Three Dimensional TransformationsThe geometric transformations play a vital role in generating images of three Dimensional objects with the help of these transformations. The location of objects relative to others can be easily expressed. Sometimes viewpoint changes rapidly, or sometimes objects move in relation to each other. For this number of transformation can be carried out repeatedly. TranslationIt is the movement of an object from one position to another position. Translation is done using translation vectors. There are three vectors in 3D instead of two. These vectors are in x, y, and z directions. Translation in the xdirection is represented using T_{x}. The translation is ydirection is represented using T_{y}. The translation in the z direction is represented using T_{z}. If P is a point having coordinates in three directions (x, y, z) is translated, then after translation its coordinates will be (x^{1} y^{1} z^{1}) after translation. T_{x} T_{y} T_{z} are translation vectors in x, y, and z directions respectively. x^{1}=x+ T_{x} Threedimensional transformations are performed by transforming each vertex of the object. If an object has five corners, then the translation will be accomplished by translating all five points to new locations. Following figure 1 shows the translation of point figure 2 shows the translation of the cube. Matrix for translationMatrix representation of point translationPoint shown in fig is (x, y, z). It become (x^{1},y^{1},z^{1}) after translation. T_{x} T_{y} T_{z} are translation vector. Example: A point has coordinates in the x, y, z direction i.e., (5, 6, 7). The translation is done in the xdirection by 3 coordinate and y direction. Three coordinates and in the z direction by two coordinates. Shift the object. Find coordinates of the new position. Solution: Coordinate of the point are (5, 6, 7) Multiply coordinates of point with translation matrix = [5+0+0+30+6+0+30+0+7+20+0+0+1] = [8991] x becomes x^{1}=8
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