The measure of the distance of the edge from q1 to q2 and the portion of that is collision free.
Distance is that produced by CollisionChecker::ComputeConfigurationDistance() for the entire edge between q1 and q2.
The portion of the edge between q1 and q2 that is collision free is encoded as the value α with the following semantics:
- α = 1: No collisions were detected. The full edge can be considered collision free. This is the only time completely_free() reports
true.
- 0 ≤ α < 1: A collision was detected between q1 and q2. α is the largest interpolation value such that an edge from q to qα can be considered collision free (where qα = interpolate(q1, q2, α)). partially_free() reports
true.
- α is undefined: q1 was found to be in collision. That means there exists no α for which the edge (q1, qα) can be collision free.
- Note
- The length of the collision-free edge can be computed via distance * α. To simplify comparisons between a number of edges, some of which may not have a defined α, the function alpha_or(default_value) is provided. This is equivalent to
edge.partially_free() ? edge.alpha() : default_value.
-
For α to be meaningful, the caller is obliged to make sure that they use the same interpolating function as the CollisionChecker did when generating the measure. Calling CollisionChecker::InterpolateBetweenConfigurations() on the same checker instance would satisfy that requirement.
Returns the value of alpha, if defined.
Note: Due to the sampling nature of the edge check, the edge (q1, qα) may not actually be collision free (due to a missed collision). There's a further subtlety. Subsequently calling CheckEdgeCollisionFree(q1, qα) may return false. This apparent contradiction is due to the fact that the samples on the edge (q1, qα) will not necessarily be the same as the samples originally tested on the edge (q1, q2). It is possible for those new samples to detect a previously missed collision. This is not a bug, merely a property of sampling-based testing.
- Precondition
- partially_free() returns
true.
