[SOLVED] Cs4610/cs5335: homework 2

PA Q1: Write a function that draws n random samples in the unit (three
dimensional) cube and returns the n × n all-pairs distance matrix between
pairs of samples. Note that this distance matrix should be symmetric and
the diagonal should be zero.
PA Q2: The distance matrix calculated in Q1 can be viewed as a fully
connected weighted graph. For a given radius and given number of samples, prune edges with weights greater than radius and randomly subsample
vertices down to the specified number. Return the corresponding adjacency
matrix.
PA Q3: For a given radius and number of samples, calculate whether the
r-disk graph on the unit cube *should* be connected or not according to
Theorem 7 of the Karaman and Frazolli paper. Compare this result with
the actual connectivity statistics you got in Q2. How are they the same or
different? Why do you think that is?
PA Q4: Write a function that calculates the sPRM graph for a given set of
samples and a given radius. You should prune any input samples that are
in collision and output the remaining samples as samplesFree. You should
output the weighted adjacency matrix for the sPRM graph. Note that we’ve
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given you two functions to help with collision checking: robotCollision and
checkEdge.
PA Q5: Write a function that implements RRT to find a path from qStart
to qGoal. Return qMilestones, an m×4 matrix of vertices (i.e. points) along
the path.
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