linear interpolation in 3D space

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

[darova]

Do you have any attepmts?

Answer 1

[Wan Ji]

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.

[Bijay Sangat]

Thanks for your reply and code. But how to interpolate coordiante in the the line segment (from p1 and p2) nearest to B ? I am thinking about linear interapolation but I don't know how to use ?

[Wan Ji]

if you need to get the coordinate in the segment that is the nearest to point a or b, i'ill help you tomorrow

[Bijay Sangat]

thanks :)

[Wan Ji]

OK, now the coordinates on the segment that is the nearest to point a or b were found @Bijay Sangat

[Bijay Sangat]

Thanks for the code, If we linearly extrapolate P1 and p2, do we get the same answer ? beacuse I think I can extrapolate lines segment as well to get the nearest point to PA or Pb

[Wan Ji]

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

[Bijay Sangat]

Thanks :)