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    Compute Rotation and Scale from Transform Object

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    • D Offline
      dburdick
      last edited by

      @martinrinehart said:

      @dburdick said:

      Is there a simple Sketchup Ruby method which returns the x,y and z rotation in degrees ...

      What's the application for this? (Scaling modifies the xform's [0,0], [1,1], [2,2] entries. Rotations modify all entries from [0,0] through [2,2]. It's not immediately obvious that you can find original operations in any non-trivial case.)

      Hi Martin,

      Thanks for jumping in on this. I read your wonderful web-page description of the 4 x 4 matrix - truly excellent - and serves as the inspiration behind what I'm trying to do.

      Basically, I need to get the exact rotation and scaling values of any component in world space in order to export an instance of that component. I already have figured out how to create the transformation by multiplying the stacked transformations of the component hierarchy, but I need to express the output rotational transformation in degrees - eg rotX, rotY, rotZ - and it needs to work even if the user decides to scale the component non-uniformly (e.g. skewing, shearing). In Sketchup, a user could for example scale a door component in only the Y direction. The current transform extension lib from TIG does not handle this correctly as the lib assumes all scaling is done uniformly to the component. So I need to understand how to adjust TIG's ruby code to accomodate this. Here's his code for example on returing the rotX value from a transform object:

      def rotX
          #(Math.atan2(self.to_a[9],self.to_a[10]))
          Math.acos(self.to_a[5]).radians
      end
      

      This works fine when the component is uniformly scaled, but fails when for example the x dimension is scaled to a value different than Y and Z. This is because the array value[5] contains a number greater than 1.0 when non-uniform scaling is introduced. So it will return an error and bomb. I;m not sure what the commented out code is above the equation.

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      • TIGT Offline
        TIG Moderator
        last edited by

        I think the bits of code that're commented out [starts with a #] are perhaps the right code ?
        Swap the two around - this was a work-in-progress that stalled...
        Try

        
        def rotX
          Math.atan2(self.to_a[9],self.to_a[10])
          ###Math.acos(self.to_a[5]).radians
        end
        

        ??????
        Let me know how it works...

        TIG

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        • D Offline
          dburdick
          last edited by

          @tig said:

          I think the bits of code that're commented out [starts with a #] are perhaps the right code ?
          Swap the two around - this was a work-in-progress that stalled...
          Try

          
          > def rotX
          >   Math.atan2(self.to_a[9],self.to_a[10])
          >   ###Math.acos(self.to_a[5]).radians
          > end
          

          ??????

          Let me know how it works...

          Hi TIG,

          Yes, when switching to the commented code versus the original lines it works better (doesn't bomb) - but it give incorrect results when two or more rotations are involved - e.g. roation around the X followed by rotation around Z. I'm going to try to see if I can return better results by working with 2 vectors intead of the whole matrix.

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          • D Offline
            dburdick
            last edited by

            I think I found a more foolproof way of doing this by using transform object axis vectors. It turns out, that the 4 x 4 matrix needs to be normalized first (e.g. sans any non-uniform scaling) before computing the rotation angles. So the way to do this is to use the already normalized axis vectors (x-axis, yaxis, etc.). So here's the revised code which returns the rotation angles in degrees:

              def rotX
                 Math.atan2(self.yaxis.z,self.yaxis.y).radians
              end
              def rotY
            	Math.atan2(self.xaxis.z,self.xaxis.x).radians
              end
              def rotZ
            	Math.atan2(self.xaxis.y,self.xaxis.x).radians
              end
            

            Update: Sorry I jumped the gun here a bit - this isn't correct. The scaling issues now work but the multi rotation problem is still here

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            • D Offline
              dburdick
              last edited by

              Okay, I got it working to return nice clean Euler angles from a transform object. Here's the code (note - it returns right-handed angles in degrees):

              def euler
              	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.radians, -ry.radians, -rz.radians
              end
              
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              • TIGT Offline
                TIG Moderator
                last edited by

                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(xyz=[])
                       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
                ###
                
                

                EDIT: typo in euler code fixed TIG 20110209

                TIG

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                • M Offline
                  MartinRinehart
                  last edited by

                  @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).

                  Author, Edges to Rubies - The Complete SketchUp Tutorial at http://www.MartinRinehart.com/models/tutorial.

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                  • D Offline
                    Djarlo
                    last edited by

                    @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?

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                    • TIGT Offline
                      TIG Moderator
                      last edited by

                      @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?

                      ๐Ÿ˜ณ 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

                      TIG

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                      • S Offline
                        shirazbj
                        last edited by

                        @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.

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                        • D Offline
                          Djarlo
                          last edited by

                          Thanks to both ๐Ÿ˜„
                          heh must have missed that type too time and again i looked it all over to see whats wrong ๐Ÿ˜›

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                          • T Offline
                            tomasz
                            last edited by

                            @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).

                            Author of [Thea Render for SketchUp](http://www.thearender.com/sketchup)

                            1 Reply Last reply Reply Quote 0
                            • R Offline
                              Ruts
                              last edited by

                              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?

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                              • Dan RathbunD Offline
                                Dan Rathbun
                                last edited by

                                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
                                ๐Ÿ˜‰

                                I'm not here much anymore.

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                                • Dan RathbunD Offline
                                  Dan Rathbun
                                  last edited by

                                  @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.

                                  I'm not here much anymore.

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                                  • R Offline
                                    Ruts
                                    last edited by

                                    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?

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                                    • Dan RathbunD Offline
                                      Dan Rathbun
                                      last edited by

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

                                      I'm not here much anymore.

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                                      • R Offline
                                        Ruts
                                        last edited by

                                        @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?

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                                        • Dan RathbunD Offline
                                          Dan Rathbun
                                          last edited by

                                          @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.

                                          I'm not here much anymore.

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                                          • J Offline
                                            Jernej Vidmar
                                            last edited by

                                            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

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