Segment-Segment Distance in 3D - Sublucid Geometry

[utterances-bot]

Segment-Segment Distance in 3D - Sublucid Geometry

One of my favorite functions projects points onto line segments.

https://zalo.github.io/blog/closest-point-between-segments/

[zalo]

The wonderful thing about vector math is that it (should) work in any number of dimensions!

Word Vector Geometry, anyone?

[zalo]

Earlier Comment (before switching to utteranc.es):

Laccer

Thank you for creating this article and making this topic accessible and beautiful!

[AxisAngles]

Love the visuals, interesting method for sure. I never thought to solve it this way!
I was inspired to try an approach, but make it completely symmetrical. This is written in lua, so it should be pretty straight forward.

--[[
	line segments defined as
	segmentA(s) = a + s*u where 0 <= s <= 1
	segmentB(t) = b + t*v where 0 <= t <= 1
]]

local function lineSegClosestPoints(a, u, b, v)
	local r = b - a

	local ru = r:Dot(u)
	local rv = r:Dot(v)
	local uu = u:Dot(u)
	local uv = u:Dot(v)
	local vv = v:Dot(v)

	local det = uu*vv - uv*uv

	-- if det is too close to 0, then they're parallel
	-- you can work out a way to handle this case

	-- compute optimal values for s and t
	local s = (ru*vv - rv*uv)/det
	local t = (ru*uv - rv*uu)/det

	-- constrain values s and t so that they describe points on the segments
	s = math.clamp(s, 0, 1)
	t = math.clamp(t, 0, 1)

	-- convert value s for segA into the corresponding closest value t for segB
	-- and vice versa
	local S = (t*uv + ru)/uu
	local T = (s*uv - rv)/vv

	-- constrain
	S = math.clamp(S, 0, 1)
	T = math.clamp(T, 0, 1)

	return a + S*u, b + T*v
end

[hamishtodd1]

You might like this https://open.substack.com/pub/hamishtodd1/p/angle-and-distance-from-anything

[virtushda]

Is the last line in the optimized method needed?

Or would it produce the same value as 'segABtoLineCD = Lerp(segA, segB, Clamp01(t));'?