ArcP3

Bases: Curve

Creates an arc curve object, generated from three points in space.

Implementation based on WikiPedia. For more information, see Curve documentation.

Parameters:

Name	Type	Description	Default
centre	Point	Arc center point	required
inverse_sector	bool	Specifies if to use the outer (True) or inner (False) sector of the swept circle. Defaults to False.	False

Source code in pymesh/geo/curves/arc3p.py

class Arc3P(Curve):
    """Creates an arc curve object, generated from three points in space.

    Implementation based on [WikiPedia](https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula).
    For more information, see Curve documentation.

    Args:
        centre (Point): Arc center point
        inverse_sector (bool): Specifies if to use the outer
            (True) or inner (False) sector of the swept circle.
            Defaults to False.
    """

    centre = AsInstanceOf(Point)
    inverse_sector = AsInstanceOf(bool)

    def __init__(
        self,
        centre: Point,
        start: Point,
        end: Point,
        inverse_sector: bool = False,
    ):
        """Initialization method.

        Args:
            centre: Arc center point
            start: Arc start point
            end: Arc end point
            inverse_sector: Specifies if to use the outer (True)
                or inner (False) sector of the swept circle.
                Defaults to False.

        Raises:
            ValueError: If the start and end points are located
                at different radii from the centre point.
            ValueError: If cross product of the centre-to-start
                and centre-to-end vectors is zero.
        """
        self.centre = centre
        self.start = start
        self.end = end
        self.inverse_sector = inverse_sector
        validate_radii_and_cross_product(centre, start, end)

    def __eq__(self, other):
        return (
            self.centre == other.centre
            and self.start == other.start
            and self.end == other.end
        )

    def __ne__(self, other):
        return not self.__eq__(other)

    def __repr__(self):
        cls = type(self).__name__
        c, s, e, i = self.centre, self.start, self.end, self.inverse_sector
        return f"{cls}(centre={c}, start={s}, end={e}, inverse_sector={i})"

    def copy(self) -> Self:
        return Arc3P(
            self.centre.copy(), self.start.copy(), self.end.copy(), self.inverse_sector
        )

    def move(
        self, dx: int | float = 0.0, dy: int | float = 0.0, dz: int | float = 0.0
    ) -> Self:
        self.centre.move(dx, dy, dz)
        self.start.move(dx, dy, dz)
        self.end.move(dx, dy, dz)
        return self

    def rotate(
        self,
        angle: int | float,
        a: int | float,
        b: int | float,
        c: int | float,
        x0: int | float = 0.0,
        y0: int | float = 0.0,
        z0: int | float = 0.0,
    ) -> Self:
        self.centre.rotate(angle, a, b, c, x0, y0, z0)
        self.start.rotate(angle, a, b, c, x0, y0, z0)
        self.end.rotate(angle, a, b, c, x0, y0, z0)
        return self

    def mirror(
        self,
        a: int | float,
        b: int | float,
        c: int | float,
        x0: int | float = 0.0,
        y0: int | float = 0.0,
        z0: int | float = 0.0,
    ) -> Self:
        self.centre.mirror(a, b, c, x0, y0, z0)
        self.start.mirror(a, b, c, x0, y0, z0)
        self.end.mirror(a, b, c, x0, y0, z0)
        return self

    @property
    def radius(self) -> float:
        return np.sqrt(np.sum((self.start - self.centre) ** 2))

    @property
    def cross_product(self) -> NDArray3[np.float64]:
        sign = -1 if self.inverse_sector else 1
        return sign * np.cross((self.start - self.centre), (self.end - self.centre))

    @property
    def plane_unit_normal(self) -> NDArray3[np.float64]:
        return self.cross_product / np.sqrt(np.sum(self.cross_product**2))

    @property
    def angle(self) -> float:
        angle = np.arccos(
            np.dot((self.start - self.centre), (self.end - self.centre))
            / (self.radius**2)
        )
        angle = 2 * math.pi - angle if self.inverse_sector else angle
        return angle

    @property
    def length(self) -> float:
        return self.radius * self.angle

    def path(self, u: int | float, flip: bool = False) -> NDArray3[np.float64]:
        u = validate_curve_path_parameters(u, flip)
        v, k, a = (self.start - self.centre), self.plane_unit_normal, self.angle
        xyz0 = self.centre.xyz
        part1 = v * math.cos(a * u)
        part2 = np.cross(k, v) * math.sin(a * u)
        part3 = k * np.dot(k, v) * (1 - math.cos(a * u))
        return xyz0 + part1 + part2 + part3

__init__

__init__(centre, start, end, inverse_sector=False)

Initialization method.

Parameters:

Name	Type	Description	Default
centre	Point	Arc center point	required
start	Point	Arc start point	required
end	Point	Arc end point	required
inverse_sector	bool	Specifies if to use the outer (True) or inner (False) sector of the swept circle. Defaults to False.	False

Raises:

Type	Description
ValueError	If the start and end points are located at different radii from the centre point.
ValueError	If cross product of the centre-to-start and centre-to-end vectors is zero.

Source code in pymesh/geo/curves/arc3p.py

def __init__(
    self,
    centre: Point,
    start: Point,
    end: Point,
    inverse_sector: bool = False,
):
    """Initialization method.

    Args:
        centre: Arc center point
        start: Arc start point
        end: Arc end point
        inverse_sector: Specifies if to use the outer (True)
            or inner (False) sector of the swept circle.
            Defaults to False.

    Raises:
        ValueError: If the start and end points are located
            at different radii from the centre point.
        ValueError: If cross product of the centre-to-start
            and centre-to-end vectors is zero.
    """
    self.centre = centre
    self.start = start
    self.end = end
    self.inverse_sector = inverse_sector
    validate_radii_and_cross_product(centre, start, end)