Degrafa Spline Approximation Over An Interval
Due to severe lack of spare time, Degrafa work is moving very slowly these days. I just added the cartesian spline approximation over an arbitrary interval. For the natural cubic spline, defined over an interval [a,b], this method produces a quadratic Bezier approximation in the interval [x1, x2], where the input interval is contained in [a,b]. This allows some interesting applications, including smooth animation of an area under a spline. This is illustrated in a new demo. A screenshot is shown below.
Next step is to add a parametric spline and work over the architecture so that the computational core of a spline is separated from the Degrafa geometry pipeline. Over the long term, this should allow anyone to add (interpolative) splines to Degrafa with little, if any, understanding of the internal Degrafa architecture and geometry pipeline.
The demo shows the entire area under the spline statically highlighted using the normal quad. approximation (which is always exact at the knots). Click the ‘Animate’ button to see the area dynamically highlighted over an arbitrary range.