Programming the Distance FormulaDate: 03/26/2001 at 22:26:50 From: Jean-Sebastien Payette Subject: Program using one of your answers I have a problem similar to one of your archived explanations. I would like to know how to use the concept you explained in "Using the Distance Formula" at: http://mathforum.org/dr.math/problems/calphool5.3.97.html to be able to find the point on a line that's distance X from a given point, but in a computer-based programming language. Date: 03/26/2001 at 23:22:39 From: Doctor Peterson Subject: Re: Program using one of your answers Hello, Jean-Sebastien. There is a considerably simpler way to do this than what was shown in that answer. If you are at all familiar with vectors, you can follow my reasoning; otherwise just take the result. Suppose we know two points A (x1,y1) and B (x2,y2) that determine a line, and want to find a point on that line that is d units from A, in the direction of B. Then the vector AB = (x2-x1,y2-y1) points in the right direction; its length is |AB| = sqrt((x2-x1)^2 + (y2-y1)^2). If we divide vector AB by its length, we get a unit vector AB/|AB| in the right direction; and if we then multiply this vector by length d, we get the vector AC that takes us to the desired point. This means that point C is: C = A + AC = A + AB * d/|AB| (x2-x1,y2-y1)*d = (x1,y1) + --------------------------- sqrt((x2-x1)^2 + (y2-y1)^2) (x2-x1)d (y2-y1)d = (x1 + -------------------------, y1 + -------------------------) sqrt((x2-x1)^2+(y2-y1)^2) sqrt((x2-x1)^2+(y2-y1)^2) This should be easy to program. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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