Minkowski sum of two Objects

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I'm trying to implement the ClearPath pathfinding algorithm, that relys on velocity obstacles.

It is assumed, that both objects have a circular hull.

However, I do not understand how to calculate the minkowski sum of two objects.
Here's an excerpt from the paper



Apparently, the minkowski sum is simply the sum of two sets (here all possible velocities that yield a collision), but it is not explained how to calculate the set of those velocity vectors. It is only explained how to calculate a single velocity vector ( λ(p,v) ). Am I missing something ?



Also, what does this mean ?




let -A denote the object A reflected in its reference point




What is an objects reference point, and what does it mean to reflect said point ?




summation




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  • 1




    See en.wikipedia.org/wiki/Minkowski_addition for information about Minkowski sum. The Minkowski sum of two circular discs is another circular disc (see math.stackexchange.com/questions/444845/…). If $-A$ means $A$ reflected in its reference point, then I think "reference point" just means the origin of the coordinate system you are using to represent $A$.
    – Rob Arthan
    Jul 29 at 19:19














up vote
0
down vote

favorite












I'm trying to implement the ClearPath pathfinding algorithm, that relys on velocity obstacles.

It is assumed, that both objects have a circular hull.

However, I do not understand how to calculate the minkowski sum of two objects.
Here's an excerpt from the paper



Apparently, the minkowski sum is simply the sum of two sets (here all possible velocities that yield a collision), but it is not explained how to calculate the set of those velocity vectors. It is only explained how to calculate a single velocity vector ( λ(p,v) ). Am I missing something ?



Also, what does this mean ?




let -A denote the object A reflected in its reference point




What is an objects reference point, and what does it mean to reflect said point ?




summation




share|cite|improve this question















  • 1




    See en.wikipedia.org/wiki/Minkowski_addition for information about Minkowski sum. The Minkowski sum of two circular discs is another circular disc (see math.stackexchange.com/questions/444845/…). If $-A$ means $A$ reflected in its reference point, then I think "reference point" just means the origin of the coordinate system you are using to represent $A$.
    – Rob Arthan
    Jul 29 at 19:19












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I'm trying to implement the ClearPath pathfinding algorithm, that relys on velocity obstacles.

It is assumed, that both objects have a circular hull.

However, I do not understand how to calculate the minkowski sum of two objects.
Here's an excerpt from the paper



Apparently, the minkowski sum is simply the sum of two sets (here all possible velocities that yield a collision), but it is not explained how to calculate the set of those velocity vectors. It is only explained how to calculate a single velocity vector ( λ(p,v) ). Am I missing something ?



Also, what does this mean ?




let -A denote the object A reflected in its reference point




What is an objects reference point, and what does it mean to reflect said point ?




summation




share|cite|improve this question











I'm trying to implement the ClearPath pathfinding algorithm, that relys on velocity obstacles.

It is assumed, that both objects have a circular hull.

However, I do not understand how to calculate the minkowski sum of two objects.
Here's an excerpt from the paper



Apparently, the minkowski sum is simply the sum of two sets (here all possible velocities that yield a collision), but it is not explained how to calculate the set of those velocity vectors. It is only explained how to calculate a single velocity vector ( λ(p,v) ). Am I missing something ?



Also, what does this mean ?




let -A denote the object A reflected in its reference point




What is an objects reference point, and what does it mean to reflect said point ?





summation





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 29 at 18:49









PAThePianoDude

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  • 1




    See en.wikipedia.org/wiki/Minkowski_addition for information about Minkowski sum. The Minkowski sum of two circular discs is another circular disc (see math.stackexchange.com/questions/444845/…). If $-A$ means $A$ reflected in its reference point, then I think "reference point" just means the origin of the coordinate system you are using to represent $A$.
    – Rob Arthan
    Jul 29 at 19:19












  • 1




    See en.wikipedia.org/wiki/Minkowski_addition for information about Minkowski sum. The Minkowski sum of two circular discs is another circular disc (see math.stackexchange.com/questions/444845/…). If $-A$ means $A$ reflected in its reference point, then I think "reference point" just means the origin of the coordinate system you are using to represent $A$.
    – Rob Arthan
    Jul 29 at 19:19







1




1




See en.wikipedia.org/wiki/Minkowski_addition for information about Minkowski sum. The Minkowski sum of two circular discs is another circular disc (see math.stackexchange.com/questions/444845/…). If $-A$ means $A$ reflected in its reference point, then I think "reference point" just means the origin of the coordinate system you are using to represent $A$.
– Rob Arthan
Jul 29 at 19:19




See en.wikipedia.org/wiki/Minkowski_addition for information about Minkowski sum. The Minkowski sum of two circular discs is another circular disc (see math.stackexchange.com/questions/444845/…). If $-A$ means $A$ reflected in its reference point, then I think "reference point" just means the origin of the coordinate system you are using to represent $A$.
– Rob Arthan
Jul 29 at 19:19















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