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Formula for finding point on a line given distance along a line.

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Wai Han
Wai Han on 10 Oct 2020
Commented: Wai Han on 18 Oct 2020
Start point - (x0, y0)
End point - (x1, y1)
x = x0 +- c/sqrt(1+m^2)
This equation is not working for my case because I only need the middle point between the two, not the one away from the end point.
I want to find the point (xt,yt).
Can anyone guide me this?
I am asking this for the path finder (rapidly exploring random trees) method.

  2 Comments

Ameer Hamza
Ameer Hamza on 10 Oct 2020
Can you explain more? What are c and m? Drawing an image and marking the points you want to find will be helpful.

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Accepted Answer

KSSV
KSSV on 10 Oct 2020
P0 = rand(1,2) ;
P1 = rand(1,2) ;
% Normalize the line
v = P1-P0 ;
vunit = v/norm(v) ;
% Get a point from P0 at a distance t
t = 0.5 ;
Pt = P0+t*vunit ;
% Check, find the diatnce btween Pt and P0
d = sqrt(sum((Pt-P0).^2)) ;
% plot
plot([P0(1) P1(1)],[P0(2) P1(2)],'r')
hold on
plot(Pt(1),Pt(2),'*k')

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