The vase is a CNC model consists of more than 116000 G01 codes with
total tool path length of 46.67m. Its B-spline representation
consists of more than 42000 quadratic curve segments.
A set of quadratic polynomials
x = a2 x^2 + a1 x + a0
y = b2 y^2 + b1 y + b0
z = c2 z^2 + c1 z + c0
is represented by
[[a0, a1, a2], [b0, b1, b2], [c0, c1, c2]]
A quadratic spline consisting of n segments defined on [0,1] is
represented by
[c1,c2,...,cn, [u1=0,u2,...,u_n,u_{n+1}=1]]
where each ci is a quadratic polynomial defined on [u_i,u_{i+1]].
We group together the splines with the same x-coordinate:
[s1,s2,...,sm]
The model consisting of k tool pathes each with a fixed x-coordinate
is represented by
[r1,...,rk]
where r_i is a group of splines with the same x-coordinate.
2011.5