Biology Reference

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Figure 2.7
Pictorial representation of the operations of translation and rotation. The

triangle drawn with an unbroken line is the original configuration. The triangle drawn

with a broken line represent a change in the triangle due to rotation on an axis with

no translation. The triangle drawn with a dotted line represents a change in the trian-

gle due to translation across the plane with no rotation. The triangle drawn with dots

and dashes represents the result of the combination of rotation and translation.

Notice that rotation of a three-dimensional object requires

specification of two angles of rotation
α

and
o
/
.

d)

Translation of an object
: Let the landmark coordinate matrix

for a given two dimensional object be denoted by
M
. Suppose

we translate this object so that all the X-coordinates are

moved by
t
1
units and the Y-coordinates are moved by
t
2
units.

The landmark coordinate matrix of the translated object is

given by
M +
1
t
where 1= , a
K
1 column vector of 1's and

t
is a 1 by 2 row vector. We call “
t
” the translation vector or a

translation parameter.

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