parametric helix around a line

Hi

I have a line,'l' specifided by two points

P1 = [0,0,0]

P2 = [1,3,-5]

The P2 was calculated using rotation matrix (R).

How could I create a parametric helix around 'l' please

Thanks

Answer 1

[Sulaymon Eshkabilov]

Here is a solution:

% Step 1. Solve for the unknowns of the helix equations using the given P2 point
P1 = [0,0,0];
P2 = [1,3,-5];
% The unknowns: x = r*cos(t), y=r*sin(t), z=c*t.
syms r c t  
Eq1 = 1==r*cos(t);
Eq2 = 3==r*sin(t);
Eq3 = -5==c*t;
Sol = solve(Eq1, Eq2, Eq3);
% Solutions
c = double(Sol.c)

c = 2×1

2.6419 -4.0031

r=double(Sol.r)

r = 2×1

-3.1623 3.1623

t=double(Sol.t)

t = 2×1

-1.8925 1.2490

% Step 2. Plot the helix taking a second solution
time = linspace(0, t(2), 200);
R = r(2);
C = c(2);
X = R*sin(time);
Y = R*sin(time);
Z = C*time;
plot3(X,Y,Z, 'ro-', 'markerfacecolor', 'y'), grid on
xlabel('x(t)'), ylabel('y(t)'), zlabel('z(t)')
axis tight

[Mel A]

Thanks very much @Sulaymon Eshkabilov