You need to open Process and click: Sketch-Import Library-Add Library-papaya to see our work. We use this library to do the matrix manipulation for our project.
Our project is Tutte Embedding and we assume all the springs of the edges are 1.
First the user can input some points which are marked as red dots by mouse click on the canvas. Please note the number of points should be more than 3, otherwise there is no way that the drawing would be 3-connected.
Then we offer two options for connecting the vertices the user has just created. They can either press Initial Graph Button to generate a default drawing or they can use mouse drag to manually link the vertices themselves. But we also have to make sure that whether the initial graph we generated is planar or not. The only constraint we posed is that when v ≥ 3 then e ≤ 3v − 6. If this holds false, then the graph is not a planar graph.
When the mouse moves to a point, it will become green and the user can simply pull a line staring here to another vertex. Here the user is supposed to know what is a 3-connected graph. If the handmade drawing ends up to be inappropriate, then the Tutte Draw Button will be come grey indicating invalid operation.
At last, with a simple click on the Tutte Draw Button, the user can see amazing dynamic changes on these elements. The first three points act as the exterior vertices and the interior vertex lies exactly in the barycentric position of its neighbors. The Reset Button is used to clear all the vertices and edges.
The user will know how to make a 3 connected graph with a given points set. And they can see how to apply the Tutte Algorithm visually once the exterior vertices are fixed which may provide them a better and more interesting way of understanding Tutte Embedding.