![]() ![]() The same process produces two-dimensional shadows from three-dimensional objects when the sun is directly overhead. This is an orthogonal projection in which the fourth coordinate, the linearly independent combination Where the third coordinate is a linear superposition of the imaginary parts of the complex variables. The surface presented above consists of the coordinate triples ![]() ![]() The real and imaginary parts of z 1 and z 2, a total of four variables, parametrize a surface in four dimensions. The nth powers of the phase factors are exponentials of multiples of 2π i , hence unity. Where the phase factors are nth roots of unity with This equation is identically solved by the coordinate combinations With two complex variables and an arbitrary integer n as exponent. The method of visualization boils down to three-dimensional projections of a surface in four dimensions defined by the equation The interactive graphic is a JavaScript implementation of the techniques described in this online reference, apart from the color coding:Ī Construction for Computer Visualization of Certain Complex Curves The integers on the buttons determine the degree of the underlying equation defining the surface. The figure can be rotated by clicking and dragging with a mouse or swiping on a touch device, as well as zoomed in or out with a mouse wheel or pinching on a touch device. ![]()
0 Comments
Leave a Reply. |