How to solve the intersections between helix and sphere?

Helix:

x=R*cos(wt)+x0,
y=R*sin(wt)+y0;
z=h*t;

Sphere:

(x-xc)^2+(y-yc)^2+(z-zc)^2=r^2

substitute the heilx into sphere:

(R*cos(wt)+x0-xc)^2+(R*sin(wt)+y0-yc)^2+(ht-zc)^2=r^2;

How to solve the "t" quickly and easily? or do you have anyother methods to solve the question? Thank you very much

Answer 1

[darova]

You have to find t where distance from center coordinates to helix equals sphere radius

x = r*cos(w*t)+x0;
y = r*sin(w*t)+y0;
z = h*t;
r1 = sqrt(x.^2 + y.^2 + z.^2);        % distance from center to helix (radius)
t0 = [t(1) t(end)];                   % just horizontal line
R0 = [R R];
[t1,~] = polyxpoly(t,r1,t0,R0);       % find t1 where radius == sphere radius

Look also HERE

[Y robot]

Thank you very much , it works

Answer 2

[KSSV]

Refer this:

https://in.mathworks.com/matlabcentral/answers/93623-how-do-i-plot-the-line-of-intersection-between-two-surfaces