PENCERMINAN PADA DIMENSI TIGA

Abstract

Abstract: The concept of reflection in three-dimensional is almost the same as the concept of reflection in the two-dimensional. However, the mirror in three-dimensional is in the form of flat plane.  Reflection in three-dimensional is a function that maps each point in such a way to meet the following requirements: distance between the prapeta point and the mirror is the distance between the mirror to the mapping result, the line connecting prapeta point with the mapping must be perpendicular to the mirror, and the structure and its reflection must be congruent. To get the reflection function, it can be carried out analytically. First, take flat plane as a mirror and the point that will be reflected in three-dimensional. A straight line is made through that point and it is perpendicular to the mirror, so the breakpoint can be determined. By utilizing shifts in three-dimensional, translucent point can be shifted in line with vector where is the point and is the starting point. So, the point as the result of mirroring can be obtained. The results of this study reveal that: mirroring in three-dimensional is a transformation because its function is a bijective. Reflection is involution which means that the results of twice multiplications are identity. Mirroring is not commutative. The result of twice parallel reflection composition can be called as reflection. The result of n multiplication of mirroring composition parallel to the coordinate and there is a distance is called as reflection.

Keywords:Involution, Composition, Transformation.