Fractals and Curves

Fractals and Curves!

murray polygon

type of peano curve, self-similar and space filling

where does murray come from

multiple radix

application of fractal curves

dithering, reduction of colour depth

similarity between hermite and interpolating curve 1

both consist of cubic polynomial segment

similarity between hermite and interpolating curve 2

both are characterised by a 4x4 matrix

similarity between hermite and interpolating curve 3

both ensure some kind of continuity

difference between hermite and interpolating curve 1

interpolating cubic curve is defined by 4 points, hermite is defined by 2 points and 2 derivatives

difference between hermite and interpolating curve 2

hermite curves are smoother

nice property of b spline 1

they guarantee c0, c1 and c2 continuity

nice property of b spline 2

tangents at join points are perfectly matched, so they are good for shading

nice property of b spline 3

no change in derivative, e.g., speed, so they are suitable for animation