projPointOnCircle3d

PROJPOINTONCIRCLE3D Project a 3D point onto a 3D circle.

   PT2 = projPointOnCircle3d(PT, CIRCLE).
   Computes the projection of 3D point PT onto the 3D circle CIRCLE. 
   
   Point PT is a N-by-3 array, and CIRCLE is a 1-by-7 array.
   Result PT2 is a N-by-3 array, containing coordinates of projections of
   PT onto the circle CIRCLE. 

   See also
   projPointOnLine3d, projPointOnPlane

   Source
   https://www.geometrictools.com/Documentation/DistanceToCircle3.pdf

 ---------
 Author: oqilipo
 Created: 2020-10-12
 Copyright 2020

0001 function point2 = projPointOnCircle3d(point, circle)
0002 %PROJPOINTONCIRCLE3D Project a 3D point onto a 3D circle.
0003 %
0004 %   PT2 = projPointOnCircle3d(PT, CIRCLE).
0005 %   Computes the projection of 3D point PT onto the 3D circle CIRCLE.
0006 %
0007 %   Point PT is a N-by-3 array, and CIRCLE is a 1-by-7 array.
0008 %   Result PT2 is a N-by-3 array, containing coordinates of projections of
0009 %   PT onto the circle CIRCLE.
0010 %
0011 %   See also
0012 %   projPointOnLine3d, projPointOnPlane
0013 %
0014 %   Source
0015 %   https://www.geometrictools.com/Documentation/DistanceToCircle3.pdf
0016 %
0017 % ---------
0018 % Author: oqilipo
0019 % Created: 2020-10-12
0020 % Copyright 2020
0021 %
0022 
0023 center = circle(1:3);
0024 radius = circle(4);
0025 
0026 % Compute transformation from local basis to world basis
0027 TFM = localToGlobal3d(center, circle(5), circle(6), circle(7));
0028 
0029 % Create circle plane
0030 circlePlaneNormal = transformVector3d([0 0 1], TFM);
0031 circlePlane = createPlane(center, circlePlaneNormal);
0032 
0033 % Project point on circle plane
0034 PTonCP = projPointOnPlane(point, circlePlane);
0035 
0036 % Calculate vector from the projected point to the center of the circle
0037 PTtoCenter = normalizeVector3d(circle(1:3) - PTonCP);
0038 
0039 % Calculate final point
0040 point2 = PTonCP + PTtoCenter.*(distancePoints3d(PTonCP, center) - radius);
0041 
0042 % Take an arbitrary point of the circle if the point is the center of the circle
0043 if any(all(isnan(point2),2))
0044     point2(all(isnan(point2),2),:) = center + normalizeVector3d(circlePlane(4:6))*radius;
0045 end
0046 % Take an arbitrary point of the circle if the point lies on the normal of the circle plane
0047 if any(sum(PTtoCenter == 0,2) == 2)
0048     point2(sum(PTtoCenter == 0,2) == 2,:) = center + normalizeVector3d(circlePlane(4:6))*radius;
0049 end
0050 end