Calculating angles between two points in 3D that is measured from positive x-direction

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I have multiple points that I need to calculate the angle between two points that respects to x-direction as shown in the image. The angle is measured from positive x direction (counter clockwise).
For 2D case as shown in the image:
% N is number of points
for j=1:N-1
for k=(j+1):N
% difference distance in x-direction
sepx=X(1,k)-X(1,j);
sepy=Y(1,k)-Y(1,j);
r = sqrt(sepx^2+sepy^2);
% use atan2d to return angle in degree between -180 to 180.
% use mod to return angle in degree between 0-360
theta=mod(atan2d(sepy,sepx),360);
end
end
For 3D case, I only changed this part
sepx=X(1,k)-X(1,j);
sepy=Y(1,k)-Y(1,j);
sepz=Z(1,k)-Z(1,j);
r = sqrt(sepx^2+sepy^2 +sepz^2);
theta=mod(atan2d(sepy,sepx),360);
I am really bad at 3D in term of visualization to project thing. Is that correct to find angle of two points in 3D that is measured from positive x-direction (counter clockwise). The counter clockwise for an observer looking from above on the xy-plane. Please helps. Thanks.
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Accepted Answer

Image Analyst
Image Analyst on 4 May 2016
Edited: Image Analyst on 4 May 2016
I thought you had (x,y,z) coordinates for all three points? If not, do you have the points in spherical coordinates like radius theta, and phi? If you have x,y,z, just use x and y, ignoring z and then use the dot product or whatever the 2D angle formula is, like this: https://www.google.com/?gws_rd=ssl#q=angle+between+two+2d+vectors
  1 Comment
Laura
Laura on 16 May 2016
I have 512 spheres that has (x,y,z) coordinates. I want to project all 512 points on the xy-plane. Do I just use x and y?

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