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#ActualTournicoti

Posted 11 March 2013 - 03:45 AM

Hello smile.png


With homogeneous coordinates, there are four components to represent a 3d vertex or a 3d vector :

  • if w != 0 , ( x , y , z , w ) represents the vertex ( x/w , y/w , z/w )
  • if w = 0 , it represents all the vectors colinear to the vector ( x , y , z ).   [ i.e. : a * ( x , y , z ) , a in lR*  ]

So for a vertex ( x , y , z ) transformed into ( x' , y' , z' ) with Transform :

  • ( X , Y , Z , W ) = ( x , y , z , 1 ) * Transform
  • ( x' , y' , z' ) = ( X , Y , Z ) / W

NB :
For the vertices, the w component is usually initially set to 1 so that the w division is not needed in rotations, translations, scalings, and any combination of them.
With this assumption, the w division is necessary only when Transform is (or 'contains') a projection matrix.

Nico


#14Tournicoti

Posted 08 October 2012 - 02:39 PM

Hello Posted Image


With homogeneous coordinates, there are four components to represent a 3d vertex or a 3d vector :
  • if w != 0 , ( x , y , z , w ) represents the vertex ( x/w , y/w , z/w )
  • if w = 0 , it represents the vector ( x , y , z )
So for a vertex ( x , y , z ) transformed into ( x' , y' , z' ) with Transform :
  • ( X , Y , Z , W ) = ( x , y , z , 1 ) * Transform
  • ( x' , y' , z' ) = ( X , Y , Z ) / W
NB :
For the vertices, the w component is usually initially set to 1 so that the w division is not needed in rotations, translations, scalings, and any combination of them.
With this assumption, the w division is necessary only when Transform is (or 'contains') a projection matrix.

Nico

#13Tournicoti

Posted 08 October 2012 - 02:39 PM

Hello Posted Image


With homogeneous coordinates, there are four components to represent a 3d vertex or a 3d vector :
  • if w != 0 , ( x , y , z , w ) represents the vertex ( x/w , y/w , z/w )
  • if w = 0 , it represents the vector ( x , y , z )
So for a vertex ( x , y , z ) transformed into ( x' , y' , z' ) with Transform :
  • ( X , Y , Z , W ) = ( x , y , z , 1 ) * Transform
  • ( x' , y' , z' ) = ( X , Y , Z ) / W
NB :
For the vertices, the w component is usually initially set to 1 so that the w division is not needed in rotations, translations, scalings, and any combinations of them.
With this assumption, the w division is necessary only when Transform is (or 'contains') a projection matrix.

Nico

#12Tournicoti

Posted 08 October 2012 - 02:32 PM

Hello Posted Image


With homogeneous coordinates, there are four components to represent a 3d vertex or a 3d vector :
  • if w != 0 , ( x , y , z , w ) represents the vertex ( x/w , y/w , z/w )
  • if w = 0 , it represents the vector ( x , y , z )
So for a vertex ( x , y , z ) transformed into ( x' , y' , z' ) with Transform :
  • ( X , Y , Z , W ) = ( x , y , z , 1 ) * Transform
  • ( x' , y' , z' ) = ( X , Y , Z ) / W
NB :
For the vertices, the w component is usually initially set to 1 so that the w division is not needed in rotations, translations and scalings.
With this assumption, the w division is necessary only when Transform is (or 'contains') a projection matrix.

Nico

#11Tournicoti

Posted 08 October 2012 - 02:31 PM

Hello Posted Image


With homogeneous coordinates, there are four components to represent a 3d vertex or a 3d vector :
  • if w != 0 , ( x , y , z , w ) represents the vertex ( x/w , y/w , z/w )
  • if w = 0 , it represents the vector ( x , y , z )
So for a vertex ( x , y , z ) transformed into ( x' , y' , z' ) with Transform :
  • ( X , Y , Z , W ) = ( x , y , z , 1 ) * Transform
  • ( x' , y' , z' ) = ( X , Y , Z ) / W
NB :
For the vertices, the w component is usually set to 1 so that the w division is not needed in rotations, translations and scalings.
With this assumption, the w division is necessary only when Transform is (or 'contains') a projection matrix.

Nico

#10Tournicoti

Posted 08 October 2012 - 02:31 PM

Hello Posted Image


With homogeneous coordinates, there are four components to represent a 3d vertex or a 3d vector :
  • if w != 0 , ( x , y , z , w ) represents the vertex ( x/w , y/w , z/w )
  • if w = 0 , it represents the vector ( x , y , z )
So for a vertex ( x , y , z ) transformed into ( x' , y' , z' ) with Transform :
  • ( X , Y , Z , W ) = ( x , y , z , 1 ) * Transform
  • ( x' , y' , z' ) = ( X , Y , Z ) / W
NB :
For the vertices, the w component is usually set to 1 so that the w division is not needed in rotations, translations and scaling.
With this assumption, the w division is necessary only when Transform is (or 'contains') a projection matrix.

Nico

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