Sorted_ARP()
            sage: G = C.plot_n_cylinders(3)
        """
        from sage.plot.graphics import Graphics
        from sage.plot.polygon import polygon
        from sage.plot.text import text
        from matrices import M3to2
        G = Graphics()
        for w,cyl in self.n_cylinders_iterator(n):
            columns = cyl.columns()
            G += polygon((M3to2*col/col.norm(1) for col in columns), fill=False) 
            if labels:
                sum_cols = sum(columns)
                G += text("{}".format(w), M3to2*sum_cols/sum_cols.norm(1))
        return G
Exemplo n.º 4
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    def plot_n_cylinders(self, n, labels=True):
        r"""
        EXAMPLES::

            sage: from slabbe.matrix_cocycle import cocycles
            sage: C = cocycles.Sorted_ARP()
            sage: G = C.plot_n_cylinders(3)
        """
        from sage.plot.graphics import Graphics
        from sage.plot.polygon import polygon
        from sage.plot.text import text
        from .matrices import M3to2
        G = Graphics()
        for w,cyl in self.n_cylinders_iterator(n):
            columns = cyl.columns()
            G += polygon((M3to2*col/col.norm(1) for col in columns), fill=False) 
            if labels:
                sum_cols = sum(columns)
                G += text("{}".format(w), M3to2*sum_cols/sum_cols.norm(1))
        return G
Exemplo n.º 5
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def polygon_plot3d(points, tilt=30, turn=30, **kwargs):
    """
    Plots a polygon viewed from an angle determined by tilt, turn, and
    vertices points.

    .. warning::

       The ordering of the points is important to get "correct"
       and if you add several of these plots together, the one added first
       is also drawn first (ie, addition of Graphics objects is not
       commutative).

    The following example produced a green-colored square with vertices
    at the points indicated.

    EXAMPLES::

        sage: from sage.groups.perm_gps.cubegroup import *
        sage: P = polygon_plot3d([[1,3,1],[2,3,1],[2,3,2],[1,3,2],[1,3,1]],rgbcolor=green)
    """
    rot = rotation_list(tilt,turn)
    points2 = [(xproj(x,y,z,rot), yproj(x,y,z,rot)) for (x,y,z) in points ]
    return polygon(points2, **kwargs)
Exemplo n.º 6
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def polygon_plot3d(points, tilt=30, turn=30, **kwargs):
    """
    Plots a polygon viewed from an angle determined by tilt, turn, and
    vertices points.
    
    .. warning::

       The ordering of the points is important to get "correct"
       and if you add several of these plots together, the one added first
       is also drawn first (ie, addition of Graphics objects is not
       commutative).
    
    The following example produced a green-colored square with vertices
    at the points indicated.
    
    EXAMPLES::
    
        sage: from sage.groups.perm_gps.cubegroup import *
        sage: P = polygon_plot3d([[1,3,1],[2,3,1],[2,3,2],[1,3,2],[1,3,1]],rgbcolor=green)
    """
    rot = rotation_list(tilt,turn)
    points2 = [(xproj(x,y,z,rot), yproj(x,y,z,rot)) for (x,y,z) in points ]
    return polygon(points2, **kwargs)
Exemplo n.º 7
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    def plot_n_cylinders(self, n, labels=True):
        r"""
        EXAMPLES::

            sage: from slabbe.markov_transformation import markov_transformations
            sage: T = markov_transformations.Selmer()
            sage: G = T.plot_n_cylinders(3)

        TESTS::

            sage: G = T.plot_n_cylinders(0)
        """
        from sage.plot.graphics import Graphics
        from sage.plot.polygon import polygon
        from sage.plot.text import text
        M3to2 = projection_matrix(3, 2)
        G = Graphics()
        for w,cyl in self.n_cylinders_iterator(n):
            columns = cyl.columns()
            G += polygon((M3to2*col/col.norm(1) for col in columns), fill=False) 
            if labels:
                sum_cols = sum(columns)
                G += text("{}".format(w), M3to2*sum_cols/sum_cols.norm(1))
        return G
Exemplo n.º 8
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 def add_rightside(i, j, k):
     return polygon(move(Rside,i,j,k), edgecolor="black", color=colors[2])
Exemplo n.º 9
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 def add_leftside(i, j, k):
     return polygon(move(Lside,i,j,k), edgecolor="black", color=colors[1])
Exemplo n.º 10
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 def add_topside(i, j, k):
     return polygon(move(Uside,i,j,k), edgecolor="black", color=colors[0])
Exemplo n.º 11
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    def render_complex(self,
                       file_name,
                       cycles=1,
                       degenerate_faces=True,
                       initial_colors=(),
                       color_dic=None):
        """
        Create 3d graphics depicting a binary operation complex.

        Vertices are placed on a helix which winds around the surface of the sphere with center (0,0,1/2) and radius 1/2.
        That is, the first vertex is placed at (0,0,0) and the last is placed at (0,0,1).

        Args:
            file_name (str): The name of the file generated.
            cycles (int): The number of times the determining helix winds around the line between the origin and (0,0,1).
            intial_colors (tuple): Colors used to display the complex. These are used before the colors in `self.initial_colors`.
            color_dic (dict): Dictionary of colors to be used when displaying the complex. This is used before the dictionary in `self.color_dic`.
        """

        elems = tuple(self.structure.elements)
        f = self.operation
        while color_dic is None:
            color_dic = self.color_dic
            color_dic = self.color_dictionary((elems, ), initial_colors)
        g = 0
        loc = lambda a, b, c: (sin(c * pi) * cos(a * 2 * pi / b), sin(c * pi) *
                               sin(a * 2 * pi / b), c)
        locations = {}
        for h in range(len(elems)):
            locations[elems[h]] = loc(cycles * h, len(elems), h / len(elems))
        for x in elems:
            for y in elems:
                z = self.operation(x, y)
                if degenerate_faces:
                    if x == y:
                        # x=y=z case
                        if x == z:
                            if locations[x] == (0, 0, 0):
                                p1, p2, p3, p4 = (0, 0, 0), loc(
                                    0, 3,
                                    -1 / 2), loc(1, 3,
                                                 -1 / 2), loc(2, 3, -1 / 2)
                                for entry in ((p1, p2, p3), (p1, p2, p4),
                                              (p1, p3, p4), (p2, p3, p4)):
                                    g += polygon(entry, colors=color_dic[x])
                            if locations[x] == (0, 0, 1):
                                p1, p2, p3, p4 = (0, 0, 1), loc(
                                    0, 3, 3 / 2), loc(1, 3,
                                                      3 / 2), loc(2, 3, 3 / 2)
                                for entry in ((p1, p2, p3), (p1, p2, p4),
                                              (p1, p3, p4), (p2, p3, p4)):
                                    g += polygon(entry, colors=color_dic[x])
                            if locations[x] != (0, 0, 0) and locations[x] != (
                                    0, 0, 1):
                                p1 = locations[x]
                                p2 = tuple(
                                    map(
                                        add,
                                        map(lambda u: 14 * u / 10,
                                            locations[x]),
                                        map(
                                            lambda u: 6 * u / 10,
                                            locations[elems[elems.index(x) +
                                                            1]])))
                                p3 = tuple(
                                    map(
                                        add,
                                        map(lambda u: 14 * u / 10,
                                            locations[x]),
                                        map(
                                            lambda u: 6 * u / 10,
                                            locations[elems[elems.index(x) -
                                                            1]])))
                                p4 = tuple(
                                    map(
                                        add,
                                        map(lambda u: 14 * u / 10,
                                            locations[x]),
                                        map(lambda u: 6 * u / 10,
                                            map(add, locations[x],
                                                (0, 0, 1)))))
                                for entry in ((p1, p2, p3), (p1, p2, p4),
                                              (p1, p3, p4), (p2, p3, p4)):
                                    g += polygon(entry, colors=color_dic[x])
                    # x=y or x=z or y=z case
                    if (x == y and x != z) or (x == z
                                               and x != y) or (y == z
                                                               and x != y):
                        if x == y: s, t = x, z
                        if x == z: s, t = x, y
                        if y == z: s, t = x, z
                        p1 = locations[s]
                        p2 = locations[t]
                        a = map(lambda u: u / 2, map(add, p1, p2))
                        b = map(subtract, p1, p2)
                        p3 = map(add, a, cross(b, (0, 0, 1)))
                        p4 = map(add, p3, (0, 0, 1 / len(elems)))
                        polys = ((p1, p2, p3), (p1, p2, p4), (p1, p3, p4),
                                 (p2, p3, p4))
                        cols = (color_dic[s], color_dic[t], color_dic[s],
                                color_dic[t])
                        for i in range(4):
                            g += polygon(polys[i], colors=cols[i])
                # x,y,z are distinct case
                if x != y and x != z and y != z:
                    if f(x, y) == f(y, x):
                        p1, p2, p3 = locations[x], locations[y], locations[z]
                        p4 = cross(map(subtract, p1, p2),
                                   map(subtract, p1, p3))
                        c1, c2, c3 = color_dic[x], color_dic[y], color_dic[z]
                        cols = (c1, c2, c3)
                        faces = ((p1, p2, p4), (p1, p3, p4), (p2, p3, p4))
                        for i in range(3):
                            g += polygon(faces[i], color=cols[i])
                    else:
                        p1, p2, p3 = locations[x], locations[y], locations[z]
                        c1, c2, c3 = color_dic[x], color_dic[y], color_dic[z]
                        sub_div = barycentric_subdivision(p1, p2, p3)
                        cols = (c1, c2, c3, c3)
                        for i in range(4):
                            g += polygon(sub_div[i], color=cols[i])
        g.save(file_name + '.x3d', axes=False)
Exemplo n.º 12
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    def render_flower(self,
                      initial_elements,
                      sides,
                      max_layer,
                      file_name,
                      dimension=2,
                      use_height=False,
                      initial_colors=(),
                      color_dic=None):
        """
        Create an image file depicting a flower complex.

        Note that the identification between colors and elements is not preserved across images with different
        `sides` and `max_layer` values unless a color dictionary is provided. Don't be misled by this.

        Also note that `max_layer` cannot be set much higher than `sides` without triangles overlapping. This can
        be dealt with in 3-space by using the `use_height` setting.

        Args:
            initial_elements (tuple): The first elements to be operated on.
            sides (int): The number of sides of the original polygon.
            max_layer (int): The number of steps out from the origin to construct.
            file_name (str): The name of the file generated.
            dim (int): The number of coordinate axes in the plot space.
            use_height (bool): If `dimension` is 3 then make use of the extra room in space.
            intial_colors (tuple): Colors used to display the complex. These are used before the colors in `self.initial_colors`.
            color_dic (dict): Dictionary of colors to be used when displaying the complex. This is used before the dictionary in `self.color_dic`.
        """

        values = self.grow_flower(initial_elements, sides, max_layer)
        while color_dic is None:
            color_dic = self.color_dic
            color_dic = self.color_dictionary(values, initial_colors)
        g = 0
        loc = lambda a, b, c=0: polar_location(
            a, b, sides, height=c, dimension=dimension)
        # initial points
        for n in range(sides - 1):
            p1 = (0, ) * dimension
            p2 = loc(1, n)
            p3 = loc(1, n + 1)
            if dimension == 3 and use_height:
                p2 = loc(1, n, 1)
                p3 = loc(1, n + 1, 1)
            c1 = color_dic[values[0][0]]  # left input
            c2 = color_dic[values[1][n]]  # right input
            c3 = color_dic[values[1][n + 1]]  # output
            sub_div = barycentric_subdivision(p1, p2, p3)
            cols = (c1, c2, c3, c3)
            for i in range(4):
                g += polygon(sub_div[i], color=cols[i])
        # subsequent points
        for r in range(1, max_layer - 1):
            for n in range(sides):
                p1 = loc(r, n)
                p2 = loc(r, n + 1)
                p3 = loc(r + 1, n)
                if dimension == 3 and use_height:
                    p1 = loc(r, n, r)
                    p2 = loc(r, n + 1, r)
                    p3 = loc(r + 1, n, r + 1)
                c1 = color_dic[values[r][n]]  # left input
                c2 = color_dic[values[r][(n + 1) % sides]]  # right input
                c3 = color_dic[values[r + 1][n]]  # output
                sub_div = barycentric_subdivision(p1, p2, p3)
                cols = (c1, c2, c3, c3)
                for i in range(4):
                    g += polygon(sub_div[i], color=cols[i])
        if dimension == 2: g.save(file_name + '.svg', axes=False)
        if dimension == 3: g.save(file_name + '.x3d')
Exemplo n.º 13
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def create_poly(face, color):
    return polygon(face_polys[face], rgbcolor=color)
Exemplo n.º 14
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def create_poly(face, color):
    return polygon(face_polys[face], rgbcolor=color)