Transformation for 3-d translation, Computer Graphics

Suppose P be the point object along with the coordinate (x,y,z). We want to translate such object point to the new position as, P'(x',y',z') through the translation Vector as V=tx.I+ty.J+tz.K , here tx , ty and tz  are the translation factor into the x, y, and z directions correspondingly, as demonstrated in Figure 8. It is, a point (x,y,z) is shifted to (x+ tx,y+ ty,z+ tz). Hence the new coordinates of a point can be written:

819_Transformation for 3-D Translation 1.png

In terms of homogeneous coordinates, above equation  becomes:

That is: P'h = Ph.Tv

1443_Transformation for 3-D Translation 2.png

 

Posted Date: 4/3/2013 6:02:41 AM | Location : United States







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