3D Vector and 3D Point

Bases: `Vector3D`

3D Point object.

Parameters
• x – Number for the X coordinate.

• y – Number for the Y coordinate.

• z – Number for the Z coordinate.

Properties:
• x

• y

• z

ToString()

Overwrite .NET ToString.

angle(other)

Get the smallest angle between this vector and another.

cross(other)

Get the cross product of this vector and another vector.

distance_to_point(point)[source]

Get the distance from this point to another Point3D.

dot(other)

Get the dot product of this vector with another.

duplicate()

Get a copy of this vector.

classmethod from_array(array)

Initialize a Vector3D/Point3D from an array.

Parameters

array – A tuple or list with three numbers representing the x, y and z values of the point.

classmethod from_dict(data)

Create a Vector3D/Point3D from a dictionary.

Parameters

data – A python dictionary in the following format

```{
"x": 10,
"y": 0,
"z": 0
}
```
classmethod from_point2d(point2d, z=0)[source]

Initialize a new Point3D from an Point2D and a z value.

Parameters
• line2d – A Point2D to be used to generate the Point3D.

• z – A number for the Z coordinate value of the line.

classmethod from_vector2d(vector2d, z=0)

Initialize a new Vector3D from an Vector2D and a z value.

Parameters
• line2d – A Vector2D to be used to generate the Vector3D.

• z – A number for the Z coordinate value of the line.

is_equivalent(other, tolerance)

Test whether this object is equivalent to another within a certain tolerance.

Note that if you want to test whether the coordinate values are perfectly equal to one another, the == operator can be used.

Parameters
• other – Another Point3D or Vector3D for which geometric equivalency will be tested.

• tolerance – The minimum difference between the coordinate values of two objects at which they can be considered geometrically equivalent.

Returns

True if equivalent. False if not equivalent.

is_zero(tolerance)

Boolean to note whether the vector is within a given zero tolerance.

Parameters

tolerance – The tolerance below which the vector is considered to be a zero vector.

move(moving_vec)[source]

Get a point that has been moved along a vector.

Parameters

moving_vec – A Vector3D with the direction and distance to move the point.

normalize()

Get a copy of the vector that is a unit vector (magnitude=1).

project(normal, origin)[source]

Get a point that is projected into a plane with a given normal and origin.

Parameters
• normal – A Vector3D representing the normal vector of the plane into which the plane will be projected. THIS VECTOR MUST BE NORMALIZED.

• origin – A Point3D representing the origin the plane into which the point will be projected.

reflect(normal, origin)[source]

Get a point reflected across a plane with the input normal vector and origin.

Parameters
• normal – A Vector3D representing the normal vector for the plane across which the point will be reflected. THIS VECTOR MUST BE NORMALIZED.

• origin – A Point3D representing the origin from which to reflect.

reverse()

Get a copy of this vector that is reversed.

rotate(axis, angle, origin)[source]

Rotate a point by a certain angle around an axis and origin.

Right hand rule applies: If axis has a positive orientation, rotation will be clockwise. If axis has a negative orientation, rotation will be counterclockwise.

Parameters
• axis – A Vector3D axis representing the axis of rotation.

• angle – An angle for rotation in radians.

• origin – A Point3D for the origin around which the point will be rotated.

rotate_xy(angle, origin)[source]

Get a point rotated counterclockwise in the XY plane by a certain angle.

Parameters
• angle – An angle in radians.

• origin – A Point3D for the origin around which the point will be rotated.

scale(factor, origin=None)[source]

Scale a point by a factor from an origin point.

Parameters
• factor – A number representing how much the point should be scaled.

• origin – A Point3D representing the origin from which to scale. If None, it will be scaled from the World origin (0, 0, 0).

to_array()

Get Vector3D/Point3D as a tuple of three numbers

to_dict()[source]

Get Point3D as a dictionary.

property magnitude

Get the magnitude of the vector.

property magnitude_squared

Get the magnitude squared of the vector.

property max

Always equal to the point itself.

This property exists to help with bounding box calculations.

property min

Always equal to the point itself.

This property exists to help with bounding box calculations.

property x

Get the X coordinate.

property y

Get the Y coordinate.

property z

Get the Z coordinate.

Bases: `object`

3D Vector object.

Parameters
• x – Number for the X coordinate.

• y – Number for the Y coordinate.

• z – Number for the Z coordinate.

Properties:
• x

• y

• z

• magnitude

• magnitude_squared

• is_zero

ToString()[source]

Overwrite .NET ToString.

angle(other)[source]

Get the smallest angle between this vector and another.

cross(other)[source]

Get the cross product of this vector and another vector.

dot(other)[source]

Get the dot product of this vector with another.

duplicate()[source]

Get a copy of this vector.

classmethod from_array(array)[source]

Initialize a Vector3D/Point3D from an array.

Parameters

array – A tuple or list with three numbers representing the x, y and z values of the point.

classmethod from_dict(data)[source]

Create a Vector3D/Point3D from a dictionary.

Parameters

data – A python dictionary in the following format

```{
"x": 10,
"y": 0,
"z": 0
}
```
classmethod from_vector2d(vector2d, z=0)[source]

Initialize a new Vector3D from an Vector2D and a z value.

Parameters
• line2d – A Vector2D to be used to generate the Vector3D.

• z – A number for the Z coordinate value of the line.

is_equivalent(other, tolerance)[source]

Test whether this object is equivalent to another within a certain tolerance.

Note that if you want to test whether the coordinate values are perfectly equal to one another, the == operator can be used.

Parameters
• other – Another Point3D or Vector3D for which geometric equivalency will be tested.

• tolerance – The minimum difference between the coordinate values of two objects at which they can be considered geometrically equivalent.

Returns

True if equivalent. False if not equivalent.

is_zero(tolerance)[source]

Boolean to note whether the vector is within a given zero tolerance.

Parameters

tolerance – The tolerance below which the vector is considered to be a zero vector.

normalize()[source]

Get a copy of the vector that is a unit vector (magnitude=1).

project(normal)[source]

Get a vector projected into a plane with a given normal.

Parameters

normal – A Vector3D representing the normal vector of the plane into which the plane will be projected. THIS VECTOR MUST BE NORMALIZED.

reflect(normal)[source]

Get a vector that is reflected across a plane with the input normal vector.

Parameters

normal – A Vector3D representing the normal vector for the plane across which the vector will be reflected. THIS VECTOR MUST BE NORMALIZED.

reverse()[source]

Get a copy of this vector that is reversed.

rotate(axis, angle)[source]

Get a vector rotated around an axis through an angle.

Right hand rule applies: If axis has a positive orientation, rotation will be clockwise. If axis has a negative orientation, rotation will be counterclockwise.

Parameters
• axis – A Vector3D axis representing the axis of rotation.

• angle – An angle in radians.

rotate_xy(angle)[source]

Get a vector rotated counterclockwise in the XY plane by a certain angle.

Parameters

angle – An angle in radians.

to_array()[source]

Get Vector3D/Point3D as a tuple of three numbers

to_dict()[source]

Get Vector3D as a dictionary.

property magnitude

Get the magnitude of the vector.

property magnitude_squared

Get the magnitude squared of the vector.

property max

Always equal to (0, 0, 0).

This property exists to help with bounding box calculations.

property min

Always equal to (0, 0, 0).

This property exists to help with bounding box calculations.

property x

Get the X coordinate.

property y

Get the Y coordinate.

property z

Get the Z coordinate.