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![](\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/05\/trackball1.png\")
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That’s because we were looking edge-on at the third direction. It’s like looking at a spinning bicycle wheel when the bicycle is heading toward you.<\/p>\n
Similarly, if you are looking at a sphere floating in space in front of you, and you are looking edge-on into a fourth dimension, then your view of any spin that rotates the ball into that fourth dimension is going to have the same problem: You are basically looking head-on at a spinning bicycle wheel.<\/p>\n
To turn a floating sphere into a four dimensional trackball, you just need to count how many ways there are to spin a bicycle wheel edge-on. It turns out there are three, since each of our familiar three dimensions can spin into that fourth dimension.<\/p>\n
If you add the three ways of spinning a sphere that only involve our familiar three dimensions, you get six spin dimensions all together:<\/p>\n
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![](\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/05\/trackball4d.png\")
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It should be pretty clear from the picture what’s going on: You can rotate the ball in three directions that don’t involve that fourth dimension at all, just like a regular track ball (the red, green and blue arrows).<\/p>\n
Or, you can rotate it in a way that swaps any of our three dimensions for that fourth dimension (the cyan, magenta and yellow arrows).<\/p>\n
Recall that some rotations on a regular virtual trackball require moving your finger in a straight line on your iPad screen (as in the first picture above). Something similar is happening here.<\/p>\n
Namely, on a 4D virtual trackball you make those last three rotations (cyan, magenta and yellow) by moving your hand in a straight line inside the sphere that is floating in front of you.<\/p>\n
I find it thrilling that you can manipulate a 4D object while staying safely inside our little 3D world. We’re working on building this stuff right now at NYU, using the Oculus Rift and our own hand tracking software. I will let you know when we have something cool to show.<\/p>\n","protected":false},"excerpt":{"rendered":"
If you recall, when you look head-on at a virtual trackball, you can’t actually see that your movements to “spin the ball up and down” and “spin the ball left and right” are creating curved motion. In the picture I first showed (below), the red and green arrows look straight to us, even though they … Continue reading “4D trackball”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/12165"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12165"}],"version-history":[{"count":18,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/12165\/revisions"}],"predecessor-version":[{"id":12184,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/12165\/revisions\/12184"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12165"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12165"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}