1 / 11

The Spherical Spiral

The Spherical Spiral. By Chris W ilson And Geoff Zelder. History. Pedro Nunes , a sixteenth century Portuguese cosmographer discovered that the shortest distance from point A to point B on a sphere is not a straight line, but an arc known as the great circle route.

wanda
Download Presentation

The Spherical Spiral

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Spherical Spiral By Chris Wilson And Geoff Zelder

  2. History Pedro Nunes, a sixteenth century Portuguese cosmographer discovered that the shortest distance from point A to point B on a sphere is not a straight line, but an arc known as the great circle route. Nunes gave early navigators two possible routes across open seas. One being the shortest route and the other being a route following a constant direction, generally about a 60 degree angle, in relation to the cardinal points known as the rhumb line or the loxodrome spiral. Pedro Nunes 1502-1579

  3. Loxodrome Spiral M C Esher (1898-1972), known for his art in optical illusions drew the Bolspiralen spiral, which is the best representation of Nunes’ theory Bolspiralen spiral 1958

  4. Mercator’s Projection Gerardus Mercator (1512-1594), used Nunes’ loxodrome spiral which revolutionized the making of world maps Map makers have to distort the geometry of the globe in order to reproduce a spherical surface on a flat surface

  5. Plotting the spiral In this case we let run from 0 to k , so the larger k is the more times the spiral will circumnavigate the sphere. We let , where controls the spacing of the spirals, and controls the closing of the top and bottom of the spiral.

  6. The Spiral

  7. A few Applications • A spherical spiral display which rotates about a vertical axis was proposed in the 60’s as a 3-D radar display. A small high intensity light beam is shot into mirrors in the center which control the azimuth and elevation. A fixed shutter with slits in it would control the number of targets that could be displayed at one time.

  8. Another use is a high definition 3-D projection technique to produce many 2-D images in different directions so the image could be viewed from any angle, this creates a sort of fishbowl effect.

  9. Some Fun with the Equation • Here we let = 1, and . We let • . We end up with a sort of 3D Clothiod type figure.

  10. Here we let , and let . • We let . We end up with a cylindrical helix.

  11. Here we let , and let We let . We end up with this.

More Related