ellipse.py

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from math import cos
from math import pi
from math import sin
from math import sqrt

from compas.geometry import Frame
from compas.geometry import Point
from compas.geometry import Vector

from .conic import Conic
from .line import Line

PI2 = 2 * pi


class Ellipse(Conic):
    """An ellipse is a curve defined by a coordinate system and a major and minor axis.

    The centre of the ellipse is at the origin of the coordinate system.
    The major axis is parallel to the local x-axis.
    The minor axis is parallel to the local y-axis.
    The parameter domain of an ellipse is ``[0, 2*pi]``.
    Moving along the ellipse in the parameter direction corresponds to moving counter-clockwise around the origin of the local coordinate system.

    Parameters
    ----------
    major : float
        The major of the ellipse.
    minor : float
        The minor of the ellipse.
    frame : :class:`compas.geometry.Frame`, optional
        The local coordinate system of the ellipse.
        The default value is ``None``, in which case the ellipse is constructed in the XY plane of the world coordinate system.
    name : str, optional
        The name of the ellipse.

    Attributes
    ----------
    frame : :class:`compas.geometry.Frame`
        The coordinate frame of the ellipse.
    transformation : :class:`Transformation`, read-only
        The transformation from the local coordinate system of the ellipse (:attr:`frame`) to the world coordinate system.
    major : float
        The major of the ellipse.
    minor : float
        The minor of the ellipse.
    plane : :class:`compas.geometry.Plane`, read-only
        The plane of the ellipse.
    area : float, read-only
        The area of the ellipse.
    circumference : float, read-only
        The length of the circumference of the ellipse.
    semifocal : float, read-only
        The semi-focal distance of the ellipse.
        This is the distance from the center of the ellipse to the focus points.
    focal : float, read-only
        The distance between the two focus points.
    eccentricity : float, read-only
        The eccentricity of the ellipse.
        This is the ratio between the semifocal length to the length of the semi-major axis.
    focus1 : :class:`compas.geometry.Point`, read-only
        The first focus point of the ellipse.
    focus2 : :class:`compas.geometry.Point`, read-only
        The second focus point of the ellipse.
    directix1 : :class:`compas.geometry.Line`, read-only
        The first directix of the ellipse.
        The directix is perpendicular to the major axis
        and passes through a point at a distance ``major **2 / semifocal`` along the positive xaxis from the center of the ellipse.
    directix2 : :class:`compas.geometry.Line`, read-only
        The second directix of the ellipse.
        The directix is perpendicular to the major axis
        and passes through a point at a distance ``major **2 / semifocal`` along the negative xaxis from the center of the ellipse.
    is_closed : bool, read-only
        True.
    is_periodic : bool, read-only
        True.
    is_circle : bool, read-only
        True if the ellipse is a circle.

    See Also
    --------
    :class:`compas.geometry.Circle`, :class:`compas.geometry.Hyperbola`, :class:`compas.geometry.Parabola`

    Examples
    --------
    Construct an ellipse in the world XY plane.

    >>> from compas.geometry import Frame, Ellipse
    >>> ellipse = Ellipse(major=3, minor=2, frame=Frame.worldXY())
    >>> ellipse = Ellipse(major=3, minor=2)

    Construct an ellipse such that its normal aligns with a given line.

    >>> from compas.geometry import Line, Frame, Plane, Ellipse
    >>> line = Line([0, 0, 0], [1, 1, 1])
    >>> plane = Plane(line.end, line.direction)
    >>> ellipse = Ellipse.from_plane_major_minor(plane, 3, 2)
    >>> ellipse = Ellipse(major=3, minor=2, frame=Frame.from_plane(plane))

    Visualise the line, ellipse, and frame of the ellipse with the COMPAS viewer.

    >>> from compas_viewer import Viewer  # doctest: +SKIP
    >>> viewer = Viewer()                    # doctest: +SKIP
    >>> viewer.scene.add(line)                  # doctest: +SKIP
    >>> viewer.scene.add(ellipse)               # doctest: +SKIP
    >>> viewer.scene.add(ellipse.frame)         # doctest: +SKIP
    >>> viewer.show()                      # doctest: +SKIP

    """

    DATASCHEMA = {
        "type": "object",
        "properties": {
            "major": {"type": "number", "minimum": 0},
            "minor": {"type": "number", "minimum": 0},
            "frame": Frame.DATASCHEMA,
        },
        "required": ["major", "minor", "frame"],
    }

    @property
    def __data__(self):
        return {
            "major": self.major,
            "minor": self.minor,
            "frame": self.frame.__data__,
        }

    @classmethod
    def __from_data__(cls, data):
        return cls(
            major=data["major"],
            minor=data["minor"],
            frame=Frame.__from_data__(data["frame"]),
        )

    def __init__(self, major=1.0, minor=1.0, frame=None, name=None):
        super(Ellipse, self).__init__(frame=frame, name=name)
        self._major = None
        self._minor = None
        self.major = major
        self.minor = minor

    def __repr__(self):
        return "{0}(major={1!r}, minor={2}, frame={3!r})".format(
            type(self).__name__,
            self.major,
            self.minor,
            self.frame,
        )

    def __eq__(self, other):
        try:
            other_frame = other.frame
            other_major = other.major
            other_minor = other.minor
        except Exception:
            return False
        return self.major == other_major and self.minor == other_minor, self.frame == other_frame

    # ==========================================================================
    # Properties
    # ==========================================================================

    @property
    def center(self):
        return self.frame.point

    @center.setter
    def center(self, point):
        self.frame.point = point

    @property
    def major(self):
        if self._major is None:
            raise ValueError("Length of major axis is not set.")
        return self._major

    @major.setter
    def major(self, major):
        if major < 0:
            raise ValueError("Major axis length cannot be negative.")
        self._major = float(major)

    @property
    def minor(self):
        if self._minor is None:
            raise ValueError("Length of minor axis is not set.")
        return self._minor

    @minor.setter
    def minor(self, minor):
        if minor < 0:
            raise ValueError("Minor axis length cannot be negative.")
        self._minor = float(minor)

    @property
    def semifocal(self):
        return sqrt(self.major**2 - self.minor**2)

    @property
    def focal(self):
        return 2 * self.semifocal

    @property
    def eccentricity(self):
        return self.semifocal / self.major

    @property
    def focus1(self):
        return self.frame.point + self.frame.xaxis * +self.semifocal

    @property
    def focus2(self):
        return self.frame.point + self.frame.xaxis * -self.semifocal

    @property
    def vertex1(self):
        return self.frame.point + self.frame.xaxis * self.major

    @property
    def vertex2(self):
        return self.frame.point + self.frame.xaxis * -self.major

    @property
    def directix1(self):
        d1 = self.major**2 / self.semifocal
        p1 = self.frame.point + self.frame.xaxis * +d1
        return Line.from_point_and_vector(p1, self.frame.yaxis)

    @property
    def directix2(self):
        d2 = self.major**2 / self.semifocal
        p2 = self.frame.point + self.frame.xaxis * -d2
        return Line.from_point_and_vector(p2, self.frame.yaxis)

    @property
    def area(self):
        return pi * self.major * self.minor

    @property
    def circumference(self):
        raise NotImplementedError

    @property
    def is_circle(self):
        return self.major == self.minor

    @property
    def is_closed(self):
        return True

    @property
    def is_periodic(self):
        return True

    # ==========================================================================
    # Constructors
    # ==========================================================================

    @classmethod
    def from_point_major_minor(cls, point, major, minor):
        """Construct a ellipse from a point and major and minor axis lengths.

        Parameters
        ----------
        point : :class:`compas.geometry.Point`
            The center point of the ellipse.
        major : float
            The major axis length.
        minor : float
            The minor axis length.

        Returns
        -------
        :class:`Ellipse`
            The constructed ellipse.

        """
        frame = Frame(point, [1, 0, 0], [0, 1, 0])
        return cls(major=major, minor=minor, frame=frame)

    @classmethod
    def from_plane_major_minor(cls, plane, major, minor):
        """Construct a ellipse from a point and major and minor axis lengths.

        Parameters
        ----------
        plane : :class:`compas.geometry.Plane`
            The plane of the ellipse.
        major : float
            The major axis length.
        minor : float
            The minor axis length.

        Returns
        -------
        :class:`Ellipse`
            The constructed ellipse.

        """
        frame = Frame.from_plane(plane)
        return cls(major=major, minor=minor, frame=frame)

    # ==========================================================================
    # Methods
    # ==========================================================================

    def point_at(self, t, world=True):
        """Compute the point at a specific parameter.

        Parameters
        ----------
        t : float
            The parameter value.
        world : bool, optional
            If ``True``, the point is returned in world coordinates.

        Returns
        -------
        :class:`compas.geometry.Point`
            The point at the parameter.

        See Also
        --------
        :meth:`normal_at`, :meth:`tangent_at`

        Notes
        -----
        The location of the point is expressed with respect to the world coordinate system.

        """
        t = t * PI2
        x = self.major * cos(t)
        y = self.minor * sin(t)
        point = Point(x, y, 0)
        if world:
            point.transform(self.transformation)
        return point

    def tangent_at(self, t, world=True):
        """Compute the tangent at a specific parameter.

        Parameters
        ----------
        t : float
            The parameter value.
        world : bool, optional
            If ``True``, the tangent is returned in world coordinates.

        Returns
        -------
        :class:`compas.geometry.Vector`
            The tangent vector at the parameter.

        See Also
        --------
        :meth:`point_at`, :meth:`normal_at`

        Notes
        -----
        The orientation of the vector is expressed with respect to the world coordinate system.

        """
        normal = self.normal_at(t, world=False)
        zaxis = Vector(0, 0, 1)
        tangent = normal.cross(zaxis)
        tangent.unitize()
        if world:
            tangent.transform(self.transformation)
        return tangent

    def normal_at(self, t, world=True):
        """Compute the normal at a specific parameter.

        Parameters
        ----------
        t : float
            The parameter value.
        world : bool, optional
            If ``True``, the normal is returned in world coordinates.

        Returns
        -------
        :class:`compas.geometry.Vector`
            The normal vector at the parameter.

        See Also
        --------
        :meth:`point_at`, :meth:`tangent_at`

        Notes
        -----
        The orientation of the vector is expressed with respect to the world coordinate system.

        """
        point = self.point_at(t, world=False)
        f1 = Point(+self.semifocal, 0, 0)
        f2 = Point(-self.semifocal, 0, 0)
        normal = (f1 - point).unitized() + (f2 - point).unitized()
        normal.unitize()
        if world:
            normal.transform(self.transformation)
        return normal