# Posts tagged ‘Cox-Deboor’

Is it possible to get the length of a curve without walking along it,  standard methods essentially split it into chunks and measure there total – the more chunks the better the accuracy. I’ll look into arc length and least square methods.

As cox-deboor are quite simple ive started looking into cubic-bernstein-polynormials. They essentially contain 4 tangents, that can be used in defining sections of a uniform b-spline. The problem arises when defining a value along the entire b-spline – As its constructed from multiple cubic curves, and which a value along these is defined as (t) being 0 – 1. So a friend of mine wanted to work out a math curve – specifically B-spline curve. In any event he worked it out before me, but it gave me the challenge too. So the basic formula is:

p = p + p1

So if we imagine 4 points in space: a,b,c,d we draw a line between these by defining vectors between each segment ab-bc and bc-cd giving us a1-b1. Finally we get a final vector between a1-b1 giving us a2. The fn acts as a pattern of 2 sets eg.

1 2 3 4 = 3 5 7 = 8 12 = 20