Find point at specified distance on a straight line

Hi,

Let us talk in some simple terms.
There are 2 points (x1,y1) and (x2,y2) and you need to find a point in between these above points which is at a distance z from the first point.
I think you will have to provide the distance between (x1,y1) and (x2,y2) also, coz after that the number of equations and number of variables will be equal and the problem will be solved.
Below is the code snippet which will give an equation in variables a & b.Likewise you can have another equation in a & b which will be the result of the distance between points (a,b) and (x2,y2).
After that write another function to solve both the equations for variables a & b and it will give your solution.

This is the first stuff which struck my mind and hope it helps...:)

public double FindDistance(){

double a=a;
double b=b;
double distance=Math.Sqrt((x1-a)*(x1-a)+(y1-b)*(y1-b))

return distance;
}

In the above code,(a,b) is the intermediate point.

Regards
Anurag

Let's assume you have written an extremely useful library for co-ordinate manipulation, which includes

PointF Add(PointF p0, PointF p1)
PointF Sub(PointF p0, PointF p1)
PointF Multiply(PointF p0, float factor)
PointF Multiply(float factor, PointF p0) // Commutativeness is not for free
float Length(PointF p0)

But you did it overriding the appropriate operators so we can conveniently use them from now on. Maybe you had to create a custom PointF class for that since System.Drawing.PointF may not be capable of being tuned in that way.

P2, seen from P1 has the coordinates

P2 - P1

which itself can be an instance of the super-cool point class you invented above.

Seen from the origin of coordinates instead as from P1, P2 would be

P1 + P2 - P1

Sounds weird, as P1 is added and subtracted, but it will help later on. Because we can look at the problem nearly entirely from P1's perspective. At the very end, we'll have to add P1's co-ordinates again and have a correct result.

P1

            X




                                        P2

So we can say this

PointF P2FromP1 = P2 - P1;
float P2DistP1 = Length(P2FromP1);
PointF NormalInP2Direction = (1 / P2DistP1) * P2FromP1;
PointF XFromP1 = xTargetDistanceFromP1 * NormalInP2Direction;

We now can add P1's coordinates and have our result for X:

PointF X = XFromP1 + P1;

And you're done. Plus you have a spectacular tool at your fingertips for future daddling-around-with-geometry.