I would like a sharp turn, not the smoothed round turn that the sub surf modifier causes. Is this possible? Notice the purple line for the mean crease, I would like it to look like that
Depending on what your mesh is like, there are several ways to do this.
3D Objects: You can accomplish this with the shortcut Shift+E while in edit mode. Select the edge you would like to crease (the "seam") first, and then press 1 or move the cursor until the crease is maxed out.
2D Objects: For two-dimensional objects (planes) you can use Loopcuts to simulate this effect. One of the main drawbacks to this method is your vertex count will be increased. Sadly the Edge Crease option does not work on 2D objects.
In edit mode, hover over the adjacent edges and press Ctrl+R, then click once and drag towards the seam. Now click again to finish the operation. Repeat for the other side.