Extend a line segment a specific distance

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 开发者_如何学编程+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.

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;

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.

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 !