Mathematica 9 is now available

Documentation / DynamicVisualizer / A2: Orientation Commands /

A2.8 The 4×4 TransformationMatrix Notation

A 4×4 matrix encodes the orientation, scale, and location of an object. An unscaled, unrotated, unmoved object is represented by the identity matrix. The last column of the 4×4 matrix is unused and should be set to {0, 0, 0, 1}.

In[52]:={ { r11 , r12 , r13 , 0 }
, { r21 , r22 , r23 , 0 }
, { r31 , r32 , r33 , 0 }
, { x , y , z , 1 } }

Out[52]=

The top left-hand corner is the 3×3 matrix previously discussed, except that it now includes scaling information. The elements x, y, and z indicate the displacement of the object.

If the orientation matrix is normalized properly, the scaling factors along each axis ", , " may be represented as

In[53]:=

Out[53]=

For example, the following 4×4 matrix represents a scaling factor of 2 along the y axis.

In[54]:={ { 1,0,0,0 }
, { 0,2,0,0 }
, { 0,0,1,0 }
, { 0,0,0,1 } }

Out[54]=

This change in scale could also be written in the following form.

In[55]:=

Out[55]=



Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.