1## Copyright (C) 2021 David Legland 2## All rights reserved. 3## 4## Redistribution and use in source and binary forms, with or without 5## modification, are permitted provided that the following conditions are met: 6## 7## 1 Redistributions of source code must retain the above copyright notice, 8## this list of conditions and the following disclaimer. 9## 2 Redistributions in binary form must reproduce the above copyright 10## notice, this list of conditions and the following disclaimer in the 11## documentation and/or other materials provided with the distribution. 12## 13## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' 14## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR 17## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR 19## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 20## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, 21## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 22## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 23## 24## The views and conclusions contained in the software and documentation are 25## those of the authors and should not be interpreted as representing official 26## policies, either expressed or implied, of the copyright holders. 27 28function point2 = projPointOnCircle3d(point, circle) 29%PROJPOINTONCIRCLE3D Project a 3D point onto a 3D circle. 30% 31% PT2 = projPointOnCircle3d(PT, CIRCLE). 32% Computes the projection of 3D point PT onto the 3D circle CIRCLE. 33% 34% Point PT is a N-by-3 array, and CIRCLE is a 1-by-7 array. 35% Result PT2 is a N-by-3 array, containing coordinates of projections of 36% PT onto the circle CIRCLE. 37% 38% See also 39% projPointOnLine3d, projPointOnPlane 40% 41% Source 42% https://www.geometrictools.com/Documentation/DistanceToCircle3.pdf 43% 44% --------- 45% Author: oqilipo 46% Created: 2020-10-12 47% Copyright 2020 48% 49 50center = circle(1:3); 51radius = circle(4); 52 53% Compute transformation from local basis to world basis 54TFM = localToGlobal3d(center, circle(5), circle(6), circle(7)); 55 56% Create circle plane 57circlePlaneNormal = transformVector3d([0 0 1], TFM); 58circlePlane = createPlane(center, circlePlaneNormal); 59 60% Project point on circle plane 61PTonCP = projPointOnPlane(point, circlePlane); 62 63% Calculate vector from the projected point to the center of the circle 64PTtoCenter = normalizeVector3d(circle(1:3) - PTonCP); 65 66% Calculate final point 67point2 = PTonCP + PTtoCenter.*(distancePoints3d(PTonCP, center) - radius); 68 69% Take an arbitrary point of the circle if the point is the center of the circle 70if any(all(isnan(point2),2)) 71 point2(all(isnan(point2),2),:) = center + normalizeVector3d(circlePlane(4:6))*radius; 72end 73% Take an arbitrary point of the circle if the point lies on the normal of the circle plane 74if any(sum(PTtoCenter == 0,2) == 2) 75 point2(sum(PTtoCenter == 0,2) == 2,:) = center + normalizeVector3d(circlePlane(4:6))*radius; 76end 77end 78