Latitudinal Tori
What we want to explore here is first how to measure the length of an orbit in a principal bundle, by applying cumulative Gactions, and then decimating it into a linear space in the form of an admissible curve with segments that measure in an equal way. Then, the result should be smooth looking Hopf fibers using only thirty cut points along the orbit. So, we defined a new function that takes a sequence of Gactions, which are spaced linearly and equally, and it spits out new Gactions that preserve the same symmetry under stereographic projection, which pushes forward a metric with nonconstant curvature. As a result we rectified the distortion that was inevitable if we wanted to capture the Hopf fibration complete as a picture and in an efficient manner. Calculated the Möbius transformtions, at each frame of the animation, by taking four complex numbers that characterize the transformation, and rotating them in the Riemann sphere about the x axis in E. Made with and
|
|