2011-05-09

Yin-Yang in 3D

Who said that Taoist monad, representing the concept of Yin and Yang, in three-dimensional space, a plane? Although it almost always appears to be this symbol. In modern parlance — in 2D. How does it look in 3D? To this question tried to answer your humble servant, and the program MathCAD.

To build a graph of our 3D images was chosen as the simplest formula of sine and cosine and the program MathCAD (version 14). The graph was constructed pointwise, i.e., set the interval of the points, and then each of them was the value functions for each of the three axes, which are displayed on the chart. Look what happened: Programm itself for MathCAD is here.

Decode variables:

- i — interval points of the build;
- a
_{i}— the angle in each point; - r
_{i}— a random variable, which we receive at every point in the range from 0 to 2*pi; - X
_{i}, Y_{i}, Z_{i}is the value of the function at each point along the three axes.

Begin to rotate the graph and see what it is from different angles.