splines

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(non-rational) Polynomial curves cannot exactly represent circles and ellipses, but they can be used to approximate them: https://en.wikipedia.org/wiki/Composite_B%C3%A9zier_curve#Approximating_circular_arcs http://spencermortensen.com/articles/bezier-circle/ https://www.tinaja.com/glib/ellipse4.pdf See also Salomon, David; Curves and Surfaces for Computer Graphics;...

mgeier

The derivative of a Bézier curve of degree n is another Bézier curve of degree n - 1, which is called "hodograph".

mgeier

For now, we mostly show examples in Euclidan space, but the equations should work with any vector space. For example, the polynomials of a given degree also form a vector...

mgeier

Does the Catmull--Rom quaternion spline ensure C2 continuity?

4

I didn't find if it is C2 continuous in the documentation. Or if it can achieve higher order of continuity?

yakunsjtu

Why the Barry-Goldman quaternions spline is always closed?

1

Hello, I'm currently working on implementing the Barry-Goldman quaternions spline in the R language. I follow your code. I am wondering why you set it closed. Is there a problem...

stla

Problem when interpolate direction vectors with rotation interpolation method

3

Hello, I am tring to interpolate a set of unit direction vectors' endpoints with spline. It means that the spline will interpolate/cross each direction vector's endpoint on a unit sphere...

sysuyl