Extend a line segment a specific distance

Question

I am trying to find a way to extend a line segment by a specific distance. For example if I have a line segment starting at 10,10 extending to 20,13 and I want to extend the length by by 3 how do I compute the new endpoint. I can get the length by sqrt(a^2 +b^2) in this example 10.44 so if I wanted to know the new endpoint from 10,10 with a length of 13.44 what would be computationally the fastest way? I also know the slope but don't know if that helps me any in this case.

Answer 1

I just stumbled upon this after searching for this myself, and to give you an out-of-the-box solution, you can have a look at the code inside a standard Vector class (in any language) and cherry pick what parts you need, but I ended up using one and the code looks like this :

vector.set(x,y);
vector.normalize();
vector.multiply(10000);// scale it by the amount that you want

Good luck !

Answer 2

You can do it by finding unit vector of your line segment and scale it to your desired length, then translating end-point of your line segment with this vector. Assume your line segment end points are A and B and you want to extend after end-point B (and lenAB is length of line segment).

#include <math.h> // Needed for pow and sqrt.
struct Point
{
    double x;
    double y;
}

...

struct Point A, B, C;
double lenAB;

...

lenAB = sqrt(pow(A.x - B.x, 2.0) + pow(A.y - B.y, 2.0));
C.x = B.x + (B.x - A.x) / lenAB * length;
C.y = B.y + (B.y - A.y) / lenAB * length;

Answer 3

If you already have the slope you can compute the new point:

x = old_x + length * cos(alpha);
y = old_y + length * sin(alpha);

I haven't done this in a while so take it with a grain of salt.