- Rafael Losada Liste
This activity belongs to the GeoGebra book Attractive projects. 2D Project: create a custom font of scalable characters. Many curves do not conform to elementary geometric figures, but they are the result of a long and complex evolution. Although theoretically a polygonal can simulate any curve increasing the number of vertices, this requires a lot of work, so in practice it is used only when the figure consists of straight segments. Note: You can quickly create several free points A1, A2 ... using the GeoGebra Spreadsheet. Then, just distribute the points following the path (or paths) of the stroke. For curves, better results are obtained by using splines. In general, a spline is a smooth (that is, differentiable) curve defined by polynomials. In GeoGebra, a spline is concretely a parametric curve c(t) = (f(t), g(t)), where f(t) and g(t) are polynomials (by default, of third degree), with t varying between 0 and 1. The result is similar to a Bézier curve. As we see, to vectorize to graph using polygonal or splines, it is necessary to divide the graph into lists of points belonging to continuous paths (Hamiltonian paths).