# Line Sphere collision

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daniel_i_l    295
Whats a fast way (for the computer) to find the closest distance between a sphere and a line that continues infinatly in direction V from point P?

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Antheus    2409
http://www.ccs.neu.edu/home/fell/CSU540/programs/RayTracingFormulas.htm

This is also a comprehensive general x vs. y intersection resource:
http://www.realtimerendering.com/int/

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jyk    2094
Quote:
 Original post by Antheushttp://www.ccs.neu.edu/home/fell/CSU540/programs/RayTracingFormulas.htmThis is also a comprehensive general x vs. y intersection resource:http://www.realtimerendering.com/int/
These actually solve a different problem than what the OP asked about. I'll try to sketch out the correct algorithm here (but may or may not get it right):
float t = dot(sphere.center - line.origin, line.direction) / (dot(line.direction, line.direction);vector3 closest = line.origin + t * line.direction;float dist_squared = length_squared(sphere.center - closest);if (dist_squared <= sphere.radius * sphere.radius) {    // Line intersects sphere} else {    float distance = sqrt(dist_squared) - sphere.radius;}
If you want to test a ray or segment rather than a line, just clamp t as appropriate.

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daniel_i_l    295
If line.direction is normalized can I just do:
float t = dot(sphere.center - line.origin, line.direction); ?
Thanks.

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jyk    2094
Quote:
 Original post by daniel_i_lIf line.direction is normalized can I just do:float t = dot(sphere.center - line.origin, line.direction); ?
Absolutely :-)

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