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

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: List[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

modelviewprojection.mathutils.compose_intermediate_fns(functions: List[InvertibleFunction[T]], relative_basis: bool = False) → Iterable[InvertibleFunction[T]][source]¶

Like compose, but returns a list of all of the partial compositions

Example

>>> from modelviewprojection.mathutils import compose_intermediate_fns, InvertibleFunction, uniform_scale, translate
>>> from modelviewprojection.mathutils1d import Vector1D
>>> from pytest import approx
>>> m = 5.0
>>> b = 2.0
>>> # natural basis
>>> fns: typing.List[InvertibleFunction[Vector1D]] = compose_intermediate_fns(
...      [translate(Vector1D(b)), uniform_scale(m)]
... )
>>> len(fns)
2
>>> fns[0](Vector1D(1))
Vector1D(x=5.0)
>>> fns[1](Vector1D(1))
Vector1D(x=7.0)
>>> # relative basis
>>> fns: typing.List[InvertibleFunction[Vector1D]] = compose_intermediate_fns(
...     [translate(Vector1D(b)), uniform_scale(m)], relative_basis=True
... )
>>> len(fns)
2
>>> fns[0](Vector1D(1))
Vector1D(x=3.0)
>>> fns[1](Vector1D(1))
Vector1D(x=7.0)

modelviewprojection.mathutils.compose_intermediate_fns_and_fn(functions: List[InvertibleFunction[T]], relative_basis: bool = False) → Iterable[InvertibleFunction[T]][source]¶

Like compose, but returns a list of all of the partial compositions

Example

>>> from modelviewprojection.mathutils import compose_intermediate_fns_and_fn, InvertibleFunction, uniform_scale, translate
>>> from modelviewprojection.mathutils1d import Vector1D
>>> from pytest import approx
>>> m = 5.0
>>> b = 2.0
>>> # natural basis
>>> for aggregate_fn, current_fn in compose_intermediate_fns_and_fn(
...      [translate(Vector1D(b)), uniform_scale(m)]):
...      print("agg " + str(aggregate_fn(Vector1D(1.0))))
...      print("current " + str(current_fn(Vector1D(1.0))))
...
agg Vector1D(x=5.0)
current Vector1D(x=5.0)
agg Vector1D(x=7.0)
current Vector1D(x=3.0)
>>> # relative basis
>>> for aggregate_fn, current_fn in compose_intermediate_fns_and_fn(
...      [translate(Vector1D(b)), uniform_scale(m)], relative_basis=True):
...      print("agg " + str(aggregate_fn(Vector1D(1.0))))
...      print("current " + str(current_fn(Vector1D(1.0))))
...
agg Vector1D(x=3.0)
current Vector1D(x=3.0)
agg Vector1D(x=7.0)
current Vector1D(x=5.0)

modelviewprojection.mathutils.translate(b: T) → InvertibleFunction[T][source]¶

modelviewprojection.mathutils.uniform_scale(m: float) → InvertibleFunction[T][source]¶

class modelviewprojection.mathutils.Vector[source]¶

Bases: ABC

abstract __add__(rhs)[source]¶

__sub__(rhs)[source]¶

\[\vec{a} + -\vec{b}\]

Example

>>> from modelviewprojection.mathutils1d import Vector1D
>>> a = Vector1D(x=2.0)
>>> b = Vector1D(x=5.0)
>>> a - b
Vector1D(x=-3.0)

abstract __mul__(scalar: float)[source]¶

__rmul__(scalar: float)[source]¶

__neg__()[source]¶

Let \(\vec{a}\) and constant \(-1\):

\[-1 * \vec{a}\]

Example

>>> from modelviewprojection.mathutils1d import Vector1D
>>> a = Vector1D(x=2.0)
>>> -a
Vector1D(x=-2.0)

Math Utils 1D¶

class modelviewprojection.mathutils1d.Vector1D(x: float)[source]¶

Bases: Vector

x: float¶

The value of the 1D mu.Vector

__add__(rhs: Self) → Self[source]¶

Add together two Vector1Ds.

Let \(\vec{a} = \begin{pmatrix} a_x \end{pmatrix}\) and \(\vec{b} = \begin{pmatrix} b_x \end{pmatrix}\):

\[\vec{a} + \vec{b} = \begin{pmatrix} a_x + b_x \end{pmatrix}\]

Parameters:

rhs (Vector1D) – The vector on the right hand side of the addition symbol

Returns:

The Vector1D that represents the additon of the two

input Vector1Ds

Return type:

Vector1D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils1d import Vector1D
>>> a = Vector1D(x=2.0)
>>> b = Vector1D(x=5.0)
>>> a + b
Vector1D(x=7.0)

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

Multiply the Vector1D by a scalar number

Let \(\vec{a} = \begin{pmatrix} a_x \end{pmatrix}\) and constant scalar \(s\):

\[s*\vec{a} = \begin{pmatrix} s*a_x \end{pmatrix}\]

Parameters:

rhs (Vector1D) – The scalar to be multiplied to the mu.Vector’s component subtraction symbol

Returns:

The Vector1D that represents scalar times the amount of the input mu.Vector1d

Return type:

Vector1D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils1d import Vector1D
>>> a = Vector1D(x=2.0)
>>> a * 4
Vector1D(x=8.0)

dot(other: Self) → float[source]¶

Math Utils 2D¶

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

Bases: Vector1D

y: float¶

The y-component of the 2D Vector

__add__(rhs: Self) → Self[source]¶

Add together two Vector2Ds.

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

\[\begin{split}\vec{a} + \vec{b} = \begin{pmatrix} a_x + b_x \\ a_y + b_y \end{pmatrix}\end{split}\]

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)

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

Multiply the Vector2D by a scalar number

Let \(\vec{a} = \begin{pmatrix} a_x \\ a_y \end{pmatrix}\) and constant scalar \(s\):

\[\begin{split}s*\vec{a} = \begin{pmatrix} s*a_x \\ s*a_y \end{pmatrix}\end{split}\]

Parameters:

rhs (Vector2D) – The scalar to be multiplied to the Vector’s component subtraction symbol

Returns:

The Vector2D that represents scalar times the amount of the input Vector2D

Return type:

Vector2D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils2d import Vector2D
>>> a = Vector2D(x=2.0, y=3.0)
>>> a * 4
Vector2D(x=8.0, y=12.0)

modelviewprojection.mathutils2d.scale(m_x: float, m_y: float) → InvertibleFunction[Vector2D][source]¶

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

modelviewprojection.mathutils2d.rotate(angle_in_radians: float) → Callable[[Vector2D], Vector2D][source]¶

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

modelviewprojection.mathutils2d.cosine(v1: Vector2D, v2: Vector2D) → bool[source]¶

modelviewprojection.mathutils2d.sine(v1: Vector2D, v2: Vector2D) → bool[source]¶

modelviewprojection.mathutils2d.is_counter_clockwise(v1: Vector2D, v2: Vector2D) → bool[source]¶

modelviewprojection.mathutils2d.is_clockwise(v1: Vector2D, v2: Vector2D) → bool[source]¶

modelviewprojection.mathutils2d.is_parallel(v1: Vector2D, v2: Vector2D) → bool[source]¶

Math Utils 3D¶

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

Bases: Vector2D

z: float¶

The z-component of the 3D Vector

__add__(rhs: Self) → Self[source]¶

Add together two Vector3Ds.

Let \(\vec{a} = \begin{pmatrix} a_x \\ a_y \\ a_z \end{pmatrix}\) and \(\vec{b} = \begin{pmatrix} b_x \\ b_y \\ b_z \end{pmatrix}\):

\[\begin{split}\vec{a} + \vec{b} = \begin{pmatrix} a_x + b_x \\ a_y + b_y \\ a_z + b_z \end{pmatrix}\end{split}\]

Parameters:

rhs (Vector3D) – The vector on the right hand side of the addition symbol

Returns:

The Vector3D that represents the additon of the two

input Vector3Ds

Return type:

Vector3D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils3d import Vector3D
>>> a = Vector3D(x=2.0, y=3.0, z=1.0)
>>> b = Vector3D(x=5.0, y=6.0, z=9.0)
>>> a + b
Vector3D(x=7.0, y=9.0, z=10.0)

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

Multiply the Vector3D by a scalar number

Let \(\vec{a} = \begin{pmatrix} a_x \\ a_y \\ a_z \end{pmatrix}\) and constant scalar \(s\):

\[\begin{split}s*\vec{a} = \begin{pmatrix} s*a_x \\ s*a_y \\ s*a_z \end{pmatrix}\end{split}\]

Parameters:

rhs (Vector3D) – The scalar to be multiplied to the Vector’s component subtraction symbol

Returns:

The Vector3D that represents scalar times the amount of the input Vector3D

Return type:

Vector3D

Raises:

Nothing –

Example

>>> from modelviewprojection.mathutils3d import Vector3D
>>> a = Vector3D(x=2.0, y=3.0, z=4.0)
>>> a * 4
Vector3D(x=8.0, y=12.0, z=16.0)

cross(rhs: Self) → Self[source]¶

modelviewprojection.mathutils3d.cos(v1: Vector3D, v2: Vector3D) → float[source]¶

modelviewprojection.mathutils3d.abs_sin(v1: Vector3D, v2: Vector3D) → float[source]¶

modelviewprojection.mathutils3d.scale(m_x: float, m_y: float, m_z: float) → InvertibleFunction[Vector3D][source]¶

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

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

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

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

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

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

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

Bases: object

stack: List[InvertibleFunction[Vector3D]]¶

push(o: object)[source]¶

pop()[source]¶

clear()[source]¶

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

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