[Closed] average planar align point helpers

How big will be your pointset more or less?

I’ve made a naive algorithm for this task, it can works pretty fast on hundreds or evens thousands of points, but it’s still naive and the running time grows exponentially as the pointset grows:

delete objects
points = #()
avg_pos = [0.0, 0.0, 0.0]
numPt = 50

for i = 1 to numPt do
(
	pos = random [-20,-20,0] [20,20,20]
	p = point pos:pos size:5 wirecolor:yellow
	append points p
	avg_pos += pos
)
--average pos
avg_pos /= numPt

--plane to show the result
pl = Plane width:100.0 length:100.0 pos:avg_pos wirecolor:white

--sum of all cross vectors
cross_sum = [0.0, 0.0, 0.0]

--calculating our cross vectors
for i = 1 to numPt do
(
	for j = i+1 to numPt do
	(
		v1 = points[i].pos - avg_pos
		v2 = points[j].pos - avg_pos
		a_cross = cross (normalize v1) (normalize v2)
		dot_p = dot (normalize a_cross) (normalize cross_sum)
		if dot_p < 0.0 then a_cross *= -1.0
		cross_sum += a_cross
		pl.dir = normalize cross_sum --comment this line, it's just for the preview
	)
	CompleteRedraw() --comment this line, it's just for the preview
)
cross_sum = normalize cross_sum
pl.dir = cross_sum

To align those points just use this function to project them on the plane:

fn pointPlaneProj pA pB pC pD =
(
	local nABC=normalize (cross (pB-pA) (pC-pA))
	pD+((dot (pA-pD) nABC)*nABC)
)