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# Source code for gaphas.geometry

    """Geometry functions.

    Rectangle is a utility class for working with rectangles (unions and
    intersections).

    A point is represented as a tuple `(x, y)`.
    """

    from __future__ import annotations

    from math import sqrt
    from collections.abc import Iterator

    Point = tuple[float, float]  # x, y
    Rect = tuple[float, float, float, float]  # x, y, width, height

    class Rectangle:
        """Python Rectangle implementation. Rectangles can be added (union),
        substituted (intersection) and points and rectangles can be tested to be in
        the rectangle.

        >>> r1= Rectangle(1,1,5,5)
        >>> r2 = Rectangle(3,3,6,7)

        Test if two rectangles intersect:

        >>> if r1 - r2: 'yes'
        'yes'

        >>> r1, r2 = Rectangle(1,2,3,4), Rectangle(1,2,3,4)
        >>> r1 == r2
        True

        >>> r = Rectangle(-5, 3, 10, 8)
        >>> r.width = 2
        >>> r
        Rectangle(-5, 3, 2, 8)

        >>> r = Rectangle(-5, 3, 10, 8)
        >>> r.height = 2
        >>> r
        Rectangle(-5, 3, 10, 2)
        """

        def __init__(
            self,
            x: float = 0,
            y: float = 0,
            width: float | None = None,
            height: float | None = None,
            x1: float = 0,
            y1: float = 0,
        ):
            if width is None:
                self.x = min(x, x1)
                self.width = abs(x1 - x)
            else:
                self.x = x
                self.width = width
            if height is None:
                self.y = min(y, y1)
                self.height = abs(y1 - y)
            else:
                self.y = y
                self.height = height

        @property
        def x1(self) -> float:
            return self.x + self.width

        @x1.setter
        def x1(self, x1: float) -> None:
            width = x1 - self.x
            width = max(width, 0)
            self.width = width

        @property
        def y1(self) -> float:
            return self.y + self.height

        @y1.setter
        def y1(self, y1: float) -> None:
            height = y1 - self.y
            height = max(height, 0)
            self.height = height

        def expand(self, delta: float) -> None:
            """
            >>> r = Rectangle(-5, 3, 10, 8)
            >>> r.expand(5)
            >>> r
            Rectangle(-10, -2, 20, 18)
            """
            self.x -= delta
            self.y -= delta
            self.width += delta * 2
            self.height += delta * 2

        def tuple(self) -> tuple[float, float, float, float]:
            """A type safe version of `tuple(rectangle)`."""
            return (self.x, self.y, self.width, self.height)

        def __repr__(self) -> str:
            """
            >>> Rectangle(5,7,20,25)
            Rectangle(5, 7, 20, 25)
            """
            if self:
                return f"{self.__class__.__name__}({self.x}, {self.y}, {self.width}, {self.height})"
            return f"{self.__class__.__name__}()"

        def __iter__(self) -> Iterator[float]:
            """
            >>> tuple(Rectangle(1,2,3,4))
            (1, 2, 3, 4)
            """
            return iter((self.x, self.y, self.width, self.height))

        def __getitem__(self, index: int) -> float:
            """
            >>> Rectangle(1,2,3,4)[1]
            2
            """
            return (self.x, self.y, self.width, self.height)[index]

        def __bool__(self) -> bool:
            """
            >>> r=Rectangle(1,2,3,4)
            >>> if r: 'yes'
            'yes'
            >>> r = Rectangle(1,1,0,0)
            >>> if r: 'no'
            """
            return self.width > 0 and self.height > 0

        def __eq__(self, other: object) -> bool:
            return (
                isinstance(other, Rectangle)
                and self.x == other.x
                and self.y == other.y
                and self.width == other.width
                and self.height == other.height
            )

        def __add__(self, obj: Rectangle | Rect) -> Rectangle:
            """Create a new Rectangle is the union of the current rectangle with
            another Rectangle, tuple `(x,y)` or tuple `(x, y, width, height)`.

            >>> r=Rectangle(5, 7, 20, 25)
            >>> r + (0, 0)
            Traceback (most recent call last):
              ...
            TypeError: Can only add Rectangle or tuple (x, y, width, height), not (0, 0).
            >>> r + (20, 30, 40, 50)
            Rectangle(5, 7, 55, 73)
            """
            return Rectangle(self.x, self.y, self.width, self.height).__iadd__(obj)

        def __iadd__(self, obj: Rectangle | Rect) -> Rectangle:
            """
            >>> r = Rectangle()
            >>> r += Rectangle(5, 7, 20, 25)
            >>> r += (0, 0, 30, 10)
            >>> r
            Rectangle(0, 0, 30, 32)
            >>> r += 'aap'
            Traceback (most recent call last):
              ...
            TypeError: Can only add Rectangle or tuple (x, y, width, height), not 'aap'.
            """
            try:
                x, y, width, height = obj
            except ValueError as e:
                raise TypeError(
                    f"Can only add Rectangle or tuple (x, y, width, height), not {obj!r}."
                ) from e

            x1, y1 = x + width, y + height
            if self:
                ox1, oy1 = self.x + self.width, self.y + self.height
                self.x = min(self.x, x)
                self.y = min(self.y, y)
                self.x1 = max(ox1, x1)
                self.y1 = max(oy1, y1)
            else:
                self.x, self.y, self.width, self.height = x, y, width, height
            return self

        def __sub__(self, obj: Rectangle | Rect) -> Rectangle:
            """Create a new Rectangle is the union of the current rectangle with
            another Rectangle or tuple (x, y, width, height).

            >>> r = Rectangle(5, 7, 20, 25)
            >>> r - (20, 30, 40, 50)
            Rectangle(20, 30, 5, 2)
            >>> r - (30, 40, 40, 50)
            Rectangle()
            """
            return Rectangle(self.x, self.y, self.width, self.height).__isub__(obj)

        def __isub__(self, obj: Rectangle | Rect) -> Rectangle:
            """
            >>> r = Rectangle()
            >>> r -= Rectangle(5, 7, 20, 25)
            >>> r -= (0, 0, 30, 10)
            >>> r
            Rectangle(5, 7, 20, 3)
            >>> r -= 'aap'
            Traceback (most recent call last):
              ...
            TypeError: Can only subtract Rectangle or tuple (x, y, width, height), not 'aap'.
            """
            try:
                x, y, width, height = obj
            except ValueError as e:
                raise TypeError(
                    f"Can only subtract Rectangle or tuple (x, y, width, height), not {obj!r}."
                ) from e

            x1, y1 = x + width, y + height

            if self:
                ox1, oy1 = self.x + self.width, self.y + self.height
                self.x = max(self.x, x)
                self.y = max(self.y, y)
                self.x1 = min(ox1, x1)
                self.y1 = min(oy1, y1)
            else:
                self.x, self.y, self.width, self.height = x, y, width, height

            return self

        def __contains__(self, obj: Rectangle | Rect | Point) -> bool:
            """Check if a point `(x, y)` in inside rectangle `(x, y, width,
            height)` or if a rectangle instance is inside with the rectangle.

            >>> r=Rectangle(10, 5, 12, 12)
            >>> (0, 0) in r
            False
            >>> (10, 6) in r
            True
            >>> (12, 12) in r
            True
            >>> (100, 4) in r
            False
            >>> (11, 6, 5, 5) in r
            True
            >>> (11, 6, 15, 15) in r
            False
            >>> Rectangle(11, 6, 5, 5) in r
            True
            >>> Rectangle(11, 6, 15, 15) in r
            False
            >>> 'aap' in r
            Traceback (most recent call last):
              ...
            TypeError: Should compare to Rectangle, tuple (x, y, width, height) or point (x, y), not 'aap'.
            """
            try:
                x, y, width, height = obj  # type: ignore[misc]
                x1, y1 = x + width, y + width
            except ValueError:
                # point
                try:
                    (x, y) = (x1, y1) = obj  # type: ignore[misc]
                except ValueError as e:
                    raise TypeError(
                        f"Should compare to Rectangle, tuple (x, y, width, height) or point (x, y), not {obj!r}."
                    ) from e

            return x >= self.x and x1 <= self.x1 and y >= self.y and y1 <= self.y1

    def distance_point_point(point1: Point, point2: Point = (0.0, 0.0)) -> float:
        """Return the distance from point ``point1`` to ``point2``.

        >>> f"{distance_point_point((0,0), (1,1)):.3f}"
        '1.414'
        """
        dx = point1[0] - point2[0]
        dy = point1[1] - point2[1]
        return sqrt(dx * dx + dy * dy)

    def distance_point_point_fast(point1: Point, point2: Point = (0.0, 0.0)) -> float:
        """Return the distance from point ``point1`` to ``point2``. This version is
        faster than ``distance_point_point()``, but less precise.

        >>> distance_point_point_fast((0,0), (1,1))
        2
        """
        dx = point1[0] - point2[0]
        dy = point1[1] - point2[1]
        return abs(dx) + abs(dy)

    def distance_rectangle_border_point(rect: Rect | Rectangle, point: Point) -> float:
        """Return the distance (fast) from a rectangle ``(x, y, width,height)`` to
        a ``point``."""
        dx = dy = 0.0
        px, py = point
        rx, ry, rw, rh = rect  # typing: ignore[misc]
        rx1 = rx + rw
        ry1 = ry + rh

        if rx < px < rx1 and ry < py < ry1:
            return -min(px - rx, rx1 - px, py - ry, ry1 - py)

        if px < rx:
            dx = rx - px
        elif px > rx1:
            dx = px - rx1

        if py < ry:
            dy = ry - py
        elif py > ry1:
            dy = py - ry1

        return abs(dx) + abs(dy)

    def distance_rectangle_point(rect: Rect | Rectangle, point: Point) -> float:
        """Return the distance (fast) from a rectangle ``(x, y, width,height)`` to
        a ``point``."""
        return max(0, distance_rectangle_border_point(rect, point))

    def point_on_rectangle(
        rect: Rect | Rectangle, point: Point, border: bool = False
    ) -> Point:
        """Return the point on which ``point`` can be projecten on the rectangle.

        ``border = True`` will make sure the point is bound to
        the border of the reactangle. Otherwise, if the point is in the
        rectangle, it's okay.
        """
        px, py = point
        rx, ry, rw, rh = rect
        x_inside = y_inside = False

        if px < rx:
            px = rx
        elif px > rx + rw:
            px = rx + rw
        elif border:
            x_inside = True

        if py < ry:
            py = ry
        elif py > ry + rh:
            py = ry + rh
        elif border:
            y_inside = True

        if x_inside and y_inside:
            if min(abs(rx - px), abs(rx + rw - px)) > min(abs(ry - py), abs(ry + rh - py)):
                py = ry if py < ry + rh / 2.0 else ry + rh
            else:
                px = rx if px < rx + rw / 2.0 else rx + rw
        return px, py

    def distance_line_point(
        line_start: Point, line_end: Point, point: Point
    ) -> tuple[float, Point]:
        """Calculate the distance of a ``point`` from a line. The line is marked by
        begin and end point ``line_start`` and ``line_end``.

        A tuple is returned containing the distance and point on the line.
        """
        # The original end point:
        true_line_end = line_end

        # "Move" the line, so it "starts" on (0, 0)
        line_end = line_end[0] - line_start[0], line_end[1] - line_start[1]
        point = point[0] - line_start[0], point[1] - line_start[1]

        line_len_sqr = line_end[0] * line_end[0] + line_end[1] * line_end[1]

        # Both points are very near each other.
        if line_len_sqr < 0.0001:
            return distance_point_point(point), (line_start[0], line_start[1])

        projlen = (line_end[0] * point[0] + line_end[1] * point[1]) / line_len_sqr

        if projlen < 0.0:
            # Closest point is the start of the line.
            return distance_point_point(point), (line_start[0], line_start[1])
        elif projlen > 1.0:
            # Point has a projection after the line_end.
            return distance_point_point(point, line_end), (
                true_line_end[0],
                true_line_end[1],
            )
        else:
            # Projection is on the line. multiply the line_end with the projlen
            # factor to obtain the point on the line.
            proj = line_end[0] * projlen, line_end[1] * projlen
            return (
                distance_point_point((proj[0] - point[0], proj[1] - point[1])),
                (line_start[0] + proj[0], line_start[1] + proj[1]),
            )

    def intersect_line_line(
        line1_start: Point, line1_end: Point, line2_start: Point, line2_end: Point
    ) -> Point | None:
        """Find the point where the lines (segments) defined by ``(line1_start,
        line1_end)`` and ``(line2_start, line2_end)`` intersect.  If no
        intersection occurs, ``None`` is returned.

        >>> intersect_line_line((3, 0), (8, 10), (0, 0), (10, 10))
        (6, 6)
        >>> intersect_line_line((0, 0), (10, 10), (3, 0), (8, 10))
        (6, 6)
        >>> intersect_line_line((0, 0), (10, 10), (8, 10), (3, 0))
        (6, 6)
        >>> intersect_line_line((8, 10), (3, 0), (0, 0), (10, 10))
        (6, 6)
        >>> intersect_line_line((0, 0), (0, 10), (3, 0), (8, 10))
        >>> intersect_line_line((0, 0), (0, 10), (3, 0), (3, 10))

        Ticket #168:
        >>> intersect_line_line((478.0, 117.0), (478.0, 166.0), (527.5, 141.5), (336.5, 139.5))
        (478.5, 141.48167539267016)
        >>> intersect_line_line((527.5, 141.5), (336.5, 139.5), (478.0, 117.0), (478.0, 166.0))
        (478.5, 141.48167539267016)

        This is a Python translation of the ``lines_intersect``, C Code from
        Graphics Gems II, Academic Press, Inc. The original routine was written
        by Mukesh Prasad.

        EULA: The Graphics Gems code is copyright-protected. In other words, you
        cannot claim the text of the code as your own and resell it. Using the code
        is permitted in any program, product, or library, non-commercial or
        commercial. Giving credit is not required, though is a nice gesture. The
        code comes as-is, and if there are any flaws or problems with any Gems
        code, nobody involved with Gems - authors, editors, publishers, or
        webmasters - are to be held responsible. Basically, don't be a jerk, and
        remember that anything free comes with no guarantee.
        """
        #
        #   This function computes whether two line segments,
        #   respectively joining the input points (x1,y1) -- (x2,y2)
        #   and the input points (x3,y3) -- (x4,y4) intersect.
        #   If the lines intersect, the output variables x, y are
        #   set to coordinates of the point of intersection.
        #
        #   All values are in integers.  The returned value is rounded
        #   to the nearest integer point.
        #
        #   If non-integral grid points are relevant, the function
        #   can easily be transformed by substituting floating point
        #   calculations instead of integer calculations.
        #
        #   Entry
        #        x1, y1,  x2, y2   Coordinates of endpoints of one segment.
        #        x3, y3,  x4, y4   Coordinates of endpoints of other segment.
        #
        #   Exit
        #        x, y              Coordinates of intersection point.
        #
        #   The value returned by the function is one of:
        #
        #        DONT_INTERSECT    0
        #        DO_INTERSECT      1
        #        COLLINEAR         2
        #
        # Error conditions:
        #
        #     Depending upon the possible ranges, and particularly on 16-bit
        #     computers, care should be taken to protect from overflow.
        #
        #     In the following code, 'long' values have been used for this
        #     purpose, instead of 'int'.
        #

        x1, y1 = line1_start
        x2, y2 = line1_end
        x3, y3 = line2_start
        x4, y4 = line2_end

        # long a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */
        # long r1, r2, r3, r4;         /* 'Sign' values */
        # long denom, offset, num;     /* Intermediate values */

        # Compute a1, b1, c1, where line joining points 1 and 2
        # is "a1 x  +  b1 y  +  c1  =  0".

        a1 = y2 - y1
        b1 = x1 - x2
        c1 = x2 * y1 - x1 * y2

        # Compute r3 and r4.

        r3 = a1 * x3 + b1 * y3 + c1
        r4 = a1 * x4 + b1 * y4 + c1

        # Check signs of r3 and r4.  If both point 3 and point 4 lie on
        # same side of line 1, the line segments do not intersect.

        if r3 and r4 and (r3 * r4) >= 0:
            return None  # ( DONT_INTERSECT )

        # Compute a2, b2, c2

        a2 = y4 - y3
        b2 = x3 - x4
        c2 = x4 * y3 - x3 * y4

        # Compute r1 and r2

        r1 = a2 * x1 + b2 * y1 + c2
        r2 = a2 * x2 + b2 * y2 + c2

        # Check signs of r1 and r2.  If both point 1 and point 2 lie
        # on same side of second line segment, the line segments do
        # not intersect.

        if r1 and r2 and (r1 * r2) >= 0:  # SAME_SIGNS( r1, r2 ))
            return None  # ( DONT_INTERSECT )

        # Line segments intersect: compute intersection point.
        # The denom / 2 is to get rounding instead of truncating.  It
        # is added or subtracted to the numerator, depending upon the
        # sign of the numerator.

        denom = a1 * b2 - a2 * b1
        x_num = b1 * c2 - b2 * c1
        y_num = a2 * c1 - a1 * c2
        if not denom:
            return None  # ( COLLINEAR )

        offset = abs(denom) / 2
        x = ((x_num - offset) if (x_num < 0) else (x_num + offset)) / denom
        y = ((y_num - offset) if (y_num < 0) else (y_num + offset)) / denom
        return x, y

    def rectangle_contains(inner: Rect, outer: Rect) -> bool:
        """Returns True if ``inner`` rect is contained in ``outer`` rect."""
        ix, iy, iw, ih = inner
        ox, oy, ow, oh = outer
        return ox <= ix and oy <= iy and ox + ow >= ix + iw and oy + oh >= iy + ih

    def rectangle_intersects(recta: Rect, rectb: Rect) -> bool:
        """Return True if ``recta`` and ``rectb`` intersect.

        >>> rectangle_intersects((5,5,20, 20), (10, 10, 1, 1))
        True
        >>> rectangle_intersects((40, 30, 10, 1), (1, 1, 1, 1))
        False
        """
        ax, ay, aw, ah = recta
        bx, by, bw, bh = rectb
        return ax <= bx + bw and ax + aw >= bx and ay <= by + bh and ay + ah >= by

    def rectangle_clip(recta: Rect, rectb: Rect) -> Rect | None:
        """Return the clipped rectangle of ``recta`` and ``rectb``. If they do not
        intersect, ``None`` is returned.

        >>> rectangle_clip((0, 0, 20, 20), (10, 10, 20, 20))
        (10, 10, 10, 10)
        """
        ax, ay, aw, ah = recta
        bx, by, bw, bh = rectb
        x = max(ax, bx)
        y = max(ay, by)
        w = min(ax + aw, bx + bw) - x
        h = min(ay + ah, by + bh) - y
        return None if w < 0 or h < 0 else (x, y, w, h)