ArcPVA

Bases: Curve

Creates a circular arc based on a point, a vector axis of rotation and an angle.

Attributes:

Name	Type	Description
angle	int | float	Angle in radians. Positive direction defined as counter-clockwise, based on the right-hand rule.
a	int | float	Axis vector x direction.
b	int | float	Axis vector y direction.
c	int | float	Axis vector z direction.
x0	int | float	Axis base x coordinate, default is zero.
y0	int | float	Axis base y coordinate, default is zero.
z0	int | float	Axis base z coordinate, default is zero.

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

class ArcPVA(Curve):
    """Creates a circular arc based on a point, a vector axis of rotation and an angle.

    Attributes:
        angle (int | float): Angle in radians.
            Positive direction defined as counter-clockwise, based on the right-hand rule.
        a (int | float): Axis vector x direction.
        b (int | float): Axis vector y direction.
        c (int | float): Axis vector z direction.
        x0 (int | float): Axis base x coordinate, default is zero.
        y0 (int | float): Axis base y coordinate, default is zero.
        z0 (int | float): Axis base z coordinate, default is zero.
    """

    angle = AsNumber(return_type=float)
    a = AsNumber(return_type=float)
    b = AsNumber(return_type=float)
    c = AsNumber(return_type=float)
    x0 = AsNumber(return_type=float)
    y0 = AsNumber(return_type=float)
    z0 = AsNumber(return_type=float)

    def __init__(
        self,
        start: Point,
        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,
    ):
        """Initialization method.

        Args:
            start: Point being rotated around the vector.
            angle: Angle in radians.
                Positive direction defined as counter-clockwise, based on the right-hand rule.
            a: Axis vector x direction.
            b: Axis vector y direction.
            c: Axis vector z direction.
            x0: Axis base x coordinate, default is zero.
            y0: Axis base y coordinate, default is zero.
            z0: Axis base z coordinate, default is zero.
        """
        self.start = start
        self.angle = angle
        self.a = a
        self.b = b
        self.c = c
        self.x0 = x0
        self.y0 = y0
        self.z0 = z0

    @property
    def end(self) -> NDArray3[np.float64]:
        x, y, z = self.path(1)
        return Point(x, y, z)

    def __eq__(self, other):
        DECIMALS = 10
        is_equal = True
        for u in np.linspace(0, 1, num=100, endpoint=True):
            u_self = np.all(np.round(self.path(u), decimals=DECIMALS))
            u_other = np.all(np.round(other.path(u), decimals=DECIMALS))
            if u_self != u_other:
                is_equal = False
                break
        return is_equal

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

    def __repr__(self):
        cls = type(self).__name__
        txt = (
            f"{cls}(start={self.start!r}, angle={self.angle:.2f}, "
            f"a={self.a:.2f}, b={self.b:.2f}, c={self.c:.2f}, "
            f"x0={self.x0:.2f}, y0={self.y0:.2f}, z0={self.z0:.2f})"
        )
        return txt

    @property
    def radius(self) -> float:
        """Returns the arc radius."""
        xyz0 = np.array([self.x0, self.y0, self.z0])
        a = self.start.xyz - xyz0
        b = np.array([self.a, self.b, self.c])
        r = a - np.dot(a, b) / np.dot(b, b) * b
        return np.sqrt(np.sum(r**2))

    @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)
        angle = self.angle
        xyz0 = np.array([self.x0, self.y0, self.z0])
        abc = np.array([self.a, self.b, self.c])
        pvec = self.start.xyz - xyz0
        part1 = pvec * math.cos(angle * u)
        part2 = np.cross(abc, pvec) * math.sin(angle * u)
        part3 = abc * np.dot(abc, pvec) * (1 - math.cos(angle * u))
        return xyz0 + part1 + part2 + part3

    def copy(self) -> Self:
        return ArcPVA(
            self.start.copy(),
            self.angle,
            self.a,
            self.b,
            self.c,
            self.x0,
            self.y0,
            self.z0,
        )

    def move(
        self, dx: int | float = 0.0, dy: int | float = 0.0, dz: int | float = 0.0
    ) -> Self:
        self.start.move(dx, dy, dz)  # also validates input
        self.x0 += float(dx)
        self.y0 += float(dy)
        self.z0 += float(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.start.rotate(angle, a, b, c, x0, y0, z0)  # also validates input
        xyz0 = np.array([self.x0, self.y0, self.z0])
        xyz0_rotated = rotate_point_xyz(
            xyz0[0], xyz0[1], xyz0[2], angle, a, b, c, x0, y0, z0
        )
        xyz1_rotated = rotate_point_xyz(
            self.a + x0, self.b + y0, self.c + z0, angle, a, b, c, x0, y0, z0
        )
        self.x0, self.y0, self.z0 = xyz0_rotated
        self.a, self.b, self.c = xyz1_rotated - xyz0
        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.start.mirror(a, b, c, x0, y0, z0)  # validates input, should be first
        xyz0 = np.array([self.x0, self.y0, self.z0])
        xyz0_mirrored = mirror_point_xyz(xyz0[0], xyz0[1], xyz0[2], a, b, c, x0, y0, z0)
        xyz1_mirrored = mirror_point_xyz(
            self.a + x0, self.b + y0, self.c + z0, a, b, c, x0, y0, z0
        )
        self.x0, self.y0, self.z0 = xyz0_mirrored
        self.a, self.b, self.c = xyz1_mirrored - xyz0
        return self

radius property

radius

Returns the arc radius.

__init__

__init__(start, angle, a, b, c, x0=0.0, y0=0.0, z0=0.0)

Initialization method.

Parameters:

Name	Type	Description	Default
start	Point	Point being rotated around the vector.	required
angle	int | float	Angle in radians. Positive direction defined as counter-clockwise, based on the right-hand rule.	required
a	int | float	Axis vector x direction.	required
b	int | float	Axis vector y direction.	required
c	int | float	Axis vector z direction.	required
x0	int | float	Axis base x coordinate, default is zero.	0.0
y0	int | float	Axis base y coordinate, default is zero.	0.0
z0	int | float	Axis base z coordinate, default is zero.	0.0

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

def __init__(
    self,
    start: Point,
    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,
):
    """Initialization method.

    Args:
        start: Point being rotated around the vector.
        angle: Angle in radians.
            Positive direction defined as counter-clockwise, based on the right-hand rule.
        a: Axis vector x direction.
        b: Axis vector y direction.
        c: Axis vector z direction.
        x0: Axis base x coordinate, default is zero.
        y0: Axis base y coordinate, default is zero.
        z0: Axis base z coordinate, default is zero.
    """
    self.start = start
    self.angle = angle
    self.a = a
    self.b = b
    self.c = c
    self.x0 = x0
    self.y0 = y0
    self.z0 = z0