class_docstr: Private class for the n-dimensional hypersphere.
  
  Class for the n-dimensional hypersphere embedded in the
  (n+1)-dimensional Euclidean space.
  
  By default, points are parameterized by their extrinsic
  (n+1)-coordinates. For dimensions 1 and 2, this can be changed with the
  `default_coords_type` parameter. For dimensions 1 (the circle),
  the intrinsic coordinates correspond angles in radians, with 0. mapping
  to point [1., 0.]. For dimension 2, the intrinsic coordinates are the
  spherical coordinates from the north pole, i.e. where angles [0., 0.]
  correspond to point [0., 0., 1.].
  
  Parameters
  ----------
  dim : int
      Dimension of the hypersphere.
  
  default_coords_type : str, {'extrinsic', 'intrinsic'}
      Type of representation for dimensions 1 and 2.
docstr: Convert point from intrinsic to extrinsic coordinates.
  
  Convert from the intrinsic coordinates in the hypersphere,
  to the extrinsic coordinates in Euclidean space.
  For dimensions 1 (the circle), the intrinsic coordinates correspond
  angles in radians, with 0. mapping to point [1., 0.]. For dimension
  2, the intrinsic coordinates are the spherical coordinates from the
  north pole, i.e. that angles [0., 0.] correspond to point [0., 0., 1.].
  
  Parameters
  ----------
  point_intrinsic : array-like, shape=[..., dim]
      Point on the hypersphere, in intrinsic coordinates.
  
  Returns
  -------
  point_extrinsic : array-like, shape=[..., dim + 1]
      Point on the hypersphere, in extrinsic coordinates in
      Euclidean space.
docstr_tok: ["Convert","point","from","intrinsic","to","extrinsic","coordinates",".","Convert","from","the","intrinsic","coordinates","in","the","hypersphere",",","to","the","extrinsic","coordinates","in","Euclidean","space",".","For","dimensions","1","(","the","circle",")",",","the","intrinsic","coordinates","correspond","angles","in","radians",",","with","0.","mapping","to","point","[","1.",",","0.","]",".","For","dimension","2",",","the","intrinsic","coordinates","are","the","spherical","coordinates","from","the","north","pole",",","i.e",".","that","angles","[","0.",",","0",".","]","correspond","to","point","[","0.",",","0.",",","1.","]",".","Parameters","--","--","--","--","--","point_intrinsic",":","array-like",",","shape=","[","...",",","dim","]","Point","on","the","hypersphere",",","in","intrinsic","coordinates",".","Returns","--","--","--","-","point_extrinsic",":","array-like",",","shape=","[","...",",","dim","+","1","]","Point","on","the","hypersphere",",","in","extrinsic","coordinates","in","Euclidean","space","."]
code: def intrinsic_to_extrinsic_coords(self, point_intrinsic):
      """Convert point from intrinsic to extrinsic coordinates.
  
      Convert from the intrinsic coordinates in the hypersphere,
      to the extrinsic coordinates in Euclidean space.
      For dimensions 1 (the circle), the intrinsic coordinates correspond
      angles in radians, with 0. mapping to point [1., 0.]. For dimension
      2, the intrinsic coordinates are the spherical coordinates from the
      north pole, i.e. that angles [0., 0.] correspond to point [0., 0., 1.].
  
      Parameters
      ----------
      point_intrinsic : array-like, shape=[..., dim]
          Point on the hypersphere, in intrinsic coordinates.
  
      Returns
      -------
      point_extrinsic : array-like, shape=[..., dim + 1]
          Point on the hypersphere, in extrinsic coordinates in
          Euclidean space.
      """
      if self.dim == 2:
          return self.spherical_to_extrinsic(point_intrinsic)
      if self.dim == 1:
          return self.angle_to_extrinsic(point_intrinsic)
  
      raise NotImplementedError(
          "Intrinsic coordinates are only implemented in dimension 1 and 2."
      )
  
imports: import logging
  import math
  from itertools import product
  from scipy.stats import beta
  import geomstats.algebra_utils
  import geomstats.backend
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import get_batch_shape, repeat_out
label_desc: Use image node_id 14 for calling the _Hypersphere obj's underlying member method code with example usage: obj.intrinsic_to_extrinsic_coords(point_intrinsic) and returns: self, self