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- """Compute the mean of two Bézier splines on a sphere using the Riemannian mean"""
- # https://morphomatics.github.io/tutorials/tutorial_bezierfold/
- import jax
- import jax.numpy as jnp
- import numpy as np
- from morphomatics.geom import BezierSpline
- from morphomatics.manifold import Bezierfold
- from morphomatics.manifold import Sphere
- import vedo
- M = Sphere()
- B = Bezierfold(M, 2, 2)
- North = jnp.array([0.0, 0.0, 1.0])
- South = jnp.array([0.0, 0.0, -1.0])
- p1 = jnp.array([1.0, 0.0, 0.0])
- o1 = jnp.array([1 / jnp.sqrt(2), 1 / jnp.sqrt(2), 0.0])
- om1 = M.connec.exp(o1, jnp.array([0, 0, -0.25]))
- op1 = M.connec.exp(o1, jnp.array([0, 0, 0.25]))
- q1 = jnp.array([0, 1, 0.0])
- B1 = BezierSpline(M, [jnp.stack((p1, om1, o1)), jnp.stack((o1, op1, q1))])
- z = M.connec.geopoint(o1, North, 0.5)
- p2 = jnp.array([1.0, 0.0, 0.0])
- o2 = M.connec.geopoint(p1, z, 0.5)
- om2 = M.connec.geopoint(p1, z, 0.4)
- op2 = M.connec.geopoint(p1, z, 0.6)
- q2 = z
- B2 = BezierSpline(M, [jnp.stack((p2, om2, o2)), jnp.stack((o2, op2, q2))])
- data = jnp.array([B.to_coords(B1), B.to_coords(B2)])
- mean = Bezierfold.FunctionalBasedStructure.mean(B, data)[0]
- mean = B.from_coords(mean)
- time = jnp.linspace(0.0, 2.0, num=100)
- pts1 = np.asarray(jax.vmap(B1.eval)(time))
- pts2 = np.asarray(jax.vmap(B2.eval)(time))
- mean_pts = np.asarray(jax.vmap(mean.eval)(time))
- sphere = vedo.Sphere().c("yellow9")
- line1 = vedo.Line(pts1, lw=3).cmap("Blues", time)
- line2 = vedo.Line(pts2, lw=3).cmap("Blues", time).add_scalarbar("Time")
- line_mean = vedo.Line(mean_pts, c="red5", lw=4)
- vedo.show(sphere, line1, line2, line_mean, __doc__, axes=1).close()
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