bspy.manifold

class Manifold:

A manifold is an abstract base class for differentiable functions with normals and tangent spaces whose range is one dimension higher than their domain.

Parameters
  • metadata (dict, optional): A dictionary of ancillary data to store with the manifold. Default is {}.
Manifold(metadata={})
minSeparation = 0.0001

If two points are within minSeparation of each each other, they are coincident.

factory = {'Hyperplane': <class 'bspy.hyperplane.Hyperplane'>, 'Spline': <class 'bspy.spline.Spline'>}

Factory dictionary for creating manifolds.

metadata
def cached_intersect(self, other, cache=None):

Intersect two manifolds, caching the result for twins (same intersection but swapping self and other).

Parameters
  • other (Manifold): The Manifold intersecting the manifold.
  • cache (dict, optional): A dictionary to cache Manifold intersections, speeding computation. The default is None.
Returns

  • intersections (list (or NotImplemented if other is an unknown type of Manifold)): A list of intersections between the two manifolds. Each intersection records either a crossing or a coincident region.

    For a crossing, intersection is a Manifold.Crossing: (left, right)

    • left : Manifold in the manifold's domain where the manifold and the other cross.
    • right : Manifold in the other's domain where the manifold and the other cross.
    • Both intersection manifolds have the same domain and range (the crossing between the manifold and the other).

    For a coincident region, intersection is Manifold.Coincidence: (left, right, alignment, transform, inverse, translation)

    • left : Solid in the manifold's domain within which the manifold and the other are coincident.
    • right : Solid in the other's domain within which the manifold and the other are coincident.
    • alignment : scalar value holding the normal alignment between the manifold and the other (the dot product of their unit normals).
    • transform : numpy.array holding the matrix transform from the boundary's domain to the other's domain.
    • inverse : numpy.array holding the matrix inverse transform from the other's domain to the boundary's domain.
    • translation : numpy.array holding the 1D translation from the manifold's domain to the other's domain.
    • Together transform, inverse, and translation form the mapping from the manifold's domain to the other's domain and vice-versa.
  • isTwin (bool): True if this intersection is the twin from the cache (the intersection with self and other swapped).
See Also

intersect: Intersect two manifolds.
Solid.slice: slice the solid by a manifold.

Notes

To invert the mapping to go from the other's domain to the manifold's domain, you first subtract the translation and then multiply by the inverse of the transform.

def complete_slice(self, slice, solid):

Add any missing inherent (implicit) boundaries of this manifold's domain to the given slice of the given solid that are needed to make the slice valid and complete.

Parameters
  • slice (Solid): The slice of the given solid formed by the manifold. The slice may be incomplete, missing some of the manifold's inherent domain boundaries. Its dimension must match self.domain_dimension().
  • solid (Solid): The solid being sliced by the manifold. Its dimension must match self.range_dimension().
See Also

Solid.slice: Slice the solid by a manifold.

Notes

For manifolds without inherent domain boundaries (like hyperplanes), the operation does nothing.

def copy(self):

Copy the manifold.

Returns
def domain_dimension(self):

Return the domain dimension.

Returns
  • dimension (int):
def evaluate(self, domainPoint):

Return the value of the manifold (a point on the manifold).

Parameters
  • domainPoint (numpy.array): The 1D array at which to evaluate the point.
Returns
  • point (numpy.array):
def flip_normal(self):

Flip the direction of the normal.

Returns
  • manifold (Manifold): The manifold with flipped normal. The manifold retains the same tangent space.
See Also

Solid.complement: Return the complement of the solid: whatever was inside is outside and vice-versa.

@staticmethod
def from_dict(dictionary):

Create a Manifold from a data in a dict.

Parameters
  • dictionary (dict): The dict containing Manifold data.
Returns
See Also

to_dict: Return a dict with Manifold data.

def full_domain(self):

Return a solid that represents the full domain of the manifold.

Returns
  • domain (Solid): The full (untrimmed) domain of the manifold.
See Also

Boundary: A portion of the boundary of a solid.

def intersect(self, other):

Intersect two manifolds (self and other).

Parameters
Returns

  • intersections (list (or NotImplemented if other is an unknown type of Manifold)): A list of intersections between the two manifolds. Each intersection records either a crossing or a coincident region.

    For a crossing, intersection is a Manifold.Crossing: (left, right)

    • left : Manifold in the manifold's domain where the manifold and the other cross.
    • right : Manifold in the other's domain where the manifold and the other cross.
    • Both intersection manifolds have the same domain and range (the crossing between the manifold and the other).

    For a coincident region, intersection is a Manifold.Coincidence: (left, right, alignment, transform, inverse, translation)

    • left : Solid in the manifold's domain within which the manifold and the other are coincident.
    • right : Solid in the other's domain within which the manifold and the other are coincident.
    • alignment : scalar value holding the normal alignment between the manifold and the other (the dot product of their unit normals).
    • transform : numpy.array holding the transform matrix from the manifold's domain to the other's domain.
    • inverse : numpy.array holding the inverse transform matrix from the other's domain to the boundary's domain.
    • translation : numpy.array holding the translation vector from the manifold's domain to the other's domain.
    • Together transform, inverse, and translation form the mapping from the manifold's domain to the other's domain and vice-versa.
See Also

cached_intersect: Intersect two manifolds, caching the result for twins (same intersection but swapping self and other).
Solid.slice: slice the solid by a manifold.

Notes

To invert the mapping to go from the other's domain to the manifold's domain, you first subtract the translation and then multiply by the inverse of the transform.

def normal(self, domainPoint, normalize=True, indices=None):

Return the normal.

Parameters
  • domainPoint (numpy.array): The 1D array at which to evaluate the normal.
  • normalize (boolean, optional): If True the returned normal will have unit length (the default). Otherwise, the normal's length will be the area of the tangent space (for two independent variables, its the length of the cross product of tangent vectors).
  • indices (iterable, optional): An iterable of normal indices to calculate. For example, indices=(0, 3) will return a vector of length 2 with the first and fourth values of the normal. If None, all normal values are returned (the default).
Returns
  • normal (numpy.array):
def range_bounds(self):

Return the range bounds for the manifold.

Returns
  • rangeBounds (np.array or None): The range of the manifold given as lower and upper bounds on each dependent variable. If the manifold has an unbounded range, None is returned.
def range_dimension(self):

Return the range dimension.

Returns
  • dimension (int):
@staticmethod
def register(manifold):

Class decorator for subclasses of Manifold that registers the subclass with the Manifold factory.

def tangent_space(self, domainPoint):

Return the tangent space.

Parameters
  • domainPoint (numpy.array): The 1D array at which to evaluate the tangent space.
Returns
  • tangentSpace (numpy.array):
def to_dict(self):

Return a dict with Manifold data.

Returns
  • dictionary (dict):
See Also

from_dict: Create a Manifold from a data in a dict.

def transform(self, matrix, matrixInverseTranspose=None):

Transform the range of the manifold.

Parameters
  • matrix (numpy.array): A square matrix transformation.
  • matrixInverseTranspose (numpy.array, optional): The inverse transpose of matrix (computed if not provided).
Returns
  • manifold (Manifold): The transformed manifold.
See Also

Solid.transform: transform the range of the solid.

def translate(self, delta):

Translate the range of the manifold.

Parameters
  • delta (numpy.array): A 1D array translation.
Returns
  • manifold (Manifold): The translated manifold.
See Also

Solid.translate: translate the range of the solid.

def trimmed_range_bounds(self, domainBounds):

Return the trimmed range bounds for the manifold.

Parameters
  • domainBounds (array-like): An array with shape (domain_dimension, 2) of lower and upper and lower bounds on each manifold parameter.
Returns
  • trimmedManifold, rangeBounds (Manifold, np.array): A manifold trimmed to the given domain bounds, and the range of the trimmed manifold given as lower and upper bounds on each dependent variable.
Notes

The returned trimmed manifold may be the original manifold, depending on the subclass of manifold.

class Manifold.Crossing(builtins.tuple):

Crossing(left, right)

Inherited Members
Crossing
Crossing
left
right
builtins.tuple
index
count
class Manifold.Coincidence(builtins.tuple):

Return type for intersect.

Inherited Members
Coincidence
Coincidence
left
right
alignment
transform
inverse
translation
builtins.tuple
index
count