Geometrical calculations : points, lines, planes : intersections, distances, angles

global polylinePosArr = #()
 
 fn drawCircle = (
 	gw.setColor #line green
 	gw.setTransform(Matrix3 1)
 	gw.Polyline polylinePosArr true
 	gw.enlargeUpdateRect #whole
 	gw.updateScreen()
 	)
 
 fn drawObjectCirle obj radius step:36 axis:1 = (
 	polylinePosArr = #()
 	-- get the object's position
 	local p = obj.pos
 	for i = 0 to (360 - step) by step do (
 		-- make a point helper
 		-- define the current angle around the circle
 		local angle = i
 		-- calculate the X and Y coordinates of the point on the circle using the current angle
 		local x = cos(angle) * radius
 		local y = sin(angle) * radius
 		-- 1 = X axis
 		-- 2 = Y axis
 		-- 3 = Z axis
 		global p3 = case axis of (
 			1:[0,x,y]
 			2:[x,0,y]
 			3:[x,y,0]
 			)
 		-- using the coordinate system of the object, define the coordinates of the current point
 		newP = ( (matrix3 [1,0,0] [0,1,0] [0,0,1] p3) * (obj.transform) ).translationPart
 		append polylinePosArr newP
 		)
 	)
 
 -- create a box
 b = box length:1 width:1 height:10 pos:(random [-10,-10,-10] [10,10,10])
 b.rotation = quat (random -1 1) (random -1 1) (random -1 1) 1
 -- get the length of the box, which will be used as the radius for the circle calculations
 l = b.height
 
 -- be careful with the "steps" parameter, too low (around 10) and Max will crash
 drawObjectCirle b l step:18 axis:2
 
 -- draw the circle
 registerRedrawViewsCallback drawCircle
 redrawViews()
 
 /* stop drawing the circle
 unregisterRedrawViewsCallback drawCircle
 */

rotAxis = [0,0,2]
rotCenter = [0,2,0]
rotAngle = 90
thePoint = [1,2,3]

q = quat rotAngle (normalize rotAxis)
pointAfterRotation = (((thePoint - rotCenter ) * q) + rotCenter)
--> [0,1,3]

 fn drawObjectCirle obj radius step:36 axis:1 = (
 	polylinePosArr = #()
	local rotCenter = obj.pos
	local rotAxis = obj.dir
	local p
	case axis of (
		1: p=[radius,0,0]*obj.transform
		2: p=[0,radius,0]*obj.transform
		3: p=[0,0,radius]*obj.transform
		)
	q = quat step rotAxis
	for i = 0 to (360 - step) by step do (
		p = ((p-rotCenter)*q) + rotCenter
		append polylinePosArr p
 		)
 	)

dependson $object_a
v1t = at time currenttime $object_a.position
a = normalize [v1t.x,v1t.y,0]-- set z to 0 because it is not needed
upv = [0,1,0] --defining a 2d "up vector" 
 
cosine = a.x * upv.x + a.y * upv.y
if cosine > 1 then cosine1 = 1
if cosine < -1 then cosine1 = -1
if (a.x * upv.y - a.y * upv.x) < 0 then
(
result = -cosine
)
else
(
result = cosine
)
result 
 

dependson $object_a
v1t = at time currenttime $object_a.position
a = normalize [v1t.x,v1t.y,0]
ndir = normalize a
 
upvector = [0,0,1]
rightvector = normalize (cross upvector ndir )
thematrix = matrix3 ndir rightvector upvector ndir
 
pitch = ((thematrix.rotation as eulerangles).z +180)*pi/180

fn PointAxisAt a which_axis b =
(
local c = normalize (b - a) 
local angle = acos (dot which_axis c)
local axis = normalize (cross which_axis c)
 
local out = (angleaxis angle axis) as quat
out
)
 
a = $Pyramid01.position
b = $Point01.position
q = PointAxisAt a z_axis b
r = q * (inverse $Pyramid01.rotation)
rotate $Pyramid01 r

thePos = [posx,posy,posz]
theDirection = [directionx,directiony,directionz]
theLength = 100.0
theTargetPos = thePos + ((normalize theDirection)*theLength)

myCam = targetCamera pos:thePos target:(targetObject pos:theTargetPos)

fn pointSegmentDist pA pB pC = 
(
	local vAB=pB-pA
	local vAC=pC-pA
	local vBC=pC-PB
	
	local c1=dot vAB vAC
	local c2=dot vAB vAB
	
	if c1 < 0 do
		return length vAC
	
	if c2 < c1 do
		return length vBC
	
	(length (cross vAB vAC))/(length vAB)
)