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CONTENTS

INTRODUCTION TO TRANSLATION
  1. Two dimensional translation
  2. Three dimensional translation

INTRODUCTION TO TRANSLATION

Translation is the straight line movement of an object from its original position to another position at a given distance and direction.


Contents Introduction Inverse 2D translation

TWO DIMENSIONAL TRANSLATION

Let be the input vertex and be the shifts in x and y directions, respectively. Recall the equation of transformation Q = P M + tr . M is an identity matrix for translation. Therefore, the translated vertex is given by

For example, let and . The translation of a square is shown in the figure below.

Thus two objects can be translated by adding the translation vector to the coordiantes of each vertex (endpoint). A homogenous coordinate is appended to each end point.

To translate a circle or an ellipse, its center coordinates are translated first, and redrawn in the new location.

Translation can be represented in matrix form as


Contents 2D 3D translation

Inverse 2D Translation

The inverse of translation is given by


Contents Inverse Inverse

THREE DIMENSIONAL TRANSLATION

Translation in 3 dimension is similar to translation in 2 dimension. Given input vector , and shifts , objects can be translated by adding the translation vector to the coordinates of each end point.

With the homogenous coordinate appended to each point, It can also be represented in the matrix form

Translation of a unit cube is shown in the figure below.


Contents 3D

Inverse 3D Translation

The inverse translation produces translation in the opposite direction. The inverse of three dimensional transformation is given by

The product of translation matrix and its inverse is an identity matrix


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Priya Asokarathinam /ADVISOR Shoaff