Uploaded a couple more videos:
This one shows the grid of points created inside the shape to later do tesselation (decompose the inside of the shape into polygons), which will be shaded using vertex colors, smoothly interpolating the colors between each vertex.
The shape is built using Java's GeneralPath, the control point coordinates are converted from Catmull-Rom to Bezier using a matrix.
This shows color interpolation for those inner points, using an algorithm that I created. Works nicely for any points in any position, even for points inside the shape (which in the literature I managed to find, presented a problem for most interpolation algorithms when dealing with polygons). I'm quite happy with the solution! :)