The Minkowski Difference between two shapes $A$ and $B$ is an [[Operation|operation]] that produces a new shape which is the pointwise difference of $A$ and $B$. $ \huge C=A-B=\set{ \vec a-\vec b, \vec a \in A,\vec b \in B } $ $ \huge \begin{align} |C| &= |A| \times |B| \end{align} $ $\huge \op{CSO}(C): \text{ convex hull of } C $ ### Properties If $A \cap B \neq \emptyset$, then $\vec O \in \op{CSO}(A-B)$, or in other words - if $A$ and $B$ intersect then the [[Origin]] point of the [[Coordinate System]] will be contained in the [[Convex Hull]] of their minkowski difference. $\text{Support}(\text{CSO}(A-B),\vec d) = \text{Support}(A,\vec d) - \text{Support}(B,-\vec d )$