How to sample ICurveGeo evenly based on the curve length? not the u coordinates

[chatyan]

Hi, I am new to this great library.
Currently, I want to get sampling points evenly on the ICurveGeo.
I have tried to use pt(double u) function and got some points based on evenly sampling the u coordination. I just wonder if there is a way to let the user sampling points based on the arc-length of the curve, so the user can get those sampling points accurately.

Thanks a lot.
Again great library for 3D modeling in Java

[satoru]

Thank you for the comment.
Unfortunately I don't have a method to sample NURBS curves evenly by the length in the XYZ space with mathematically accurate inverse calculation from XYZ to U.
What I would do is just approximate it by lengths of line segments like the code below.
You could replace the length calculation with arc-length calculation by 3 points or 2 points + tangent vectors to make it more accurate, or simply increase resolution of the line segment approximation depending on how much accuracy you need.
Thanks!
Satoru

`
import igeo.*;
size(1000,800,IG.GL);
ICurve crv = new ICurve(IG.v(0,0,0, 100,0,0, 110,50,0, 120,0,0, 50,-50,0),3);

int div = 10;
double len = 0;
// you could also use len() method, which is also linear approximation.
//double len = crv.len();
int res = 1000;
IVec prevPt = crv.pt(0);
for(int i=1; i<=res; i++){
IVec pt = crv.pt(i*1./res);
len += pt.dist(prevPt);
prevPt = pt;
}

int idx = 0;
double curlen = 0;
prevPt = crv.pt(0);
for(int i=1; i<=res; i++){
IVec pt = crv.pt(i1./res);
curlen += prevPt.dist(pt);
for(; curlen >= len/dividx; idx++){
double ratio = (curlen - len/div*idx)/ prevPt.dist(pt);
double u = (i-ratio)/res;
new IPoint(crv.pt(u)).clr(1.,0,0);
}
prevPt = pt;
}
`

[chatyan]

Your comment really helps me a lot!
Many thanks!