Re: Fw: [script] normal vector to xyz rotation?

["peterb" <peter_b(at)skynet.be>]

yes,

as it seems the formula for arccos below is correct.

(i've found several sources that confirm)

however, in case of a 1 you get a division by zero.

but... the arccos of 1 is 0, and the arccos of -1 is PI

so thats quickly added into the script with a condition, and yet a few more lines. where the simple "arccos" should be all :-(

 

so I got my 2 scripts running (hurrah!), but the version with the arccos isnt giving proper results.

could be my math, could be my script... or both

 

I've added them at the bottom of this mail, if anyone wants to look, see whats wrong

(or laugh at my scripting :-)

 

 

peter

 

That would be correct (cos always returns a value between -1 and 1) - if you've got a dot product greater than that your vectors weren't unit vectors (normalized).

Hope this helps.

Cheers,

Alan.

On 9/5/05, peterb <peter_b(at)skynet.be> wrote:

>hm I m not gonna switch languages because of a math function now?

>thats like deciding to switch to japanese because you feel there's some characters missing in our alphabet. (yeah its a flawed comparison)

>

>now I did work it out with the acos, and I ll be needing this,

>since I wanna do this on particles, and they dont have a transform matrix.

>

>btw it ran MUCH faster that way, but there can be some other things that are influencing it.

>right now I have one version, with the matrix method, to place nulls on points,

>and another version using the arccos method, to place particles on points, the second being more performant.

>

>however, it seems that the formula is flawed, I get 'division by zero' errors.

>and its quite obvious: if X=1 then (x*x + 1) gives zero.

>Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)

 

apparently the arccos function only accepts numbers between -1 and 1 at the input...

 

 

>

>I'll have to try and find a better arccos formula somewhere..

 

,

Glad you got it sorted - microsoft's acos solution truly is elegant ;-) A google seems to provide strange results - some places mention a math object in VBScript though doesn't seem to work for me.

If your other solution is working then I'd go with that - at least until you shift languages

Cheers,

Alan.

On 9/5/05, peterb <peter_b(at)skynet.be> wrote:

 

Hi Alan, seems like your answer was on right on the spot.

 

but on kims suggestion I found back the thread on xsibase:

http://www.xsibase.com/forum/index.php?board=6;action=""

 

I got it working with Rafaelle's method, that doesnt involve dot product, nor inverse cosine.

just cross product, normalize and putting it into a matrix that goes straight to an object's transform.

 

on the bottom of the page there is a method by Andrea, that is pretty much exactly what you suggested.

this uses the inverse cosine of the dot product and so on:

...

var angle = Math.acos(upVec.dot(polyNormal)); 
...

 

cant find one in vbscript though.

 

what I did come up with is

http://msdn.microsoft.com/library/default.asp?url=""

where inverse cosine is made up like this:

Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)

 

microsoft helps to keep things simple :-)

if anyone knows of an inverse cosine function in vbscript, I'd love to know.

 

 

peter

 

 

Excuse my laziness I didn't real through all your code so I've no idea how you're tackling this, but here's a simple approach I'd recommend anyway (I'll explain the math rather than coding it out.)

Take the direction you want to be "up" on your object (probably the y axis I guess so 0,1,0). Get the cross product of that with the normal you want it to rotate to. The result is the axis you want to rotate your object around. To get the angle you want to rotate your object get the dot product of the up axis and the normal. Then get the inverse cosine of this and that will be the angle in radians you want to rotate it. The only problem you'll probably come into this way is defining how it rotates around the normal. You may want to look at doing this with a direction vector which could be global or using the U and V directions or whatever.

Cheers,

 

'this is the script that is working fine, based on rafaelle's suggested method

'select a mesh and run, it creates nulls, aligned to the mesh's points

'---------------------------------------------------

option explicit

dim sel, oGeometry, oPoints, pnt, oNull

Dim V1, V2, vUP, oMatrix, vNORM, transfo

set V1 = XSIMath.CreateVector3

set V2 = XSIMath.CreateVector3

set vUP = XSImath.CreateVector3

set oMatrix = XSIMath.CreateMatrix3

set vNORM = XSImath.CreateVector3

set transfo = XSIMath.CreateTransform

vUP.set 0.0,1.0,0.0

set sel = selection(0)

set oGeometry = sel.activeprimitive.geometry

set oPoints = oGeometry.Points

for each pnt in oPoints

vNORM.set pnt.normal.x,pnt.normal.y,pnt.normal.z

MatrixFromNormal (vNORM)

 

transfo.setRotationFromMatrix3 oMatrix

transfo.SetTranslationFromValues pnt.position.x, pnt.position.y, pnt.position.z

set ("name" & pnt.index)

oNull.Kinematics.local.transform = transfo

next

Function MatrixFromNormal (norm)

V1.cross norm,vUP

V2.cross V1,norm

V1.normalizeInPlace

V2.normalizeInPlace

norm.normalizeInPlace

oMatrix.set V1.x, V1.y, V1.z,_

norm.x, norm.y, norm.z,_

V2.x, V2.y, V2.z

set MatrixFromNormal = oMatrix

end Function

 

'----------------------------------------------------

'this is the script that is not working fine, based on the math  method

'the nulls are not properly aligned...

'---------------------------------------------------

set sel = selection(0)

set oGeometry = sel.activeprimitive.geometry

set oPointer = oGeometry.Points

set rot = XSIMath.CreateRotation

set vUP = XSIMath.CreateVector3

set axis = XSIMath.CreateVector3

set vNORM = XSIMath.CreateVector3

set vPos = XSIMath.CreateVector3

set vRot = XSIMath.CreateVector3

vUP.set 0,1,0

for i = 0 to oPointer.count-1

set oPoint = oGeometry.Points(i)

 

set vPos = oPoint.Position

set vNORM = oPoint.Normal

RotationFromNormal (vNORM)

rot.GetXYZAngles vRot

 

set ("name" & i)

oNull.Kinematics.local.parameters("posx").value = vPos.x

oNull.Kinematics.local.parameters("posy").value = vPos.y

oNull.Kinematics.local.parameters("posz").value = vPos.z

oNull.Kinematics.global.parameters("rotx").value = xsimath.radianstodegrees(vRot.x)

oNull.Kinematics.global.parameters("roty").value = xsimath.radianstodegrees(vRot.y)

oNull.Kinematics.global.parameters("rotz").value = xsimath.radianstodegrees(vRot.z)

next

Function RotationFromNormal (norm)

axis.cross vUP, norm

DOT = vUP.dot(norm)

if DOT => 1 then

angle = 0

elseif DOT <= -1 then

angle = XSIMath.PI

else

angle = 2*atn(1) - atn(DOT/sqr(1-DOT*DOT))

end if

rot.SetFromAxisAngle axis, angle

set RotationFromNormal = rot

end Function

'----------------------------------------------------------------