A diagram of the trefoil knot
The diagram of a knot differs from a projection of the knot on a plane because every crossing is marked with an indication of the type (a branch of the crossing can pass over or under the other one). So, it is possible to reconstruct the knot with its diagram, a projection wouldn't be enough.
© matematita
The image belongs to the sections...:
Images from the topology section (From the exhibitions of matematita)
Trefoil knot (Topology)