math - Hermit Spline Tangents estimation -


hermite spline tangent estimation

i'm trying come algorithm or method allow me estimate tangent's magnitude (the direction given) such interpolated spline best fit given curve (blue dots) in general points in 3d space, 2d solution put me on track.

this hermit spline form:

vector3d p0, p1, m0 (tangent @ p0), m1 (tangent @ p1)

p = (2*t^3 - 3*t^2 + 1)*p0 + (t^3-2*t^2+t)*m0 + (3*t^2 - 2*t^3)*p1 + (t^3-t^2)*m1;

my intuition suggest me sort of least squares method using m0 , m1 magnitudes unknowns (could apply least squares each coordinates ecuation?) somehow should involve projecting , transforming spline equation on vector p1-p0 , instead of returning 3d point, distance of point base p1-p0. guess got lost there :(

perhaps solution easy , love light darkness. in advance time!

well, found solution myself

http://farsthary.com/2016/02/07/spline-fitting/

in case else find useful :)


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