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linear interpolation in 3D space

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Bijay Sangat
Bijay Sangat 2021-8-21
评论： Bijay Sangat 2021-8-22
Hi I have a two [X,Y,Z] coordinates [0 3500 115] and [900 4000 113.5] ,which will help me to create a line. Now I have two coordinate, A= [700,2100,185] and [1500,3300,210]. so I have find the find,out of A or B, which point is near to line segment, and co-ordinates at the line segment which is closest to either A or B
Thanks

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Wan Ji
Wan Ji 2021-8-21
编辑：Wan Ji 2021-8-22
Using point2segmentDistance function
function [distance, nearestPointOnSeg ]= point2segmentDistance(point, segmentPoint1, segmentPoint2)
point = point(:);
segmentPoint1 = segmentPoint1(:);
segmentPoint2 = segmentPoint2(:);
V = segmentPoint2 - segmentPoint1;
V1 = point - segmentPoint1;
V2 = point - segmentPoint2;
L1 = norm(V1);
L2 = norm(V2);
L = norm(V);
theta1 = acos(V'*V1/(L*L1));
theta2 = acos(-V'*V2/(L*L2));
if(theta1>=pi/2)
distance = L1; nearestPointOnSeg = segmentPoint1;
elseif(theta2>=pi/2)
distance = L2; nearestPointOnSeg = segmentPoint2;
else
distance = L1*sin(theta1);
nearestPointOnSeg = segmentPoint1 + V/L * L1*cos(theta1);
end
end
Then calculate in the command line
P1 = [0 3500 115];
P2 = [900 4000 113.5];
PA= [700,2100,185];
PB = [1500,3300,210];
[disA2Seg, A_nearestPseg ] = point2segmentDistance(PA, P1, P2)
[disB2Seg, B_nearestPseg ] = point2segmentDistance(PB, P1, P2)
plot3([P1(1),P2(1)], [P1(2),P2(2)],[P1(3),P2(3)],'r-o','markerfacecolor','r','linewidth', 2)
hold on
text(P1(1), P1(2), P1(3), 'P_1');
text(P2(1), P2(2), P2(3), 'P_2');
text(PA(1), PA(2), PA(3), 'P_A');
text(PB(1), PB(2), PB(3), 'P_B');
text(A_nearestPseg(1), A_nearestPseg(2), A_nearestPseg(3), '\_\_\_P(Nearest to A)');
text(B_nearestPseg(1), B_nearestPseg(2), B_nearestPseg(3)+eps, '\_\_\_P(Nearest to B)');
plot3([PA(1),A_nearestPseg(1)], [PA(2),A_nearestPseg(2)],[PA(3),A_nearestPseg(3)],...
'g-h','markerfacecolor','g','linewidth', 2)
plot3([PB(1),B_nearestPseg(1)], [PB(2),B_nearestPseg(2)],[PB(3),B_nearestPseg(3)],...
'b-s','markerfacecolor','b','linewidth', 2)
With answer
disA2Seg =
1.566812049991957e+03
A_nearestPseg =
0
3500
115
disB2Seg =
9.269909654360176e+02
B_nearestPseg =
1.0e+03 *
0.900000000000000
4.000000000000000
0.113500000000000
So point B is closer to the segment. And the nearest points on segment to Point A or B are found.
  7 个评论
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Wan Ji
Wan Ji 2021-8-22
编辑：Wan Ji 2021-8-22
The answer is uncertain, because you elongate this segment, the nearest point on the elongated segment to PA or PB mybe go out of the original segment. You can do any test or experiment on the function i offered.
% P1 = [1, 0, 0]; % after elongation ( extrapolation)
P1 = [-1, 0, 0]; % before elongation ( extrapolation)
P2 = [4, 0, 0];
PA = [0, 1, 0];
PB = [3, 1, 0];
[disA2Seg, A_nearestPseg ] = point2segmentDistance(PA, P1, P2)
[disB2Seg, B_nearestPseg ] = point2segmentDistance(PB, P1, P2)
plot3([P1(1),P2(1)], [P1(2),P2(2)],[P1(3),P2(3)],'r-o','markerfacecolor','r','linewidth', 2)
hold on
text(P1(1), P1(2), P1(3), 'P_1');
text(P2(1), P2(2), P2(3), 'P_2');
text(PA(1), PA(2), PA(3), 'P_A');
text(PB(1), PB(2), PB(3), 'P_B');
text(A_nearestPseg(1), A_nearestPseg(2), A_nearestPseg(3), 'to A','color','c');
text(B_nearestPseg(1), B_nearestPseg(2), B_nearestPseg(3)+eps, 'to B','color','c');
view(30,67)
plot3([PA(1),A_nearestPseg(1)], [PA(2),A_nearestPseg(2)],[PA(3),A_nearestPseg(3)],...
'g-h','markerfacecolor','g','linewidth', 2)
plot3([PB(1),B_nearestPseg(1)], [PB(2),B_nearestPseg(2)],[PB(3),B_nearestPseg(3)],...
'b-s','markerfacecolor','b','linewidth', 2)
before elongation
after elongation
So you can see from the figures that the elongation (extrapolation) of segment may change the nearest point position

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