# How to get a list of 3D coordinates using point and rotation

I have one point:

p1={82,80,0}


I want to rotate it around the Y axis.

The start time is 0 seconds ($0s$) and the end time is 5 seconds ($5s$).

t1=0;t2=5;


I want to subdivide the time into 150 fractions.

With the code below I get you all the fractions of time that I need to analyze

fractions = 150;
listTime = Subdivide[(t2 - t1), fractions - 1] // N


With the code below I can find the equation that defines the trajectory and gives me the fractions of angle for each time.

θ1 = 0; θ2 = 90;
eq1 = Fit[{{tI, θ1}, {tF, θ2}}, {1, x}, x]
points = eq1 /. x -> listTime


I tried using RotationTransform, RotationMatrix, to get what I need, but I did not succeed

What do I need to do to get a list with all the coordinates for each time taking point p1 at time $0s$?

• Does the answer not suit your needs? You should give its author some feedback. – anderstood Feb 22 '18 at 20:49

Something like?

p1= {82,80,0};
ω = (Pi/2)/5;

(*build a list of angles*)
angles = Table[ω t, {t, 0, 5, 1/150}];

(*map rotation over angles*)
pts = Map[RotationTransform[#, {0, 1, 0}][p1] &, angles];

angles[[1 ;; 10]]
(* {0, π/1500, π/750, π/500, π/375, π/300, π/250, (7 π)/1500, (2 π)/375, (3 π)/500} *)

pts[[1 ;; 10]]
(* {{82, 80, 0}, {82 Cos[π/1500],
80, -82 Sin[π/1500]}, {82 Cos[π/750],
80, -82 Sin[π/750]}, {82 Cos[π/500],
80, -82 Sin[π/500]}, {82 Cos[π/375],
80, -82 Sin[π/375]}, {82 Cos[π/300],
80, -82 Sin[π/300]}, {82 Cos[π/250],
80, -82 Sin[π/250]}, {82 Cos[(7 π)/1500],
80, -82 Sin[(7 π)/1500]}, {82 Cos[(2 π)/375],
80, -82 Sin[(2 π)/375]}, {82 Cos[(3 π)/500],
80, -82 Sin[(3 π)/500]}} *)