Ambient space steering and tangent space steering
Two blue curved constraint manifolds. On the left, four candidate nodes on a line toward an ambient-space sample travel along long orange projection arrows and land close together on the manifold. On the right, three nodes sampled on a green tangent plane travel along short purple projection arrows and land farther apart. The left sequence plays first, followed by the right sequence.
Ambient space steering
Tangent space steering
Tangent space
Long
projection distance
Short
projection distance
Random sample
Nearest neighbor
Random sample
on Tangent space
Nearest neighbor
on Tangent space
Ignores manifold geometry
Long projection distance. May yield little progress after projection
Uses local manifold geometry
Short projection distance. Promotes progress along the manifold
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