API Reference¶

Math Utils¶

class modelviewprojection.mathutils.Vector[source]¶

Bases: object

__add__(rhs: Self) → Self[source]¶

Add together two Vectors, component-wise.

Parameters:: rhs (Vector) – The vector on the right hand side of the addition symbol
Returns:: The Vector that represents the additon of the two input Vectors
Return type:: Vector

Example

>>> from modelviewprojection.mathutils import Vector1D
>>> a = Vector1D(x=2)
>>> b = Vector1D(x=5)
>>> a + b
Vector1D(x=7)
>>> from modelviewprojection.mathutils import Vector2D
>>> a = Vector2D(x=2, y=3)
>>> b = Vector2D(x=5, y=6)
>>> a + b
Vector2D(x=7, y=9)
>>> from modelviewprojection.mathutils import Vector3D
>>> a = Vector3D(x=2, y=3, z=1)
>>> b = Vector3D(x=5, y=6, z=10)
>>> a + b
Vector3D(x=7, y=9, z=11)

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

Multiply the Vector by a scalar number, component-wise

Parameters:: rhs (Vector) – The scalar to be multiplied to the Vector’s component subtraction symbol
Returns:: The Vector that represents scalar times the amount of the input Vector
Return type:: Vector

Example

>>> from modelviewprojection.mathutils import Vector1D
>>> a = Vector1D(x=2)
>>> a * 4
Vector1D(x=8)
>>> from modelviewprojection.mathutils import Vector2D
>>> a = Vector2D(x=2, y=3)
>>> a * 4
Vector2D(x=8, y=12)
>>> from modelviewprojection.mathutils import Vector3D
>>> a = Vector3D(x=2, y=3, z=5)
>>> a * 4
Vector3D(x=8, y=12, z=20)

__neg__() → Self[source]¶

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

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

Example

>>> from modelviewprojection.mathutils import Vector1D
>>> a = Vector1D(x=2)
>>> -a
Vector1D(x=-2)

__sub__(rhs: Self) → Self[source]¶

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

Example

>>> from modelviewprojection.mathutils import Vector1D
>>> a = Vector1D(x=2)
>>> b = Vector1D(x=5)
>>> a - b
Vector1D(x=-3)

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

isclose(other: Self) → float[source]¶

component_wise_with_index(other: Self)[source]¶

dot(other: Self) → float[source]¶

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

Bases: Vector

x: float¶: The value of the 1D Vector

class modelviewprojection.mathutils.InvertibleFunction(func: Callable[[Vector], Vector], inverse: Callable[[Vector], Vector], latex_repr: str, latex_repr_inv: str)[source]¶

Bases: object

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[[Vector], Vector]¶: The wrapped function

inverse: Callable[[Vector], Vector]¶: The inverse of the wrapped function

latex_repr: str¶: The LaTeX representation of the function

latex_repr_inv: str¶: The LaTeX representation of the inverse function

__call__(x: Vector) → Vector[source]¶

Execute a function with the given value.

Parameters:

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

Vector

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, latex_repr="", latex_repr_inv="")
>>> foo
InvertibleFunction(func=<...>, inverse=<...>, latex_repr=..., latex_repr_inv=...)
>>> foo(5)
7
>>> inverse(foo)
InvertibleFunction(func=<...>, inverse=<...>, latex_repr=..., latex_repr_inv=...)
>>> inverse(foo)(foo(5))
5

__matmul__(f2: InvertibleFunction) → InvertibleFunction[source]¶

Override @ for function composition. This is abusing the @ symbol, which is normally for matrix multiplication.

Parameters:: f2 (mathutils.InvertibleFunction) – A function that self is composed with and returns a value of the same type Vector.
Returns:: The composed function.
Return type:: InvertibleFunction

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, latex_repr="", latex_repr_inv="")
>>> foo(5)
7
>>> (foo @ foo)(5)
9
>>> inverse(foo @ foo)(5)
1
>>> (foo @ inverse(foo))(5)
5

__rmatmul__(f2: InvertibleFunction) → InvertibleFunction[source]¶

modelviewprojection.mathutils.identity() → InvertibleFunction[source]¶

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

Get the inverse of the InvertibleFunction

Parameters:: f – InvertibleFunction: A function with it’s associated inverse function.
Returns:: The Inverse of the function.
Return type:: InvertibleFunction

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, latex_repr="", latex_repr_inv="")
>>> foo
InvertibleFunction(func=<...>, inverse=<...>, latex_repr=..., latex_repr_inv=...)
>>> foo(5)
7
>>> inverse(foo)
InvertibleFunction(func=<...>, inverse=<...>, latex_repr=..., latex_repr_inv=...)
>>> inverse(foo)(foo(5))
5

modelviewprojection.mathutils.compose(functions: list[InvertibleFunction]) → InvertibleFunction[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 (list[InvertibleFunction]) – Variable number of InvertibleFunctions to compose. At least on value must be provided.
Returns:: One function that is the aggregate function.
Return type:: Vector

Example

>>> from modelviewprojection.mathutils import compose
>>> from modelviewprojection.mathutils import translate as T
>>> from modelviewprojection.mathutils import uniform_scale as S
>>> from modelviewprojection.mathutils import Vector2D
>>> fn = compose([S(2), T(Vector2D(3, 4))])
>>> fn(Vector2D(1,1))
Vector2D(x=8, y=10)

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

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

Example

>>> from modelviewprojection.mathutils import compose_intermediate_fns
>>> from modelviewprojection.mathutils import InvertibleFunction
>>> from modelviewprojection.mathutils import uniform_scale
>>> from modelviewprojection.mathutils import translate
>>> from modelviewprojection.mathutils import Vector1D
>>> from pytest import approx
>>> m = 5
>>> b = 2
>>> # natural basis
>>> fns: list[InvertibleFunction] = compose_intermediate_fns(
...      [translate(Vector1D(b)), uniform_scale(m)]
... )
>>> len(fns)
3
>>> fns[0](Vector1D(1))
Vector1D(x=1)
>>> fns[1](Vector1D(1))
Vector1D(x=5)
>>> fns[2](Vector1D(1))
Vector1D(x=7)
>>> # relative basis
>>> fns: list[InvertibleFunction] = compose_intermediate_fns(
...     [translate(Vector1D(b)), uniform_scale(m)], relative_basis=True
... )
>>> len(fns)
3
>>> fns[0](Vector1D(1))
Vector1D(x=1)
>>> fns[1](Vector1D(1))
Vector1D(x=3)
>>> fns[2](Vector1D(1))
Vector1D(x=7)

modelviewprojection.mathutils.compose_intermediate_fns_and_fn(functions: list[InvertibleFunction], relative_basis: bool = False) → list[tuple[InvertibleFunction, InvertibleFunction]][source]¶

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

Example

>>> from modelviewprojection.mathutils import compose_intermediate_fns_and_fn
>>> from modelviewprojection.mathutils import InvertibleFunction
>>> from modelviewprojection.mathutils import uniform_scale
>>> from modelviewprojection.mathutils import translate
>>> from modelviewprojection.mathutils import Vector1D
>>> from pytest import approx
>>> m = 5
>>> b = 2
>>> # 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))))
...      print("current " + str(current_fn(Vector1D(1))))
...
agg Vector1D(x=1)
current Vector1D(x=5)
agg Vector1D(x=5)
current Vector1D(x=3)
agg Vector1D(x=7)
current Vector1D(x=1)
>>> # 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))))
...      print("current " + str(current_fn(Vector1D(1))))
...
agg Vector1D(x=1)
current Vector1D(x=1)
agg Vector1D(x=3)
current Vector1D(x=3)
agg Vector1D(x=7)
current Vector1D(x=5)

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

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

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

Bases: Vector1D

y: float¶: The y-component of the 2D Vector

modelviewprojection.mathutils.scale_non_uniform_2d(m_x: float, m_y: float) → InvertibleFunction[source]¶

modelviewprojection.mathutils.rotate_90_degrees() → InvertibleFunction[source]¶

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

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

modelviewprojection.mathutils.sine(v1: Vector, v2: Vector) → float[source]¶

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

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

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

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

Bases: Vector2D

z: float¶: The z-component of the 3D Vector

cross(rhs: Self) → Self[source]¶

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

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

modelviewprojection.mathutils.scale_non_uniform_3d(m_x: float, m_y: float, m_z: float) → InvertibleFunction[source]¶

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

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

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

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

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

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

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

Bases: object

stack: list[InvertibleFunction]¶

push(o: InvertibleFunction)[source]¶

pop() → InvertibleFunction[source]¶

clear()[source]¶

modelspace_to_ndc_fn() → InvertibleFunction[source]¶

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