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

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.

[Star Strider]

I cannot understand what you want to do. Rather than doing your own conversions, use pol2cart, sph2cart and their inverse functions (linked at the end of the page for each).

Note that for spherical coordinates, there are 2 angles and the radius. For polar coordinates, there is 1 angle and the radius.

(I am not listing this as an Answer because it is not one.)

[Image Analyst]

I don't understand either. I don't know what "with respect to the x-direction" means. Let's say you were to project those points into either the flat x-z plane, the y-z plane, or the x-y plane. Would any of those planes have the angle that you want?

[Laura]

project those points into x-y plane. There is no angle between two points except the angle is defined as shown in the figure. That angle theta is measured from the positive x-axis.

[Image Analyst]

Then just use the 2-D formula, ignoring your Z values completely.

[Laura]

the distance r needs to have Z components in there right?

[Star Strider]

Only for 3D (spherical) representation.

Answer 1

[Image Analyst]

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

[Laura]

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?