API Reference¶

Math Utils¶

class modelviewprojection.mathutils.InvertibleFunction(func: Callable[[T], T], inverse: Callable[[T], T])[source]¶

Bases: Generic[T]

Class that wraps a function and its inverse function. The function takes type T as it’s argument and it’s evaluation results in a value of type T.

func: Callable[[T], T]¶

The wrapped function

inverse: Callable[[T], T]¶

The inverse of the wrapped function

__call__(x: T) → T[source]¶

Execute a function with the given value.

Parameters:

• func (Callable[[T], T]) – A function that takes a value of type T and returns a value of the same type T.

• value (T) – The input value to pass to the function

Returns:

The result of calling func(value). Will be the same type as the

input value.

Return type:

T

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils import InvertibleFunction
>>> from modelviewprojection.mathutils import inverse
>>> def f(x):
...     return 2 + x
...
>>> def f_inv(x):
...     return x - 2
...
>>> foo = InvertibleFunction(func=f, inverse=f_inv)
>>> foo 
InvertibleFunction(func=<function f at 0x...>, inverse=<function f_inv at 0x...>)
>>> foo(5)
7
>>> inverse(foo) 
InvertibleFunction(func=<function f_inv at 0x...>, inverse=<function f at 0x...>)
>>> inverse(foo)(foo(5))
5

__init__(func: Callable[[T], T], inverse: Callable[[T], T]) → None¶

modelviewprojection.mathutils.inverse(f: InvertibleFunction[T]) → InvertibleFunction[T][source]¶

Get the inverse of the InvertibleFunction

Parameters:

f – InvertibleFunction[T]: A function with it’s associated inverse function.

Returns:

The Inverse of the function

function.

Return type:

InvertibleFunction[T]

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils import InvertibleFunction
>>> from modelviewprojection.mathutils import inverse
>>> def f(x):
...     return 2 + x
...
>>> def f_inv(x):
...     return x - 2
...
>>> foo = InvertibleFunction(func=f, inverse=f_inv)
>>> foo 
InvertibleFunction(func=<function f at 0x...>, inverse=<function f_inv at 0x...>)
>>> foo(5)
7
>>> inverse(foo) 
InvertibleFunction(func=<function f_inv at 0x...>, inverse=<function f at 0x...>)
>>> inverse(foo)(foo(5))
5

modelviewprojection.mathutils.compose(*functions: InvertibleFunction[T]) → InvertibleFunction[T][source]¶

Compose a sequence of functions.

If two functions are passed as arguments, named \(f\) and \(g\):

\((f \circ g)(x) = f(g(x))\).

If \(n\) functions are passed as arguments, \(f_1...f_n\):

\((f_1 \circ (f_2 \circ (... f_n )(x) = f_1(f_2...(f_n(x))\).

Parameters:

*functions (InvertibleFunction[T]) – Variable number of InvertibleFunctions to compose. At least on value must be provided.

Returns:

One function that is the aggregate function of the argument

functions composed.

Return type:

T

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils import compose
>>> compose(lambda x: 5)(1)
5
>>> compose(lambda x: 2*x)(1)
2
>>> compose(lambda x: x+4, lambda x: 2*x)(1)
6
>>> compose(lambda x: x+ 10, lambda x: x+4, lambda x: 2*x)(1)
16

Math Utils 2D¶

class modelviewprojection.mathutils2d.Vector2D(x: 'float', y: 'float')[source]¶

Bases: object

x: float¶

The x-component of the 2D Vector

y: float¶

The y-component of the 2D Vector

__add__(rhs: Vector2D) → Vector2D[source]¶

Add together two Vector2Ds.

Let \(\vec{a} = (a_x, a_y)\) and \(\vec{b} = (b_x, b_y)\):

\[\vec{a} + \vec{b} = (a_x + b_x, a_y + b_y)\]

Parameters:

rhs (Vector2D) – The vector on the right hand side of the addition symbol

Returns:

The Vector2D that represents the additon of the two

input Vector2Ds

Return type:

Vector2D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils2d import Vector2D
>>> a = Vector2D(x=2.0, y=3.0)
>>> b = Vector2D(x=5.0, y=6.0)
>>> a + b
Vector2D(x=7.0, y=9.0)

__sub__(rhs: Vector2D) → Vector2D[source]¶

Subtract the right hand side Vector2D from the left hand side Vector2D.

Let \(\vec{a} = (a_x, a_y)\) and \(\vec{b} = (b_x, b_y)\):

\[\vec{a} - \vec{b} = (a_x - b_x, a_y - b_y)\]

Parameters:

rhs (Vector2D) – The vector on the right hand side of the subtraction symbol

Returns:

The Vector2D that represents the subtraction of the

right hand side Vector2D from the left hand side Vector2D

Return type:

Vector2D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils2d import Vector2D
>>> a = Vector2D(x=2.0, y=3.0)
>>> b = Vector2D(x=5.0, y=2.0)
>>> a - b
Vector2D(x=-3.0, y=1.0)

__mul__(scalar: float) → Vector2D[source]¶

__rmul__(scalar: float) → Vector2D[source]¶

__init__(x: float, y: float) → None¶

modelviewprojection.mathutils2d.translate(translate_amount: Vector2D) → InvertibleFunction[source]¶

modelviewprojection.mathutils2d.uniform_scale(scalar: float) → InvertibleFunction[source]¶

modelviewprojection.mathutils2d.scale(scale_x: float, scale_y: float) → InvertibleFunction[source]¶

modelviewprojection.mathutils2d.rotate_90_degrees() → InvertibleFunction[Vector2D][source]¶

modelviewprojection.mathutils2d.rotate(angle_in_radians: float) → InvertibleFunction[source]¶

modelviewprojection.mathutils2d.rotate_around(angle_in_radians: float, center: Vector2D) → InvertibleFunction[source]¶

Math Utils 3D¶

class modelviewprojection.mathutils3d.Vector3D(x: 'float', y: 'float', z: 'float')[source]¶

Bases: object

x: float¶

The x-component of the 3D Vector

y: float¶

The y-component of the 3D Vector

z: float¶

The z-component of the 3D Vector

__add__(rhs: Vector3D) → Vector3D[source]¶

__sub__(rhs: Vector3D) → Vector3D[source]¶

__mul__(scalar: float) → Vector3D[source]¶

__rmul__(scalar: float) → Vector3D[source]¶

__init__(x: float, y: float, z: float) → None¶

modelviewprojection.mathutils3d.translate(translate_amount: Vector3D) → InvertibleFunction[source]¶

modelviewprojection.mathutils3d.rotate_x(angle_in_radians: float) → Vector3D[source]¶

modelviewprojection.mathutils3d.rotate_y(angle_in_radians: float) → Vector3D[source]¶

modelviewprojection.mathutils3d.rotate_z(angle_in_radians: float) → Vector3D[source]¶

modelviewprojection.mathutils3d.uniform_scale(scalar: float) → InvertibleFunction[source]¶

modelviewprojection.mathutils3d.scale(scale_x: float, scale_y: float, scale_z: float) → Vector3D[source]¶

modelviewprojection.mathutils3d.ortho(left: float, right: float, bottom: float, top: float, near: float, far: float) → Vector3D[source]¶

modelviewprojection.mathutils3d.perspective(field_of_view: float, aspect_ratio: float, near_z: float, far_z: float) → Vector3D[source]¶

modelviewprojection.mathutils3d.cs_to_ndc_space_fn(vector: Vector3D) → Vector3D[source]¶

class modelviewprojection.mathutils3d.FunctionStack(stack: 'List[InvertibleFunction[Vector3D]]' = <factory>)[source]¶

Bases: object

stack: List[InvertibleFunction[Vector3D]]¶

push(o: object)[source]¶

pop()[source]¶

clear()[source]¶

modelspace_to_ndc_fn() → InvertibleFunction[Vector3D][source]¶

__init__(stack: ~typing.List[~modelviewprojection.mathutils.InvertibleFunction[~modelviewprojection.mathutils3d.Vector3D]] = <factory>) → None¶

modelviewprojection.mathutils3d.push_transformation(f)[source]¶