# polytope

Tags:

Updated:

polytope either converts a set of vertices to a set defining a polytope (in a lifted space), or converts a polytopic set to an MPT polytope

## Syntax

P = polytope(v,x)
P = polytope(M)


## Example

The native YALMIP use is for defing a polytope $$x = \sum_{i=1}^N \lambda_i v_i, \lambda \geq 0, \sum_{i=1}^N \lambda_i = 1$$ from a set of vertices $$v_i$$.

v = randn(2,10);
x = sdpvar(2,1);
P = polytope(v,x)


The opeprator does not perform any convex hull computation to reduce the numer of vertices. Note also that the polytope is defined in the $$x,\lambda$$-space. Hence, if you want plot it, you are most likely interested in the projection to $$x$$

plot(P,x)


The command also serves as the interface between YALMIP objects and MPT objects, allow us to convert objects. To generate a polytopic MPT object, simply apply the operator on a purely linear object.

x = sdpvar(2,1);
P = polytope([-1 <= x <= 1]);