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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> b = Vector1D(x=5) >>> a + b Vector1D(x=7) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> b = Vector2D(x=5, y=6) >>> a + b Vector2D(x=7, y=9) >>> from modelviewprojection.mathutils3d 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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> a * 4 Vector1D(x=8) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> a * 4 Vector2D(x=8, y=12) >>> from modelviewprojection.mathutils3d 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.mathutils1d import Vector1D >>> a = Vector1D(x=2.0) >>> -a Vector1D(x=-2.0) 
 
- class modelviewprojection.mathutils.InvertibleFunction(func: Callable[[Vector], Vector], inverse: Callable[[Vector], Vector])[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. 
- 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
- function. 
 
- Return type:
- 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]) 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 of the argument
- functions composed. 
 
- Return type:
- 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], 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, InvertibleFunction, uniform_scale, translate >>> from modelviewprojection.mathutils1d import Vector1D >>> from pytest import approx >>> m = 5.0 >>> b = 2.0 >>> # natural basis >>> fns: list[InvertibleFunction] = 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: list[InvertibleFunction] = 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], 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, 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: Vector) InvertibleFunction[source]¶
- modelviewprojection.mathutils.uniform_scale(m: float) InvertibleFunction[source]¶
Math Utils 1D¶
- class modelviewprojection.mathutils1d.Vector1D(x: float)[source]¶
- Bases: - Vector- x: float¶
- The value of the 1D mu.Vector 
 
- modelviewprojection.mathutils1d.translate(b: Vector) InvertibleFunction[source]¶
- modelviewprojection.mathutils1d.uniform_scale(m: float) InvertibleFunction[source]¶
- class modelviewprojection.mathutils1d.InvertibleFunction(func: Callable[[Vector], Vector], inverse: Callable[[Vector], Vector])[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. 
- modelviewprojection.mathutils1d.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
- function. 
 
- Return type:
- 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.mathutils1d.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 of the argument
- functions composed. 
 
- Return type:
- 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 
- class modelviewprojection.mathutils1d.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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> b = Vector1D(x=5) >>> a + b Vector1D(x=7) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> b = Vector2D(x=5, y=6) >>> a + b Vector2D(x=7, y=9) >>> from modelviewprojection.mathutils3d 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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> a * 4 Vector1D(x=8) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> a * 4 Vector2D(x=8, y=12) >>> from modelviewprojection.mathutils3d 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.mathutils1d import Vector1D >>> a = Vector1D(x=2.0) >>> -a Vector1D(x=-2.0) 
 
Math Utils 2D¶
- class modelviewprojection.mathutils2d.Vector2D(x: float, y: float)[source]¶
- Bases: - Vector1D- y: float¶
- The y-component of the 2D Vector 
 
- modelviewprojection.mathutils2d.scale(m_x: float, m_y: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils2d.rotate_90_degrees() InvertibleFunction[source]¶
- modelviewprojection.mathutils2d.rotate(angle_in_radians: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils2d.rotate_around(angle_in_radians: float, center: Vector2D) InvertibleFunction[source]¶
- modelviewprojection.mathutils2d.translate(b: Vector) InvertibleFunction[source]¶
- modelviewprojection.mathutils2d.uniform_scale(m: float) InvertibleFunction[source]¶
- class modelviewprojection.mathutils2d.InvertibleFunction(func: Callable[[Vector], Vector], inverse: Callable[[Vector], Vector])[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. 
- modelviewprojection.mathutils2d.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
- function. 
 
- Return type:
- 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.mathutils2d.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 of the argument
- functions composed. 
 
- Return type:
- 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 
- class modelviewprojection.mathutils2d.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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> b = Vector1D(x=5) >>> a + b Vector1D(x=7) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> b = Vector2D(x=5, y=6) >>> a + b Vector2D(x=7, y=9) >>> from modelviewprojection.mathutils3d 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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> a * 4 Vector1D(x=8) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> a * 4 Vector2D(x=8, y=12) >>> from modelviewprojection.mathutils3d 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.mathutils1d import Vector1D >>> a = Vector1D(x=2.0) >>> -a Vector1D(x=-2.0) 
 
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 
 
- modelviewprojection.mathutils3d.scale(m_x: float, m_y: float, m_z: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.rotate_x(angle_in_radians: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.rotate_y(angle_in_radians: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.rotate_z(angle_in_radians: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.ortho(left: float, right: float, bottom: float, top: float, near: float, far: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.perspective(field_of_view: float, aspect_ratio: float, near_z: float, far_z: float) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.cs_to_ndc_space_fn(vector: Vector3D) InvertibleFunction[source]¶
- class modelviewprojection.mathutils3d.FunctionStack(stack: list[modelviewprojection.mathutils.InvertibleFunction] = <factory>)[source]¶
- Bases: - object- stack: list[InvertibleFunction]¶
 - push(o: InvertibleFunction)[source]¶
 - modelspace_to_ndc_fn() InvertibleFunction[source]¶
 
- modelviewprojection.mathutils3d.translate(b: Vector) InvertibleFunction[source]¶
- modelviewprojection.mathutils3d.uniform_scale(m: float) InvertibleFunction[source]¶
- class modelviewprojection.mathutils3d.InvertibleFunction(func: Callable[[Vector], Vector], inverse: Callable[[Vector], Vector])[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. 
- modelviewprojection.mathutils3d.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
- function. 
 
- Return type:
- 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.mathutils3d.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 of the argument
- functions composed. 
 
- Return type:
- 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 
- class modelviewprojection.mathutils3d.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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> b = Vector1D(x=5) >>> a + b Vector1D(x=7) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> b = Vector2D(x=5, y=6) >>> a + b Vector2D(x=7, y=9) >>> from modelviewprojection.mathutils3d 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:
- Raises:
- Nothing – 
 - Example - >>> from modelviewprojection.mathutils1d import Vector1D >>> a = Vector1D(x=2) >>> a * 4 Vector1D(x=8) >>> from modelviewprojection.mathutils2d import Vector2D >>> a = Vector2D(x=2, y=3) >>> a * 4 Vector2D(x=8, y=12) >>> from modelviewprojection.mathutils3d 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.mathutils1d import Vector1D >>> a = Vector1D(x=2.0) >>> -a Vector1D(x=-2.0)