Operators¶

Every transformation operator (versor) you can add to a scene, together with its visualization style class, the style parameters, and a static inline example. Each example is rendered serverlessly via display_snapshot().

For the underlying data classes and algebra coverage, see operators.md under the geometry section.

In [1]:

from typing import Any

import math

from pytanga.geometry import (
    Dilator,
    Direction,
    GeneralRotor,
    Inversion,
    Motor,
    Point,
    ReflectionLine,
    ReflectionPlane,
    ReflectionPoint,
    Rotor,
    Translator,
)
from pytanga.viz import CameraConfig3d, ReflectionPlaneStyle, Visualizer

_NOTE = "You can interactively rotate, pan, and zoom this view."


def show(entity: Any, height: int = 340, **kwargs: Any) -> Any:
    # Render a single operator in a fresh scene, inline and serverless.
    viz = Visualizer(
        title="Operators - " + type(entity).__name__,
        add_default_axes=False,
        annotation=_NOTE,
        camera=CameraConfig3d(position=(2.5, 1.5, 3), target=(0, 0, 0)),
    )
    viz.add(entity, **kwargs)
    return viz.display_snapshot(height=height)

from typing import Any import math from pytanga.geometry import ( Dilator, Direction, GeneralRotor, Inversion, Motor, Point, ReflectionLine, ReflectionPlane, ReflectionPoint, Rotor, Translator, ) from pytanga.viz import CameraConfig3d, ReflectionPlaneStyle, Visualizer _NOTE = "You can interactively rotate, pan, and zoom this view." def show(entity: Any, height: int = 340, **kwargs: Any) -> Any: # Render a single operator in a fresh scene, inline and serverless. viz = Visualizer( title="Operators - " + type(entity).__name__, add_default_axes=False, annotation=_NOTE, camera=CameraConfig3d(position=(2.5, 1.5, 3), target=(0, 0, 0)), ) viz.add(entity, **kwargs) return viz.display_snapshot(height=height)

ReflectionPlane¶

Reflection in a plane through the origin. Reflection is an alias.

Field	Type	Description
color	str	CSS colour
opacity	float	0-1
extent	float	Drawn size in world units

In [2]:

show(
    ReflectionPlane(Direction(0, 0, 1)),
    style=ReflectionPlaneStyle(extent=3.0),
)

show( ReflectionPlane(Direction(0, 0, 1)), style=ReflectionPlaneStyle(extent=3.0), )

Out[2]:

ReflectionLine¶

Reflection about a line through the origin.

Field	Type	Description
color	str	CSS colour
opacity	float	0-1
length	float	Drawn length in world units
thickness	float	Line width in screen pixels

In [3]:

show(ReflectionLine(Direction(0, 0, 1)))

show(ReflectionLine(Direction(0, 0, 1)))

Out[3]:

ReflectionPoint¶

Reflection about a point (point inversion through the given center).

ReflectionPointStyle is defined in pytanga.viz._styles but is not exported from the top-level pytanga.viz namespace.

Field	Type	Description
color	str	CSS colour
opacity	float	0-1
extent	float	Drawn size in world units

In [4]:

show(ReflectionPoint(Point(0, 0, 0)))

show(ReflectionPoint(Point(0, 0, 0)))

Out[4]:

Inversion¶

Inversion in a sphere centered at the origin.

Field	Type	Description
color	str	CSS colour
opacity	float	0-1

In [5]:

show(Inversion(Point(0, 0, 0)))

show(Inversion(Point(0, 0, 0)))

Out[5]:

Rotor¶

A rotation (disc arc plus axis line).

Field	Type	Description
color	str	CSS colour
opacity	float	0-1
disc_radius	float	Radius of the rotation disc

In [6]:

show(Rotor(angle=math.pi / 2, axis=Direction(0, 0, 1)))

show(Rotor(angle=math.pi / 2, axis=Direction(0, 0, 1)))

Out[6]:

Translator¶

A translation (3D arrow).

Field	Type	Description
color	str	CSS colour
opacity	float	0-1
length	float	Arrow length in world units

In [7]:

show(Translator(vector=Direction(2, 0, 0)), color="#44aaff")

show(Translator(vector=Direction(2, 0, 0)), color="#44aaff")

Out[7]:

Dilator¶

A uniform scaling (concentric expanding rings).

Field	Type	Description
color	str	CSS colour
opacity	float	0-1
ring_count	int	Number of concentric rings
max_radius	float	Radius of the outermost ring

In [8]:

show(
    Dilator(factor=2.0, origin=Point(0, 0, 0)),
    color="#ffcc44",
)

show( Dilator(factor=2.0, origin=Point(0, 0, 0)), color="#ffcc44", )

Out[8]:

Motor¶

A rigid body motion (screw): rotation about a displaced axis plus a translation along that axis. See the decomposition for the maths.

Field	Type	Description
color	str	CSS colour
opacity	float	0-1

In [9]:

show(
    Motor(
        rotor=Rotor(angle=math.pi / 2, axis=Direction(0, 0, 1)),
        translator=Translator(vector=Direction(1, 1, 1)),
    ),
    color="#ff66cc",
)

show( Motor( rotor=Rotor(angle=math.pi / 2, axis=Direction(0, 0, 1)), translator=Translator(vector=Direction(1, 1, 1)), ), color="#ff66cc", )

Out[9]:

GeneralRotor¶

A rotation about an axis that does not pass through the origin.

Field	Type	Description
color	str	CSS colour
opacity	float	0-1

In [10]:

show(
    GeneralRotor(
        angle=0.5,
        axis=Direction(0, 0, 1),
        origin=Point(1, 0, 0),
    ),
)

show( GeneralRotor( angle=0.5, axis=Direction(0, 0, 1), origin=Point(1, 0, 0), ), )

Out[10]: