fibomat.shapes.parametric_curve module#

Provides the ParametricCurve class.

class fibomat.shapes.parametric_curve.ParametricCurve(func: Callable[[ndarray], ndarray], d_func: Callable[[ndarray], ndarray], d2_func: Callable[[ndarray], ndarray], domain: Tuple[float, float], bounding_box: BoundingBox, curvature: Callable[[ndarray], ndarray] | None = None, length: Callable[[float, float], float] | None = None, description: str | None = None)[source]#

Bases: Shape, ArcSplineCompatible

Parametric curve f: [a, b] -> R^2 with f in C^inf

E.g. f(u) = (cos(u), sin(u)).

TODO: handle bounding box! TODO: Put references here (thesis + 2 papers)

__init__(func: Callable[[ndarray], ndarray], d_func: Callable[[ndarray], ndarray], d2_func: Callable[[ndarray], ndarray], domain: Tuple[float, float], bounding_box: BoundingBox, curvature: Callable[[ndarray], ndarray] | None = None, length: Callable[[float, float], float] | None = None, description: str | None = None)[source]#

All Callables must be vectorized. Hence

  • func(1) should return np.array([x, y])

  • func([1, 2]) should return np.array([[x1, y1], [x2, y2]])

If length is not provided, it will be calculated numerically.

Args:

func (Callable[[np.ndarray], np.ndarray]): function value of parametric curve d_func (Callable[[np.ndarray], np.ndarray]): function value of first derivative d2_func (Callable[[np.ndarray], np.ndarray]): function value of second derivative domain (Tuple[float, float]): parametric domain of curve bounding_box (BoundingBox): bounding box of curve curvature (Optional[Callable[[np.ndarray], np.ndarray]], optional): curvature of parametric curve. length (Optional[Callable[[float, float], float]], optional):

arc length of parametric curve in interval u_1, u_2

description (str, optional): description

classmethod from_sympy_curve(curve: Curve, try_length_integration: bool = False, description: str | None = None)[source]#

Create a ParametricCurve from a sympy curve. All derivatives are calculated automatically.

Args:

curve (sympy.geometry.Curve): parametric curve. try_length_integration (bool):

if True, it is attempted to solve arc length parametrization integral analytically.

description (str, optional): description

Returns:

ParametricCurve

classmethod from_splipy_curve(splipy_curve: Curve, description: str | None = None)[source]#
to_arc_spline(rasterize_pitch: float | None = None, epsilon: float | None = None) → ArcSpline[source]#

Transform shape to ArcSpline.

Returns:

ArcSpline

property domain: Tuple[float, float]#

Parametric domain of curve.

Access:

get

Returns:

Tuple[float, float]

property is_closed: bool#

bool: True if shape is closes. This property should not be defined for 0-dim shapes

Access:

get

property length: float#

Arc length of curve.

Access:

get

Returns:

float

f(t: float | ndarray) → ndarray[source]#

Function values of param. curve.

Args:

t (float, np.ndarray): time points for evaluation.

Returns:

np.ndarray

df(t)[source]#

Function values of first derivative of param. curve.

Args:

t (float, np.ndarray): time points for evaluation.

Returns:

np.ndarray

d2f(t)[source]#

Function values of second derivative of param. curve.

Args:

t (float, np.ndarray): time points for evaluation.

Returns:

np.ndarray

curvature(t)[source]#

Curvature of param. curve.

Args:

t (float, np.ndarray): time points for evaluation.

Returns:

np.ndarray

rasterize(pitch: float, domain: Tuple[float, float] | None = None, safety: float = 1.25, add_endpoint: bool = False) → ndarray[source]#

Rasterize the param. curve equally.

Args:

pitch (float): distance of rasteruized points on the curve. domain (Tuple[float, float], optional): parametric domain to be used. Default to self.domain. safety (float):

The upper bound of the function parameter of a point is estimated with the tangent vector t of the previous point with t_next_up = t_prev + pitch * safety / ||t||. If the function has large gradients, thesafety factor must be increased. Otherwise, t_next_up is not an upper bound anymore. Default to 1.5

add_endpoint (bool): if True, the point at f(domain[1]) is added to the rasterized points, if the distance

to the point before is smaller than the pitch.

Returns:

np.ndarray: function parameters (NOT function values)

Raises:

RuntimeError: Raised if safety is to small.

rasterize_at(pitch: float, domain: Tuple[float, float] | None = None)[source]#

Rasterize the param. curve equally.

Args:

pitch (float): distance of rasteruized points on the curve. domain (Tuple[float, float], optional): parametric domain to be used. Default to self.domain.

Returns:

np.ndarray: function values

property bounding_box: BoundingBox#

BoundingBox: bounding box of transformable

Access:

get

property center: Vector#

center of the (geometric) object

Access:

get

Returns:

Any

clone() → T#

Create a deepcopy of the object.

Returns:

Describable

property description: str | None#

Description str.

Access:

get

Returns:

Optional[str]

mirrored(mirror_plane: VectorT) → SelfT#

Return a mirrored object mirrored about mirror_plane.

Args:

mirror_plane (VectorLike): mirror plane to be used.

Returns:

TransformableBase

property pivot: VectorT#

Origin of the (geometric) object. If origin is set to None, Transformable.center will be returned.

Pivot must be set to a callable function without parameters.

transformable_obj = ...
transformable_obj.pivot = lambda: return Vector(1, 2)
print(transformable_obj.pivot)  # will print Vector(1, 2)
Access:

get/set

Returns:

Vector

rotated(theta: float, origin: VectorT | str | None = None) → SelfT#

Return a rotated copy around origin with angle theta in math. positive direction (counterclockwise).

Args:

theta (float): rotation angle in rad origin (Optional[Union[linalg.VectorLike, str]], optional):

origin of rotation. If not set, (0,0) is used as origin. If origin == ‘center’, the Transformable.center of the object will be used. The same applies for the case that origin == ‘origin’ with the Transformable.origin property. Default to None.

Returns:

TransformableBase

scaled(fac: float, origin: VectorT | str | None = None) → SelfT#

Return a scale object homogeneously about origin with factor s.

Args:

fac (float): rotation angle in rad origin (Optional[Union[linalg.VectorLike, str]], optional):

origin of rotation. If not set, (0,0) is used as origin. If origin == ‘center’, the Transformable.center of the object will be used. The same applies for the case that origin == ‘origin’ with the Transformable.origin property. Default to None.

Returns:

TransformableBase

transformed(transformations: _TransformationBuilder[VectorT]) → SelfT#
Return a transformed object. the transformation can be build by the following functions:

  • translate()

  • rotate()

  • scale()

  • mirror()

E.g.

transformable_obj.transform(translate([1, 2]) | rotate(np.pi/3) | mirror([3,4])
Args:

transformations (_TransformationBuilder): transformation

Returns:

TransformableBase

translated(trans_vec: VectorT) → SelfT#

Return a translated copy of the object by trans_vec.

Args:

trans_vec (VectorLike): translation vector

Returns:

TransformableBase

translated_to(pos: VectorT) → SelfT#

Return a translated copy of the object so that self.pivot == pos

Args:

pos: new position of object

Returns:

TransformableBase

with_changed_description(new_descr: str) → T#

Clones the object and set the description to new_descr.

Args:

new_descr: new description

Returns:

Describable