Get intersection of vector in the middle of the screen

Question

My screen resolution is 640x480 and I have two Vector2 objects located at (10,10) and (600, 320).

How can I connect these two objects and extend the line to encompass the whole screens width, how can I get the Y for the intersection at the center of the width (320)?

Answer 1

you have to use the equation of a line. I prefer to use parametric representation P(t)= 1-t*(v1) + t*V2 ; then you solve the equation where P1 = P2 ...

here is the detailed solution http://paulbourke.net/geometry/lineline2d/ you can also google "line line intersection"

Answer 2

Do you mean midpoint?

You can always set the two vectors equal to each other with a scalar multiple for each and solve, but this situation is not clear. Are we to assume they are pointing at each other?

---

Updated for clarity

You are asking for the point of intersection between two lines, one that is vertical - splitting the screen - at x=320, and one that is at some other non parallel point. With two lines, the point of intersection is the point where they are equal to each other.

I used the example of a vertical line (x=320) and a second line (y=13x+2) and all you have to do is set them equal to each other and solve. Since one line is x=320, so no matter what you do the x value needs to be 320. When you plug that value into the second equation, you get y=13(320)+2

This will give you the y position for the system of equations. You can find the line by using the vectors slope, or rise/run (change in y/change in x), and solve for the offset (y=mx+b, because your lines origin gives you the x and y positions.

Ex.

Two points (300,30), (450, 330);
The slope is (330-30)/(450-300)=(300/150)=2;
The y intercept is y=mx+b -> (30)=(2)(300)+b -> b=-570;
The line is thus y=(2)x-570; 
This line intersects the x=320 line at:
y=(2)x-570 == x=320 -> y=(2)(320)-570 = 70
the point of intersection is: (320, 70)

http://www.analyzemath.com/Calculators_2/intersection_lines.html

Answer 3

If I understand correctly, there is a line from (10,10) to (600,320). Let's call these (x1,y1) and (x2,y2). The line needs to be extended to x=0 and x=640, and divided at x=320. This implies finding y for these 3 values of x.

You need to know the equation which describes the line. For a straight line, this will be in the form of:

y = slope*x + intercept

i.e. for all points on the line, this formula will be true.

Slope is just:

(change in y) / (change in x)

So:

y = ((y2-y1) / (x2-x1) * x) + intercept

Rearrange:

intercept = y - ((y2-y1) / (x2-x1) * x)

Substitute in x and y from either one of your known points. (x1,y1) used here:

intercept = y1 - ((y2-y1) / (x2-x1) * x1)

Subsitute the expressions you now have for slope and intercept back into the line equation:

y = slope*x + intercept

And you can then find y for any value of x.