I have two points (A, B) and the length of d. How can I find point C?
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2 Answers
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Compute a vector V from A to B, and normalize it.
V = (B - A) / |B - A|
Since the vector is normalized, it will have a length of one, and it will indicate the direction of B relative to A. If you then scale the vector by d you will have the displacement from A to C
V' = d * V
which you can simply add to A to yield C:
C = V' + A
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\$\begingroup\$ btw: could anyone recommend me a book where I can learn about stuff like that? :) \$\endgroup\$– eempeeOct 10, 2011 at 20:40
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\$\begingroup\$ 3D Math primer is a good one: amazon.com/Primer-Graphics-Development-Wordware-Library/dp/…. \$\endgroup\$– Ricky AHOct 11, 2011 at 8:03
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\$\begingroup\$ Didn't read this one, but I've been told that is also pretty good amazon.com/Mathematics-Programming-Computer-Graphics-Second/dp/… \$\endgroup\$– Ricky AHOct 11, 2011 at 8:05
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1\$\begingroup\$ See this question: gamedev.stackexchange.com/questions/1210/… \$\endgroup\$– user1430Oct 11, 2011 at 15:06
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\$\begingroup\$ btw this is the last couple steps in ray intersection algorithms: you figure out how far along the ray the intersection point is, and then you get the coordinates of the point geomalgorithms.com/a05-_intersect-1.html#Plane-Intersections \$\endgroup\$– jhockingDec 17, 2013 at 17:42
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In case your d is a ratio instead of a length, e.g 0.5 puts it on equal distance from A and B, you can do the following and avoid a normalization:
C = A * (1 - ratio) + B * ratio
