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Calculate angle between two points

Posted on 2009-06-29
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Math math mat! :D

I got two XY points, what Im trying todo is set the first XY1 to "move towards" XY2, in my application. I assign new XY positions for XY1 every 100ms or so. So to the math:
What I remember from school is that I need to use some sort of variation of the phytagoras theorem?
The new X and Y are C1 and C2 of the right angled triangle, and the hypotenuse is the direction in wich XY2 is relation to XY1.

So I know the length of the hypotenuse and calculate the angle between XY1 and XY2, can I calculate the C1 and C2 from that?

Hope I made sense, math is hellova fun, it's just to hard to manage for some of us.. :P
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Question by:Squeese
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by:Squeese
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Ive made a small image illustrating the "problem"


myproblem.gif
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by:ozo
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I don't know what you are naming C1 and C2, but
a point that is 100m from X1,Y1 in the direction of X2,Y2 is
X=X1+100m*(X2-X1)/sqrt((X2-X1)^2+(Y2-Y1)^2)
Y=Y1+100m*(Y2-Y1)/sqrt((X2-X1)^2+(Y2-Y1)^2
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by:Infinity08
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All points while "moving towards" the second point are on the line between the two points.

The equation of a line between two points p1(x1,y1) and p2(x2,y2) is :

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

(when x1 is not equal to x2)

To let a point move from p1 to p2, you just let x vary from x1 to x2, and calculate the corresponding y with the above equation.


In the special case where x1 is equal to x2, the equation becomes :

    x = x1

And to let a point move from p1 to p2, you just let y vary from y1 to y2, and calculate the corresponding x with the above equation.
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ozo earned 500 total points
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based on your diagram, it looks like
C1=10*(Y2-Y1)/sqrt((X2-X1)^2+(Y2-Y1)^2)
C2=10*(X2-X1)/sqrt((X2-X1)^2+(Y2-Y1)^2)
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by:Squeese
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Im naming C1 and C2 out of ignorance to the proper terms I guess, used the shorts for naming the sides of an right angled triangle according to wikipedia: http://en.wikipedia.org/wiki/Cathetus ;P

I tried your solution first ozo and it works absolutely perfect. Much abliged!
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by:ozo
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One thing that seemed confusing, was that despite the question title, we nowhere calculated an angle.
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by:Squeese
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Oh, my lack of mathematical expertise is lacking. :P
Should I rename the Question to a more fitting title, as to help anyone else with similiar problems?

I initially thought it was a prerequisite to solve the math, thw angle that is.
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by:Infinity08
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He probably meant the slope of the line, in which case I did make direct use of it ... (and your solution also indirectly uses it)
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by:Squeese
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Meaning, if you knew the length of the hypotenuse and the angle, you could thus calculate the length of both cathetus (?).
But what little I actually understand from the given solution, you only need distance between the points to solve it?

C2=10*(X2-X1)/sqrt((X2-X1)^2+(Y2-Y1)^2)
Is that: H = sqrt(c1^2 + c2^2)

Can you use the same formulae to calculate any side of the right angled triange if you know two of them, not only the hypotenuse (as the unknow) ?
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