`Torus`#

class ansys.geometry.core.shapes.surfaces.torus.Torus(origin: numpy.ndarray | ansys.geometry.core.typing.RealSequence | ansys.geometry.core.math.point.Point3D, major_radius: pint.Quantity | ansys.geometry.core.misc.measurements.Distance | ansys.geometry.core.typing.Real, minor_radius: pint.Quantity | ansys.geometry.core.misc.measurements.Distance | ansys.geometry.core.typing.Real, reference: numpy.ndarray | ansys.geometry.core.typing.RealSequence | ansys.geometry.core.math.vector.UnitVector3D | ansys.geometry.core.math.vector.Vector3D = UNITVECTOR3D_X, axis: numpy.ndarray | ansys.geometry.core.typing.RealSequence | ansys.geometry.core.math.vector.UnitVector3D | ansys.geometry.core.math.vector.Vector3D = UNITVECTOR3D_Z)#

Bases: ansys.geometry.core.shapes.surfaces.surface.Surface

Provides 3D torus representation.

Parameters:

originndarray | RealSequence | Point3D: Centered origin of the torus.
major_radiusQuantity | Distance | Real: Major radius of the torus.
minor_radiusQuantity | Distance | Real: Minor radius of the torus.
referencendarray | RealSequence | UnitVector3D | Vector3D: X-axis direction.
axisndarray | RealSequence | UnitVector3D | Vector3D: Z-axis direction.

Overview#

Abstract methods

`contains_param`	Check a parameter is within the parametric range of the surface.
`contains_point`	Check a point is contained by the surface.

Methods

`transformed_copy`	Create a transformed copy of the torus from a transformation matrix.
`mirrored_copy`	Create a mirrored copy of the torus along the y-axis.
`evaluate`	Evaluate the torus at the given parameters.
`parameterization`	Parameterize the torus surface as a tuple (U and V respectively).
`project_point`	Project a point onto the torus and evaluate the torus.

Properties

`origin`	Origin of the torus.
`major_radius`	Semi-major radius of the torus.
`minor_radius`	Semi-minor radius of the torus.
`dir_x`	X-direction of the torus.
`dir_y`	Y-direction of the torus.
`dir_z`	Z-direction of the torus.
`volume`	Volume of the torus.
`surface_area`	Surface_area of the torus.

Special methods

__eq__

Equals operator for the Torus class.

Import detail#

from ansys.geometry.core.shapes.surfaces.torus import Torus

Property detail#

property Torus.origin: ansys.geometry.core.math.point.Point3D#: Origin of the torus.

property Torus.major_radius: pint.Quantity#: Semi-major radius of the torus.

property Torus.minor_radius: pint.Quantity#: Semi-minor radius of the torus.

property Torus.dir_x: ansys.geometry.core.math.vector.UnitVector3D#: X-direction of the torus.

property Torus.dir_y: ansys.geometry.core.math.vector.UnitVector3D#: Y-direction of the torus.

property Torus.dir_z: ansys.geometry.core.math.vector.UnitVector3D#: Z-direction of the torus.

property Torus.volume: pint.Quantity#: Volume of the torus.

property Torus.surface_area: pint.Quantity#: Surface_area of the torus.

Method detail#

Torus.__eq__(other: Torus) → bool#: Equals operator for the Torus class.

Torus.transformed_copy(matrix: ansys.geometry.core.math.matrix.Matrix44) → Torus#

Create a transformed copy of the torus from a transformation matrix.

Parameters:

matrixMatrix44: 4x4 transformation matrix to apply to the torus.

Returns:

Torus: New torus that is the transformed copy of the original torus.

Torus.mirrored_copy() → Torus#

Create a mirrored copy of the torus along the y-axis.

Returns:

Torus: New torus that is a mirrored copy of the original torus.

Torus.evaluate(parameter: ansys.geometry.core.shapes.parameterization.ParamUV) → TorusEvaluation#

Evaluate the torus at the given parameters.

Parameters:

parameterParamUV: Parameters (u,v) to evaluate the torus at.

Returns:

TorusEvaluation: Resulting evaluation.

Torus.parameterization() → tuple[ansys.geometry.core.shapes.parameterization.Parameterization, ansys.geometry.core.shapes.parameterization.Parameterization]#

Parameterize the torus surface as a tuple (U and V respectively).

The U parameter specifies the longitude angle, increasing clockwise (east) about the axis (right-hand corkscrew law). It has a zero parameter at Geometry.Frame.DirX and a period of 2*pi.

The V parameter specifies the latitude, increasing north, with a zero parameter at the equator. For the donut, where the major radius is greater than the minor radius, the range is [-pi, pi] and the parameterization is periodic. For a degenerate torus, the range is restricted accordingly and the parameterization is non-periodic.

Returns:

tuple[Parameterization, Parameterization]: Information about how a torus’s u and v parameters are parameterized, respectively.

Torus.project_point(point: ansys.geometry.core.math.point.Point3D) → TorusEvaluation#

Project a point onto the torus and evaluate the torus.

Parameters:

pointPoint3D: Point to project onto the torus.

Returns:

TorusEvaluation: Resulting evaluation.

abstractmethod Torus.contains_param(param_uv: ansys.geometry.core.shapes.parameterization.ParamUV) → bool#: Check a parameter is within the parametric range of the surface.

abstractmethod Torus.contains_point(point: ansys.geometry.core.math.point.Point3D) → bool#

Check a point is contained by the surface.

The point can either lie within the surface or on its boundary.