Introducing the right-hand coordinate system and the necessary considerations in Monte Carlo calculations
The right-hand coordinate system is used in Monte Carlo computing systems. Understanding this coordinate helps to get the right imaginations in 3D modeling. In this article, the most important points that are necessary when working with Monte Carlo code are stated along with the main points of the right-coordinate system.
Table of Contents
1) Comparison of right-handed and left-handed coordinates
While a good understanding of 3D mathematics will certainly be helpful, it is not absolutely necessary. Now all you need to know is that we define an object in three dimensions (hence, three-dimensional) using the common symbol x, y, and z, where x is the position along the x-axis; y is along the y-axis and z is along the z-axis.
In addition, we define the position of these axes using a term called left-handed or right-handed coordinate system.
right-hand system: If we rotate the fingers of our right hand from the X-axis to the Y-axis, the direction of the Z-axis is in the direction of the thumb finger.
left-handed system: If we rotate the fingers of our left hand from the X-axis to the Y-axis, the direction of the Z-axis is in the direction of the thumb finger.
2) Monte Carlo code coordinate system
The coordinate system used in Monte Carlo codes is a cartesian system. below rules must be considered in 3d modeling
1) It is a right-handed coordinate system of Cartesian type.
2) This system should be the criterion of geometric modeling.
3) This system can not be changed.
4) In the MCNP code, the unit of the system is in centimeters, while in Geant4 and GATE codes, the unit is adjustable.
5) The criterion for rotating devices is counterclockwise.
3) Rotation in the coordinate system
Rotation in the three-dimensional coordinate system follows the special rules shown below.
3-1) Rotation around the X-axis
Rotation about the x-axis rotates the y-axis toward the z-axis.
3-2) Rotation around the Y-axis
Rotation about the y-axis rotates the z-axis toward the x-axis.
3-3) Rotation around the Z-axis
Rotation around the Z-axis rotates the X-axis toward the Y-axis.
