Hi, this is Burt, also known as BClaw on the Tetraspace Forum. I don't know to what level of detail you want to go to, so I'll give you some details, and if you need more, I'll send the code snippets. First of all, the way I did the translations was just as you described, but they are always applied in order on the base object. That way I never have to worry about how complex rotations are going to come back to their origin. I apply the rotations in this order: xy, xz, yz, xw, yw, zw, (xv, yv, zv, wv). OK here we go!
4-Cube 1: total animation, frame 0 to 600
xy: 0-90 deg, frame 30 to 215
xz: 0-90 deg, frame 105 to 290
yz: 0-90 deg, frame 180 to 365
xw: 0-90 deg, frame 255 to 440
yw: 0-90 deg, frame 330 to 515
zw: 0-90 deg, frame 405 to 590
4-Cube 2: total animation, frame 0 to 720
xy: 0-360 deg, frame 210 to 420
xz: 0-360 deg, frame 120 to 330
yz: 0-360 deg, frame 390 to 600
xw: 0-360 deg, frame 30 to 240
yw: 0-360 deg, frame 300 to 510
zw: 0-360 deg, frame 480 to 690
5-Cube 1: total animation, frame 0 to 1080
xy: 0-90 deg, frame 30 to 105: 90-0 deg, frame 150 to 240
xz: 0-90 deg, frame 120 to 195: 90-0 deg, frame 240 to 330
yz: 0-90 deg, frame 210 to 285: 90-0 deg, frame 330 to 420
xw: 0-90 deg, frame 300 to 375: 90-0 deg, frame 420 to 510
yw: 0-90 deg, frame 390 to 465: 90-0 deg, frame 510 to 600
zw: 0-90 deg, frame 480 to 555: 90-0 deg, frame 600 to 690
xv: 0-90 deg, frame 570 to 645: 90-0 deg, frame 690 to 780
yv: 0-90 deg, frame 660 to 735: 90-0 deg, frame 780 to 870
zv: 0-90 deg, frame 750 to 825: 90-0 deg, frame 870 to 960
wv: 0-90 deg, frame 840 to 915: 90-0 deg, frame 960 to 1050
5-Cube 2: total animation, frame 0 to 630
xy: 0-90 deg, frame 30 to 120: 90-0 deg, frame 150 to 210
xz: 0-90 deg, frame 210 to 300: 90-0 deg, frame 330 to 390
yz: 0-90 deg, frame 75 to 165: 90-0 deg, frame 195 to 255
xw: 0-90 deg, frame 300 to 390: 90-0 deg, frame 420 to 480
yw: 0-90 deg, frame 390 to 480: 90-0 deg, frame 510 to 570
zw: 0-90 deg, frame 120 to 210: 90-0 deg, frame 240 to 300
xv: 0-90 deg, frame 345 to 435: 90-0 deg, frame 465 to 525
yv: 0-90 deg, frame 435 to 525: 90-0 deg, frame 555 to 615
zv: 0-90 deg, frame 255 to 345: 90-0 deg, frame 375 to 435
wv: 0-90 deg, frame 165 to 255: 90-0 deg, frame 285 to 345
The last thing I need to tell you is that in all of these rotations, I've tried to smooth them out by having them start rotating very slowly, then speed up to a maximum rotation speed at the mid-point of the rotation, then slow back down to barely moving. If you need that level of accuracy, I'll give you the formulas I used to calculate this.
Good luck, and I can't wait to see what you come up with! Also, I was very impressed when I took a look at your website. At some future point I'd like to talk to you about how to generate the 24, 120, and 600-cells.
BClaw wrote:Pat? I thought I emailed you a copy of the rotations...
BClaw wrote:Good luck, and I can't wait to see what you come up with! Also, I was very impressed when I took a look at your website. At some future point I'd like to talk to you about how to generate the 24, 120, and 600-cells.
pat wrote:
Thank you for the compliments. And, here's the first animations I've come up with given your rotations.
4-cube 1
4-cube 2
I haven't put much time into making the cube look too pretty. Right now, it is just colored based upon location on the unrotated cube. The red channel varies with the y-coordinate. The green channel varies with the z-coordinate. The blue channel varies with the w-coordinate.
I may try to explode your animation into frames a make a composite animation of one of these. I think seeing the wireframe flattened version could really help in understanding my version.
pat wrote:There is now also an animation corresponding to your '5 cube 2' rotations:
5-cube 2
Unfortunately, it's a very sizeable file and is already overcompressed. Argle.
I updated my raytracer page a slight bit, too, to include these animations and a couple of other sneak-peeks at the upcoming version.
BClaw wrote:Oh, and the 5D cube is *very cool*!!!
BClaw wrote:Let me know if it works for you!
pat wrote:Glomar-Coordinate Animation
BClaw wrote:You could do the same thing with 4 spheres on a hypersphere! One each for xyz, xyw, xzw, and yzw!
pat wrote:BClaw wrote:You could do the same thing with 4 spheres on a hypersphere! One each for xyz, xyw, xzw, and yzw!
That is a great idea... hope you don't mind: Axial Spherinders
BClaw wrote:I really like how you've made each of the four axial spherinders a little different in size, so you can *really* see what is going on!
BClaw wrote:I did it! Thanks to some help on the coordinates from the folks at Polytopia on Yahoo. I'm so excited!
Users browsing this forum: No registered users and 19 guests