import warp as wp

from warp.fem.types import ElementIndex, Coords, Sample, make_free_sample, OUTSIDE
from warp.fem.cache import cached_arg_value

from .geometry import Geometry
from .element import Square, LinearEdge


@wp.struct
class Grid2DCellArg:
    res: wp.vec2i
    cell_size: wp.vec2
    origin: wp.vec2


class Grid2D(Geometry):
    """Two-dimensional regular grid geometry"""

    dimension = 2

    Permutation = wp.types.matrix(shape=(2, 2), dtype=int)
    ROTATION = wp.constant(Permutation(0, 1, 1, 0))

    def __init__(self, res: wp.vec2i, bounds_lo: wp.vec2 = wp.vec2(0.0), bounds_hi: wp.vec2 = wp.vec2(1.0)):
        """Constructs a dense 2D grid

        Args:
            res: Resolution of the grid along each dimension
            bounds_lo: Position of the lower bound of the axis-aligned grid
            bounds_up: Position of the upper bound of the axis-aligned grid
        """

        self.bounds_lo = bounds_lo
        self.bounds_hi = bounds_hi

        self._res = res

    @property
    def extents(self) -> wp.vec3:
        # Avoid using native sub due to higher over of calling builtins from Python
        return wp.vec2(
            self.bounds_hi[0] - self.bounds_lo[0],
            self.bounds_hi[1] - self.bounds_lo[1],
        )

    @property
    def cell_size(self) -> wp.vec2:
        ex = self.extents
        return wp.vec2(
            ex[0] / self.res[0],
            ex[1] / self.res[1],
        )

    def cell_count(self):
        return self.res[0] * self.res[1]

    def vertex_count(self):
        return (self.res[0] + 1) * (self.res[1] + 1)

    def side_count(self):
        return 2 * self.cell_count() + self.res[0] + self.res[1]

    def boundary_side_count(self):
        return 2 * (self.res[0] + self.res[1])

    def reference_cell(self) -> Square:
        return Square()

    def reference_side(self) -> LinearEdge:
        return LinearEdge()

    @property
    def res(self):
        return self._res

    @property
    def origin(self):
        return self.bounds_lo

    @property
    def strides(self):
        return wp.vec2i(self.res[1], 1)

    # Utility device functions
    CellArg = Grid2DCellArg
    Cell = wp.vec2i

    @wp.func
    def _to_2d_index(x_stride: int, index: int):
        x = index // x_stride
        y = index - x_stride * x
        return wp.vec2i(x, y)

    @wp.func
    def _from_2d_index(x_stride: int, index: wp.vec2i):
        return x_stride * index[0] + index[1]

    @wp.func
    def cell_index(res: wp.vec2i, cell: Cell):
        return Grid2D._from_2d_index(res[1], cell)

    @wp.func
    def get_cell(res: wp.vec2i, cell_index: ElementIndex):
        return Grid2D._to_2d_index(res[1], cell_index)

    @wp.struct
    class Side:
        axis: int  # normal; 0: horizontal, 1: vertical
        origin: wp.vec2i  # index of vertex at corner (0,0)

    @wp.struct
    class SideArg:
        cell_count: int
        axis_offsets: wp.vec2i
        cell_arg: Grid2DCellArg

    SideIndexArg = SideArg

    @wp.func
    def _rotate(axis: int, vec: wp.vec2i):
        return wp.vec2i(
            vec[Grid2D.ROTATION[axis, 0]],
            vec[Grid2D.ROTATION[axis, 1]],
        )

    @wp.func
    def _rotate(axis: int, vec: wp.vec2):
        return wp.vec2(
            vec[Grid2D.ROTATION[axis, 0]],
            vec[Grid2D.ROTATION[axis, 1]],
        )

    @wp.func
    def side_index(arg: SideArg, side: Side):
        alt_axis = Grid2D.ROTATION[side.axis, 0]
        if side.origin[0] == arg.cell_arg.res[alt_axis]:
            # Upper-boundary side
            longitude = side.origin[1]
            return 2 * arg.cell_count + arg.axis_offsets[side.axis] + longitude

        cell_index = Grid2D.cell_index(arg.cell_arg.res, Grid2D._rotate(side.axis, side.origin))
        return side.axis * arg.cell_count + cell_index

    @wp.func
    def get_side(arg: SideArg, side_index: ElementIndex):
        if side_index < 2 * arg.cell_count:
            axis = side_index // arg.cell_count
            cell_index = side_index - axis * arg.cell_count
            origin = Grid2D._rotate(axis, Grid2D.get_cell(arg.cell_arg.res, cell_index))
            return Grid2D.Side(axis, origin)

        axis_side_index = side_index - 2 * arg.cell_count
        if axis_side_index < arg.axis_offsets[1]:
            axis = 0
        else:
            axis = 1

        altitude = arg.cell_arg.res[Grid2D.ROTATION[axis, 0]]
        longitude = axis_side_index - arg.axis_offsets[axis]

        origin_loc = wp.vec2i(altitude, longitude)
        return Grid2D.Side(axis, origin_loc)

    # Geometry device interface

    @cached_arg_value
    def cell_arg_value(self, device) -> CellArg:
        args = self.CellArg()
        args.res = self.res
        args.cell_size = self.cell_size
        args.origin = self.bounds_lo
        return args

    @wp.func
    def cell_position(args: CellArg, s: Sample):
        cell = Grid2D.get_cell(args.res, s.element_index)
        return (
            wp.vec2(
                (float(cell[0]) + s.element_coords[0]) * args.cell_size[0],
                (float(cell[1]) + s.element_coords[1]) * args.cell_size[1],
            )
            + args.origin
        )

    @wp.func
    def cell_deformation_gradient(args: CellArg, s: Sample):
        return wp.diag(args.cell_size)

    @wp.func
    def cell_inverse_deformation_gradient(args: CellArg, s: Sample):
        return wp.diag(wp.cw_div(wp.vec2(1.0), args.cell_size))

    @wp.func
    def cell_lookup(args: CellArg, pos: wp.vec2):
        loc_pos = wp.cw_div(pos - args.origin, args.cell_size)
        x = wp.clamp(loc_pos[0], 0.0, float(args.res[0]))
        y = wp.clamp(loc_pos[1], 0.0, float(args.res[1]))

        x_cell = wp.min(wp.floor(x), float(args.res[0]) - 1.0)
        y_cell = wp.min(wp.floor(y), float(args.res[1]) - 1.0)

        coords = Coords(x - x_cell, y - y_cell, 0.0)
        cell_index = Grid2D.cell_index(args.res, Grid2D.Cell(int(x_cell), int(y_cell)))

        return make_free_sample(cell_index, coords)

    @wp.func
    def cell_lookup(args: CellArg, pos: wp.vec2, guess: Sample):
        return Grid2D.cell_lookup(args, pos)

    @wp.func
    def cell_measure(args: CellArg, s: Sample):
        return args.cell_size[0] * args.cell_size[1]

    @wp.func
    def cell_normal(args: CellArg, s: Sample):
        return wp.vec2(0.0)

    @cached_arg_value
    def side_arg_value(self, device) -> SideArg:
        args = self.SideArg()

        args.axis_offsets = wp.vec2i(
            0,
            self.res[0],
        )
        args.cell_count = self.cell_count()
        args.cell_arg = self.cell_arg_value(device)
        return args

    def side_index_arg_value(self, device) -> SideIndexArg:
        return self.side_arg_value(device)

    @wp.func
    def boundary_side_index(args: SideArg, boundary_side_index: int):
        """Boundary side to side index"""

        axis_side_index = boundary_side_index // 2
        border = boundary_side_index - 2 * axis_side_index

        if axis_side_index < args.axis_offsets[1]:
            axis = 0
        else:
            axis = 1

        longitude = axis_side_index - args.axis_offsets[axis]
        altitude = border * args.cell_arg.res[axis]

        side = Grid2D.Side(axis, wp.vec2i(altitude, longitude))
        return Grid2D.side_index(args, side)

    @wp.func
    def side_position(args: SideArg, s: Sample):
        side = Grid2D.get_side(args, s.element_index)

        coord = wp.select((side.origin[0] == 0) == (side.axis == 0), 1.0 - s.element_coords[0], s.element_coords[0])

        local_pos = wp.vec2(
            float(side.origin[0]),
            float(side.origin[1]) + coord,
        )

        pos = args.cell_arg.origin + wp.cw_mul(Grid2D._rotate(side.axis, local_pos), args.cell_arg.cell_size)

        return pos

    @wp.func
    def side_deformation_gradient(args: SideArg, s: Sample):
        side = Grid2D.get_side(args, s.element_index)

        sign = wp.select((side.origin[0] == 0) == (side.axis == 0), -1.0, 1.0)

        return wp.cw_mul(Grid2D._rotate(side.axis, wp.vec2(0.0, sign)), args.cell_arg.cell_size)

    @wp.func
    def side_inner_inverse_deformation_gradient(args: SideArg, s: Sample):
        return Grid2D.cell_inverse_deformation_gradient(args.cell_arg, s)

    @wp.func
    def side_outer_inverse_deformation_gradient(args: SideArg, s: Sample):
        return Grid2D.cell_inverse_deformation_gradient(args.cell_arg, s)

    @wp.func
    def side_measure(args: SideArg, s: Sample):
        side = Grid2D.get_side(args, s.element_index)
        long_axis = Grid2D.ROTATION[side.axis, 1]
        return args.cell_arg.cell_size[long_axis]

    @wp.func
    def side_measure_ratio(args: SideArg, s: Sample):
        side = Grid2D.get_side(args, s.element_index)
        alt_axis = Grid2D.ROTATION[side.axis, 0]
        return 1.0 / args.cell_arg.cell_size[alt_axis]

    @wp.func
    def side_normal(args: SideArg, s: Sample):
        side = Grid2D.get_side(args, s.element_index)

        sign = wp.select(side.origin[0] == 0, 1.0, -1.0)

        local_n = wp.vec2(sign, 0.0)
        return Grid2D._rotate(side.axis, local_n)

    @wp.func
    def side_inner_cell_index(arg: SideArg, side_index: ElementIndex):
        side = Grid2D.get_side(arg, side_index)

        inner_alt = wp.select(side.origin[0] == 0, side.origin[0] - 1, 0)

        inner_origin = wp.vec2i(inner_alt, side.origin[1])

        cell = Grid2D._rotate(side.axis, inner_origin)
        return Grid2D.cell_index(arg.cell_arg.res, cell)

    @wp.func
    def side_outer_cell_index(arg: SideArg, side_index: ElementIndex):
        side = Grid2D.get_side(arg, side_index)

        alt_axis = Grid2D.ROTATION[side.axis, 0]
        outer_alt = wp.select(
            side.origin[0] == arg.cell_arg.res[alt_axis], side.origin[0], arg.cell_arg.res[alt_axis] - 1
        )

        outer_origin = wp.vec2i(outer_alt, side.origin[1])

        cell = Grid2D._rotate(side.axis, outer_origin)
        return Grid2D.cell_index(arg.cell_arg.res, cell)

    @wp.func
    def side_inner_cell_coords(args: SideArg, side_index: ElementIndex, side_coords: Coords):
        side = Grid2D.get_side(args, side_index)

        inner_alt = wp.select(side.origin[0] == 0, 1.0, 0.0)

        side_coord = wp.select((side.origin[0] == 0) == (side.axis == 0), 1.0 - side_coords[0], side_coords[0])

        coords = Grid2D._rotate(side.axis, wp.vec2(inner_alt, side_coord))
        return Coords(coords[0], coords[1], 0.0)

    @wp.func
    def side_outer_cell_coords(args: SideArg, side_index: ElementIndex, side_coords: Coords):
        side = Grid2D.get_side(args, side_index)

        alt_axis = Grid2D.ROTATION[side.axis, 0]
        outer_alt = wp.select(side.origin[0] == args.cell_arg.res[alt_axis], 0.0, 1.0)

        side_coord = wp.select((side.origin[0] == 0) == (side.axis == 0), 1.0 - side_coords[0], side_coords[0])

        coords = Grid2D._rotate(side.axis, wp.vec2(outer_alt, side_coord))
        return Coords(coords[0], coords[1], 0.0)

    @wp.func
    def side_from_cell_coords(
        args: SideArg,
        side_index: ElementIndex,
        element_index: ElementIndex,
        element_coords: Coords,
    ):
        side = Grid2D.get_side(args, side_index)
        cell = Grid2D.get_cell(args.cell_arg.res, element_index)

        if float(side.origin[0] - cell[side.axis]) == element_coords[side.axis]:
            long_axis = Grid2D.ROTATION[side.axis, 1]
            axis_coord = element_coords[long_axis]
            side_coord = wp.select((side.origin[0] == 0) == (side.axis == 0), 1.0 - axis_coord, axis_coord)
            return Coords(side_coord, 0.0, 0.0)

        return Coords(OUTSIDE)

    @wp.func
    def side_to_cell_arg(side_arg: SideArg):
        return side_arg.cell_arg