@@ -10,7 +10,7 @@ import scipy.spatial

 from ..notebook_integration import ensure_holoviews

 from .base_learner import BaseLearner

-from .triangulation import Triangulation

+from .triangulation import Triangulation, point_in_simplex, circumsphere

 import random

 from math import factorial

@@ -115,12 +115,19 @@ def choose_point_in_simplex(simplex, transform=None):

     if transform is not None:

         simplex = np.dot(simplex, transform)

-    distances = scipy.spatial.distance.pdist(simplex)

-    distance_matrix = scipy.spatial.distance.squareform(distances)

-    i, j = np.unravel_index(np.argmax(distance_matrix), distance_matrix.shape)

+    # choose center iff the shape of the simplex is nice,

+    # otherwise the longest edge

+    center, radius = circumsphere(simplex)

+    if point_in_simplex(center, simplex):

+        point = np.average(simplex, axis=0)

+    else:

+        distances = scipy.spatial.distance.pdist(simplex)

+        distance_matrix = scipy.spatial.distance.squareform(distances)

+        i, j = np.unravel_index(np.argmax(distance_matrix), distance_matrix.shape)

+

+        point = (simplex[i, :] + simplex[j, :]) / 2

-    point = (simplex[i, :] + simplex[j, :]) / 2

-    return np.linalg.solve(transform, point)

+    return np.linalg.solve(transform, point)  # undo the transform

 class LearnerND(BaseLearner):