Compute Rotation and Scale from Transform Object

MartinRinehart

I read your wonderful web-page description of the 4 x 4 matrix - ...

Very kind words, indeed. Many thanks.

For those not versed in the Transformation Matrix, my tutorial's Appendix T, introduces it, Appendix MM explains matrix multiplication and Chapter 16 explains how you can live without it (and includes a Matrix class, just in case).

Djarlo

@tig said:

Thanks for the input...
Here's my revised code using you ideas - it's still in radians and I have tried not to clash with your method naming etc - it now finds x/y/z rotations and [x,y,z] rotation as an array and has extra methods to set rotations from a 3 item array, referring either to the model axes or object's axes...

### transformation.extensions.rb (c) TIG 2009
> ### From original ideas by TBD and others ? ### TIG 20091010
> ### The euler rotation ideas from Dave Burdick 20100324
> ### It extends the methods for Geom;;Transformation...
> ### The built-in method "object.transformation.origin" return a point3d 
> ###   that is the object's origin/insertion; the new method 
> ###   object.transformation.getX etc returns the X location of the  
> ###   object [or Y or Z].
> ### The setX(x) resets the X value of the object [or Y or Z]; it 
> ###   returns a new transformation that can then be used to reset the 
> ###   original transformation; thus;
> ###   object.transformation=object.transformation.setX(another_object.transformation.getX)
> ###   - here it makes the object's X = another_object's X ; 
> ###     it also could be given a float, e.g. 12.345 or a 'variable'...
> ### The object.transformation.scaleX etc returns the scale on that axis.
> ### The object.transformation.rotX etc returns the rotation on that axis
> ###   in radians; use ... .rotX.radians to get it in degrees...
> ### It uses different names to TBD's, e.g. 'rotZ' instead of 'zrot' etc.
> ### Note the capitalization... this is because some 'compiled scripts' 
> ### use 'rotz' already etc - [and they return the rotation in degrees!]
> ### object.transformation.rotXYZ
> ###   returns a 3 item array giving the rotations in x/y/z
> ### object.transformation.rot_a
> ###   returns an 11 item array of the transformation's rotation/scaling 
> ###   - it can be used to extract some data more easily or as below...
> ### object.transformation=object.transformation.rotation_from_rot_a(another_object.transformation.rot_a) 
> ###   this applies another_object's 'rot_a' to change the object.
> ### object.transformation=object.transformation.rotation_from(another_object.transformation) 
> ###   this applies another_object's rotation/scaling to the object.
> ###   it returns a new transformation that can then be used to reset the original...
> ### object.transformation=object.transformation.origin_from(another_object.transformation) 
> ###   this applies another_object's origin/location to the object.
> ###   it returns a new transformation that can then be used to reset the original...
> ### object.transformation=object.transformation.rotation_from_xyz([xrot,yrot,zrot])
> ###   this applies a 3 item array of x/y/z rotations about the model's x/y/z-axes, 
> ###   this could also be the array returned by rotXYZ.
> ###   it returns a new transformation that can then be used to reset the original...
> ### object.transformation=object.transformation.rotation_from_xyz_locally([xrot,yrot,zrot])
> ###   this applies a 3 item array of x/y/z rotations about the objects's x/y/z-axes, 
> ###   this could also be the array returned by rotXYZ.
> ###   it returns a new transformation that can then be used to reset the original...
> ###
> class Geom;;Transformation
>     def euler_angle(xyx=[])
>        m = self.xaxis.to_a + self.yaxis.to_a + self.zaxis.to_a
>        if m[6] != 1 and m[6]!= 1
>           ry = -Math.asin(m[6])
>           rx = Math.atan2(m[7]/Math.cos(ry),m[8]/Math.cos(ry))
>           rz = Math.atan2(m[3]/Math.cos(ry),m[0]/Math.cos(ry))
>        else
>           rz = 0
>           phi = Math.atan2(m[1],m[2])
>           if m[6] == -1
>              ry = Math;;PI/2
>              rx = rz + phi
>           else
>              ry = -Math;;PI/2
>              rx = -rz + phi
>           end
>        end   
>        return -rx if xyz==0
>        return -ry if xyz==1
>        return -rz if xyz==2
>        return [-rx,-ry,-rz] if xyz==[]
>   end
>   def getX
>     self.to_a[12]
>   end
>   def getY
>     self.to_a[13]
>   end
>   def getZ
>     self.to_a[14]
>   end
>   def setX(x)
>     if not x.class==Float and not x.class==Integer
>       puts "Transformation;;setX( ) expects a Float or Integer."
>       return nil
>     end#if
>     x=x.to_f
>     t=self.to_a
>     t[12]=x
>     return self.set!(t)
>   end
>   def setY(y)
>     if not y.class==Float and not y.class==Integer
>       puts "Transformation;;setY( ) expects a Float or Integer."
>       return nil
>     end#if
>     y=y.to_f
>     t=self.to_a
>     t[13]=y
>     return self.set!(t)
>   end
>   def setZ(z)
>     if not z.class==Float and not z.class==Integer
>       puts "Transformation;;setZ( ) expects a Float or Integer."
>       return nil
>     end#if
>     z=z.to_f
>     t=self.to_a
>     t[14]=z
>     return self.set!(t)
>   end
>   def scaleX
>     Math.sqrt(self.to_a[0]**2+self.to_a[1]**2+self.to_a[2]**2)
>   end
>   def scaleY
>     Math.sqrt(self.to_a[4]**2+self.to_a[5]**2+self.to_a[6]**2)
>   end
>   def scaleZ
>     Math.sqrt(self.to_a[8]**2+self.to_a[9]**2+self.to_a[10]**2)
>   end
>   def rotX
>     #(Math.atan2(self.to_a[9],self.to_a[10]))
>      #Math.acos(self.to_a[5])
>      euler_angle(0)
>   end
>   def rotY
>     #(Math.arcsin(self.to_a[8]))
>     #Math.acos(self.to_a[0])
>     euler_angle(1)
>   end
>   def rotZ
>     #(-Math.atan2(self.to_a[4],self.to_a[0]))
>     #Math.asin(self.to_a[4])
>     euler_angle(2)
>   end
>   def rotXYZ
>     euler_angle
>   end
>   def rot_a ### rotation matrix 4x3 3 and 7 are nil
>     t=self.to_a
>     r=[]
>     [0,1,2,3,4,5,6,7,8,9,10].each{|i|r[i]=t[i]}
>     r[3]=nil
>     r[7]=nil
>     return r
>   end
>   def rotation_from_xyz(xyz)
>     if not xyz.class==Array and not xyz[2] and not xyz[0].class==Float and not xyz[1].class==Float and not xyz[2].class==Float
>       puts "Transformation;;rotation_from_xyz( ) expects a 3 Item Array of Angles [as Floats]."
>       return nil
>     end#if
>     tx=Geom;;Transformation.rotation(self.origin,X_AXIS,xyz[0])
>     ty=Geom;;Transformation.rotation(self.origin,Y_AXIS,xyz[1])
>     tz=Geom;;Transformation.rotation(self.origin,Z_AXIS,xyz[2])
>     t=(tx*ty*tz)
>     return self.set!(t)
>   end
>   def rotation_from_xyz_locally(xyz)
>     if not xyz.class==Array and not xyz[2] and not xyz[0].class==Float and not xyz[1].class==Float and not xyz[2].class==Float
>       puts "Transformation;;rotation_from_xyz_locally( ) expects a 3 Item Array of Angles [as Floats]."
>       return nil
>     end#if
>     tx=Geom;;Transformation.rotation(self.origin,self.xaxis,xyz[0])
>     ty=Geom;;Transformation.rotation(self.origin,self.yaxis,xyz[1])
>     tz=Geom;;Transformation.rotation(self.origin,self.zaxis,xyz[2])
>     t=(tx*ty*tz)
>     return self.set!(t)
>   end
>   def rotation_from_rot_a(rot_a)
>     if not rot_a.class==Array and not rot_a[10]
>       puts "Transformation;;rotation_from_rot_a( ) expects an 11 Item Array."
>       return nil
>     end#if
>     t=self.to_a
>     [0,1,2,4,5,6,8,9,10].each{|i|t[i]=rot_a[i].to_f}
>     return self.set!(t)
>   end
>   def rotation_from(trans)
>     if not trans.class==Geom;;Transformation
>       puts "Transformation;;rotation_from( ) expects a Sketchup;;Transformation."
>       return nil
>     end#if
>     t=self.to_a
>     tt=trans.to_a
>     [0,1,2,4,5,6,8,9,10].each{|i|t[i]=tt[i].to_f}
>     return self.set!(t)
>   end
>   def origin_from(trans)
>     if not trans.class==Geom;;Transformation
>       puts "Transformation;;origin_from( ) expects a Sketchup;;Transformation."
>       return nil
>     end#if
>     t=self.to_a
>     tt=trans.to_a
>     [12,13,14].each{|i|t[i]=tt[i].to_f}
>     return self.set!(t)
>   end
> end#class
> ###
>

Hey Tig, thanks for the great code, i might be doing something wrong here but this:

	Selection = Sketchup.active_model.selection[0]
	Rotation = Selection.transformation.rotXYZ

Gives an error,

Error; #<NameError; undefined local variable or method `xyz' for #<Geom;;Transformation;0xa747534>>
D;/PROGRA~1/Google/GOOGLE~1/Plugins/test.rb;128;in `euler_angle'
D;/PROGRA~1/Google/GOOGLE~1/Plugins/test.rb;197;in `rotXYZ'
D;/PROGRA~1/Google/GOOGLE~1/Plugins/test.rb;64

Any suggestions what could be going wrong?

TIG

@djarlo said:

@tig said:

Thanks for the input...
Here's my revised code using you ideas - it's still in radians and I have tried not to clash with your method naming etc - it now finds x/y/z rotations and [x,y,z] rotation as an array and has extra methods to set rotations from a 3 item array, referring either to the model axes or object's axes...

### transformation.extensions.rb (c) TIG 2009
> > ### From original ideas by TBD and others ? ### TIG 20091010
> > ### The euler rotation ideas from Dave Burdick 20100324
> > ### It extends the methods for Geom;;Transformation...
> > ### The built-in method "object.transformation.origin" return a point3d 
> > ###   that is the object's origin/insertion; the new method 
> > ###   object.transformation.getX etc returns the X location of the  
> > ###   object [or Y or Z].
> > ### The setX(x) resets the X value of the object [or Y or Z]; it 
> > ###   returns a new transformation that can then be used to reset the 
> > ###   original transformation; thus;
> > ###   object.transformation=object.transformation.setX(another_object.transformation.getX)
> > ###   - here it makes the object's X = another_object's X ; 
> > ###     it also could be given a float, e.g. 12.345 or a 'variable'...
> > ### The object.transformation.scaleX etc returns the scale on that axis.
> > ### The object.transformation.rotX etc returns the rotation on that axis
> > ###   in radians; use ... .rotX.radians to get it in degrees...
> > ### It uses different names to TBD's, e.g. 'rotZ' instead of 'zrot' etc.
> > ### Note the capitalization... this is because some 'compiled scripts' 
> > ### use 'rotz' already etc - [and they return the rotation in degrees!]
> > ### object.transformation.rotXYZ
> > ###   returns a 3 item array giving the rotations in x/y/z
> > ### object.transformation.rot_a
> > ###   returns an 11 item array of the transformation's rotation/scaling 
> > ###   - it can be used to extract some data more easily or as below...
> > ### object.transformation=object.transformation.rotation_from_rot_a(another_object.transformation.rot_a) 
> > ###   this applies another_object's 'rot_a' to change the object.
> > ### object.transformation=object.transformation.rotation_from(another_object.transformation) 
> > ###   this applies another_object's rotation/scaling to the object.
> > ###   it returns a new transformation that can then be used to reset the original...
> > ### object.transformation=object.transformation.origin_from(another_object.transformation) 
> > ###   this applies another_object's origin/location to the object.
> > ###   it returns a new transformation that can then be used to reset the original...
> > ### object.transformation=object.transformation.rotation_from_xyz([xrot,yrot,zrot])
> > ###   this applies a 3 item array of x/y/z rotations about the model's x/y/z-axes, 
> > ###   this could also be the array returned by rotXYZ.
> > ###   it returns a new transformation that can then be used to reset the original...
> > ### object.transformation=object.transformation.rotation_from_xyz_locally([xrot,yrot,zrot])
> > ###   this applies a 3 item array of x/y/z rotations about the objects's x/y/z-axes, 
> > ###   this could also be the array returned by rotXYZ.
> > ###   it returns a new transformation that can then be used to reset the original...
> > ###
> > class Geom;;Transformation
> >     def euler_angle(xyx=[])
> >        m = self.xaxis.to_a + self.yaxis.to_a + self.zaxis.to_a
> >        if m[6] != 1 and m[6]!= 1
> >           ry = -Math.asin(m[6])
> >           rx = Math.atan2(m[7]/Math.cos(ry),m[8]/Math.cos(ry))
> >           rz = Math.atan2(m[3]/Math.cos(ry),m[0]/Math.cos(ry))
> >        else
> >           rz = 0
> >           phi = Math.atan2(m[1],m[2])
> >           if m[6] == -1
> >              ry = Math;;PI/2
> >              rx = rz + phi
> >           else
> >              ry = -Math;;PI/2
> >              rx = -rz + phi
> >           end
> >        end   
> >        return -rx if xyz==0
> >        return -ry if xyz==1
> >        return -rz if xyz==2
> >        return [-rx,-ry,-rz] if xyz==[]
> >   end
> >   def getX
> >     self.to_a[12]
> >   end
> >   def getY
> >     self.to_a[13]
> >   end
> >   def getZ
> >     self.to_a[14]
> >   end
> >   def setX(x)
> >     if not x.class==Float and not x.class==Integer
> >       puts "Transformation;;setX( ) expects a Float or Integer."
> >       return nil
> >     end#if
> >     x=x.to_f
> >     t=self.to_a
> >     t[12]=x
> >     return self.set!(t)
> >   end
> >   def setY(y)
> >     if not y.class==Float and not y.class==Integer
> >       puts "Transformation;;setY( ) expects a Float or Integer."
> >       return nil
> >     end#if
> >     y=y.to_f
> >     t=self.to_a
> >     t[13]=y
> >     return self.set!(t)
> >   end
> >   def setZ(z)
> >     if not z.class==Float and not z.class==Integer
> >       puts "Transformation;;setZ( ) expects a Float or Integer."
> >       return nil
> >     end#if
> >     z=z.to_f
> >     t=self.to_a
> >     t[14]=z
> >     return self.set!(t)
> >   end
> >   def scaleX
> >     Math.sqrt(self.to_a[0]**2+self.to_a[1]**2+self.to_a[2]**2)
> >   end
> >   def scaleY
> >     Math.sqrt(self.to_a[4]**2+self.to_a[5]**2+self.to_a[6]**2)
> >   end
> >   def scaleZ
> >     Math.sqrt(self.to_a[8]**2+self.to_a[9]**2+self.to_a[10]**2)
> >   end
> >   def rotX
> >     #(Math.atan2(self.to_a[9],self.to_a[10]))
> >      #Math.acos(self.to_a[5])
> >      euler_angle(0)
> >   end
> >   def rotY
> >     #(Math.arcsin(self.to_a[8]))
> >     #Math.acos(self.to_a[0])
> >     euler_angle(1)
> >   end
> >   def rotZ
> >     #(-Math.atan2(self.to_a[4],self.to_a[0]))
> >     #Math.asin(self.to_a[4])
> >     euler_angle(2)
> >   end
> >   def rotXYZ
> >     euler_angle
> >   end
> >   def rot_a ### rotation matrix 4x3 3 and 7 are nil
> >     t=self.to_a
> >     r=[]
> >     [0,1,2,3,4,5,6,7,8,9,10].each{|i|r[i]=t[i]}
> >     r[3]=nil
> >     r[7]=nil
> >     return r
> >   end
> >   def rotation_from_xyz(xyz)
> >     if not xyz.class==Array and not xyz[2] and not xyz[0].class==Float and not xyz[1].class==Float and not xyz[2].class==Float
> >       puts "Transformation;;rotation_from_xyz( ) expects a 3 Item Array of Angles [as Floats]."
> >       return nil
> >     end#if
> >     tx=Geom;;Transformation.rotation(self.origin,X_AXIS,xyz[0])
> >     ty=Geom;;Transformation.rotation(self.origin,Y_AXIS,xyz[1])
> >     tz=Geom;;Transformation.rotation(self.origin,Z_AXIS,xyz[2])
> >     t=(tx*ty*tz)
> >     return self.set!(t)
> >   end
> >   def rotation_from_xyz_locally(xyz)
> >     if not xyz.class==Array and not xyz[2] and not xyz[0].class==Float and not xyz[1].class==Float and not xyz[2].class==Float
> >       puts "Transformation;;rotation_from_xyz_locally( ) expects a 3 Item Array of Angles [as Floats]."
> >       return nil
> >     end#if
> >     tx=Geom;;Transformation.rotation(self.origin,self.xaxis,xyz[0])
> >     ty=Geom;;Transformation.rotation(self.origin,self.yaxis,xyz[1])
> >     tz=Geom;;Transformation.rotation(self.origin,self.zaxis,xyz[2])
> >     t=(tx*ty*tz)
> >     return self.set!(t)
> >   end
> >   def rotation_from_rot_a(rot_a)
> >     if not rot_a.class==Array and not rot_a[10]
> >       puts "Transformation;;rotation_from_rot_a( ) expects an 11 Item Array."
> >       return nil
> >     end#if
> >     t=self.to_a
> >     [0,1,2,4,5,6,8,9,10].each{|i|t[i]=rot_a[i].to_f}
> >     return self.set!(t)
> >   end
> >   def rotation_from(trans)
> >     if not trans.class==Geom;;Transformation
> >       puts "Transformation;;rotation_from( ) expects a Sketchup;;Transformation."
> >       return nil
> >     end#if
> >     t=self.to_a
> >     tt=trans.to_a
> >     [0,1,2,4,5,6,8,9,10].each{|i|t[i]=tt[i].to_f}
> >     return self.set!(t)
> >   end
> >   def origin_from(trans)
> >     if not trans.class==Geom;;Transformation
> >       puts "Transformation;;origin_from( ) expects a Sketchup;;Transformation."
> >       return nil
> >     end#if
> >     t=self.to_a
> >     tt=trans.to_a
> >     [12,13,14].each{|i|t[i]=tt[i].to_f}
> >     return self.set!(t)
> >   end
> > end#class
> > ###
> >

Hey Tig, thanks for the great code, i might be doing something wrong here but this:

	Selection = Sketchup.active_model.selection[0]
> 	Rotation = Selection.transformation.rotXYZ

Gives an error,

Error; #<NameError; undefined local variable or method `xyz' for #<Geom;;Transformation;0xa747534>>
> D;/PROGRA~1/Google/GOOGLE~1/Plugins/test.rb;128;in `euler_angle'
> D;/PROGRA~1/Google/GOOGLE~1/Plugins/test.rb;197;in `rotXYZ'
> D;/PROGRA~1/Google/GOOGLE~1/Plugins/test.rb;64

Any suggestions what could be going wrong?

There's a typo in the code that I corrected but never posted !
def euler_angle(xyx=[])
should be
def euler_angle(xyz=[])
also note what Dan said about naming conventions.....

Here's a link to the corrected code http://forums.sketchucation.com/viewtopic.php?p=190874#p190874

shirazbj

@martinrinehart said:

@dburdick said:

I read your wonderful web-page description of the 4 x 4 matrix - ...

I am reading it too. Great job.Thanks.

Djarlo

Thanks to both
heh must have missed that type too time and again i looked it all over to see whats wrong

tomasz

@martinrinehart said:

@dburdick said:

I read your wonderful web-page description of the 4 x 4 matrix - ...

Very kind words, indeed. Many thanks.

For those not versed in the Transformation Matrix, my tutorial's Appendix T, introduces it, Appendix MM explains matrix multiplication and Chapter 16 explains how you can live without it (and includes a Matrix class, just in case).

Thank you Martin for those wonderful tutorials. I wasn't aware that transformation.to_a[15] is a divisor for a translation! As far as I am aware SketchUp itself keeps it equal to 1, but some plugins modify Wt (i.e. Component Stringer).

Ruts

I have a question about the euler_angle method, especially about the xyz. I have searched the web and found information about this case, but it didn't result in an answer.

Here's how I read this piece of code:

when you call the method euler_angles you create an empty array under variable xyz as parameter. Then nothing happens with the array for the whole piece of code. At the end the array can be ==0 (contains one element which is equal to zero), ==1, ==2 or still empty. How can it be that the array can contain elements?

Dan Rathbun

Words in ALLCAPS are reserved for constants.
Words in Titlecase are for Class and Module Identifiers, (which are also constants. Any word the starts with a capital character is a constant.)

Bad:
Selection = Sketchup.active_model.selection[0] Rotation = Selection.transformation.rotXYZ

Good for variables:
selection = Sketchup.active_model.selection[0] rotation = selection.transformation.rotXYZ

Dan Rathbun

@ruts said:

...when you call the method euler_angle you create an empty array under variable xyz as parameter.

The secret is that Ruby does not really "have" variables, even though the books use that name. Ruby has references that point at objects, and a reference can be made to point at any class of object, and then later be re-assigned to point at any other object of any class, at any time.
This is referred to as "weakly typed", but really Ruby references are not type locked at all.

@ruts said:

Then nothing happens with the array for the whole piece of code.

Because it (the argument) is just being used as a switch to tell the method what the coder wants as an output. An empty array object is simply the default, which tells the method the calling code expects an array as a return object.

@ruts said:

At the end the array can be ==0 (contains one element which is equal to zero), ==1, ==2 or still empty. How can it be that the array can contain elements?

It cannot. You mis-understand. The method is not testing an array, it is testing a reference to the method argument to see if is pointing at integers 0 or 1 or 2, or still pointing at [] (the default empty array object,) and then returning either the indicated values, or an array of all three.

IF you call the method with no arguments, or like euler_angle([]) you will get an array of 3 values.
IF you call the method thus: euler_angle(0) you will get the x value returned.
IF you call the method thus: euler_angle(1) you will get the y value returned.
IF you call the method thus: euler_angle(2) you will get the z value returned.

The 0, 1 and 2 subscripts come from the SketchUp API's extension of the Array class, where 3 element arrays can act like points and vectors.

Still have not read the book, I see.

Ruts

I did delete the rotX/Y/Z methods, that's why I didn't understand where the variable xyz came from and why it could get value = 0/1/2. I do understand how methods with there variables work. Sorry was confused.

On the other hand, I have been working with the euler_angle method for a while and now that I'm closely getting to a complete script I have noticed this method only partial works (for me?). Does it work for you guys? When I did draw shapes with a given rotation, the method didn't succeed to calculate the right angles for me so I did some research and made some changes. Here's the code I use:

	def self.rotation(trans)
		b = [trans.xaxis.to_a, trans.yaxis.to_a, trans.zaxis.to_a]
		m = b.transpose.flatten!
		if m[6] != 1 and m[6] != -1
			ry = -Math.asin(m[6])
			rx = Math.atan2(m[7]/Math.cos(ry),m[8]/Math.cos(ry))
			rz = Math.atan2(m[3]/Math.cos(ry),m[0]/Math.cos(ry))
		else
			rz = 0
			phipos = Math.atan2(m[1],m[2])
			phineg = Math.atan2(-m[1],-m[2])
			if m[6] == -1
				ry = Math;;PI/2
				rx = rz + phipos
			else
				ry = -Math;;PI/2
				rx = -rz + phineg
			end
		end   
	return [rx.radians,ry.radians,rz.radians]
	end

First I found this document (page 5) that explains the calculations the way you do it. But it seems that you miss little pieces of code to make it complete.

When I did calculate the angles it yet didn't calculate the right angles. So I did try some things and found out that the angles that were calculated represent the transpose matrix of the rotation that I need. So I fixed this by transposing the rotation matrix before the calculations.

With these changes this piece of code does calculate the right angles. Did your code work for you?

Dan Rathbun

You realize that this topic thread is like 4 and 1/2 years old ?

Ruts

@dan rathbun said:

You realize that this topic thread is like 4 and 1/2 years old ?

Yes, I have seen it. That does not mean that people can't come here and look for code that works? That's how I landed here. I was looking for some code that could convert the rotation matrix to euler angles. I found out that this code didn't work for me, so I did correct it and now I share it here just in case people experience the same problem as me. I'm just excited that I finally can contribute a little instead of always asking things!

Nothing wrong with that, right?

Dan Rathbun

@ruts said:

@dan rathbun said:

You realize that this topic thread is like 4 and 1/2 years old ?

Yes, I have seen it. ... Nothing wrong with that, right?

I was referring to your asking questions of original posters, who might not remember, or might not even have been active here for some time.

Jernej Vidmar

Hello transformation gurus!

just to double check the euler_angle(xyz=[]) method ... is the condition:

if m[6] != 1 and m[6]!= 1

at the beginning correct? Why double checking the same variable against the same value? Or is it meant to be:

if m[6] != 1 and m[6]!= -1

?

Cheers,
Jernej

TIG

An olde typo - use 1 for the second test...