When t is not one of those five values the radii may still move away from 1.
Here's some more calculated data from your new equations (t=0 left | t=pi/6 right):
- Code: Select all
u v t w x y z r | u v t w x y z r
-3.14 -3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | -3.14 -3.14 0.52 -0.87 0.00 0.00 0.50 1.00
-3.14 -2.62 0.00 -0.87 0.00 -0.50 0.00 1.00 | -3.14 -2.62 0.52 -0.75 0.00 -0.18 0.43 0.89
-3.14 -2.09 0.00 -0.50 0.00 -0.87 0.00 1.00 | -3.14 -2.09 0.52 -0.43 0.00 -0.32 0.25 0.59
-3.14 -1.57 0.00 0.00 0.00 -1.00 0.00 1.00 | -3.14 -1.57 0.52 0.00 0.00 -0.37 0.00 0.37
-3.14 -1.05 0.00 0.50 0.00 -0.87 0.00 1.00 | -3.14 -1.05 0.52 0.43 0.00 -0.32 -0.25 0.59
-3.14 -0.52 0.00 0.87 0.00 -0.50 0.00 1.00 | -3.14 -0.52 0.52 0.75 0.00 -0.18 -0.43 0.89
-3.14 0.00 0.00 1.00 0.00 0.00 0.00 1.00 | -3.14 0.00 0.52 0.87 0.00 0.00 -0.50 1.00
-3.14 0.52 0.00 0.87 0.00 0.50 0.00 1.00 | -3.14 0.52 0.52 0.75 0.00 0.18 -0.43 0.89
-3.14 1.05 0.00 0.50 0.00 0.87 0.00 1.00 | -3.14 1.05 0.52 0.43 0.00 0.32 -0.25 0.59
-3.14 1.57 0.00 0.00 0.00 1.00 0.00 1.00 | -3.14 1.57 0.52 0.00 0.00 0.37 0.00 0.37
-3.14 2.09 0.00 -0.50 0.00 0.87 0.00 1.00 | -3.14 2.09 0.52 -0.43 0.00 0.32 0.25 0.59
-3.14 2.62 0.00 -0.87 0.00 0.50 0.00 1.00 | -3.14 2.62 0.52 -0.75 0.00 0.18 0.43 0.89
-3.14 3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | -3.14 3.14 0.52 -0.87 0.00 0.00 0.50 1.00
----------------------------------------------------------------|-------------------------------------------------------------
u v t w x y z r | u v t w x y z r
0.00 -3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 0.00 -3.14 0.52 -1.37 0.00 0.00 0.00 1.37
0.00 -2.62 0.00 -0.87 0.00 0.00 -0.50 1.00 | 0.00 -2.62 0.52 -1.18 0.00 -0.25 -0.43 1.28
0.00 -2.09 0.00 -0.50 0.00 0.00 -0.87 1.00 | 0.00 -2.09 0.52 -0.68 0.00 -0.43 -0.75 1.10
0.00 -1.57 0.00 0.00 0.00 0.00 -1.00 1.00 | 0.00 -1.57 0.52 0.00 0.00 -0.50 -0.87 1.00
0.00 -1.05 0.00 0.50 0.00 0.00 -0.87 1.00 | 0.00 -1.05 0.52 0.68 0.00 -0.43 -0.75 1.10
0.00 -0.52 0.00 0.87 0.00 0.00 -0.50 1.00 | 0.00 -0.52 0.52 1.18 0.00 -0.25 -0.43 1.28
0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 | 0.00 0.00 0.52 1.37 0.00 0.00 0.00 1.37
0.00 0.52 0.00 0.87 0.00 0.00 0.50 1.00 | 0.00 0.52 0.52 1.18 0.00 0.25 0.43 1.28
0.00 1.05 0.00 0.50 0.00 0.00 0.87 1.00 | 0.00 1.05 0.52 0.68 0.00 0.43 0.75 1.10
0.00 1.57 0.00 0.00 0.00 0.00 1.00 1.00 | 0.00 1.57 0.52 0.00 0.00 0.50 0.87 1.00
0.00 2.09 0.00 -0.50 0.00 0.00 0.87 1.00 | 0.00 2.09 0.52 -0.68 0.00 0.43 0.75 1.10
0.00 2.62 0.00 -0.87 0.00 0.00 0.50 1.00 | 0.00 2.62 0.52 -1.18 0.00 0.25 0.43 1.28
0.00 3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 0.00 3.14 0.52 -1.37 0.00 0.00 0.00 1.37
----------------------------------------------------------------|-------------------------------------------------------------
u v t w x y z r | u v t w x y z r
0.52 -3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 0.52 -3.14 0.52 -1.35 0.00 0.00 -0.13 1.36
0.52 -2.62 0.00 -0.87 -0.06 -0.11 -0.48 1.00 | 0.52 -2.62 0.52 -1.17 -0.18 -0.31 -0.53 1.33
0.52 -2.09 0.00 -0.50 -0.11 -0.19 -0.84 1.00 | 0.52 -2.09 0.52 -0.67 -0.31 -0.54 -0.79 1.21
0.52 -1.57 0.00 0.00 -0.13 -0.22 -0.97 1.00 | 0.52 -1.57 0.52 0.00 -0.36 -0.63 -0.84 1.11
0.52 -1.05 0.00 0.50 -0.11 -0.19 -0.84 1.00 | 0.52 -1.05 0.52 0.67 -0.31 -0.54 -0.66 1.13
0.52 -0.52 0.00 0.87 -0.06 -0.11 -0.48 1.00 | 0.52 -0.52 0.52 1.17 -0.18 -0.31 -0.31 1.26
0.52 0.00 0.00 1.00 0.00 0.00 0.00 1.00 | 0.52 0.00 0.52 1.35 0.00 0.00 0.13 1.36
0.52 0.52 0.00 0.87 0.06 0.11 0.48 1.00 | 0.52 0.52 0.52 1.17 0.18 0.31 0.53 1.33
0.52 1.05 0.00 0.50 0.11 0.19 0.84 1.00 | 0.52 1.05 0.52 0.67 0.31 0.54 0.79 1.21
0.52 1.57 0.00 0.00 0.13 0.22 0.97 1.00 | 0.52 1.57 0.52 0.00 0.36 0.63 0.84 1.11
0.52 2.09 0.00 -0.50 0.11 0.19 0.84 1.00 | 0.52 2.09 0.52 -0.67 0.31 0.54 0.66 1.13
0.52 2.62 0.00 -0.87 0.06 0.11 0.48 1.00 | 0.52 2.62 0.52 -1.17 0.18 0.31 0.31 1.26
0.52 3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 0.52 3.14 0.52 -1.35 0.00 0.00 -0.13 1.36
----------------------------------------------------------------|-------------------------------------------------------------
u v t w x y z r | u v t w x y z r
1.05 -3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 1.05 -3.14 0.52 -1.30 0.00 0.00 -0.25 1.32
1.05 -2.62 0.00 -0.87 -0.22 -0.13 -0.43 1.00 | 1.05 -2.62 0.52 -1.13 -0.40 -0.23 -0.59 1.35
1.05 -2.09 0.00 -0.50 -0.38 -0.22 -0.75 1.00 | 1.05 -2.09 0.52 -0.65 -0.70 -0.40 -0.77 1.29
1.05 -1.57 0.00 0.00 -0.43 -0.25 -0.87 1.00 | 1.05 -1.57 0.52 0.00 -0.81 -0.47 -0.75 1.20
1.05 -1.05 0.00 0.50 -0.38 -0.22 -0.75 1.00 | 1.05 -1.05 0.52 0.65 -0.70 -0.40 -0.52 1.16
1.05 -0.52 0.00 0.87 -0.22 -0.13 -0.43 1.00 | 1.05 -0.52 0.52 1.13 -0.40 -0.23 -0.16 1.23
1.05 0.00 0.00 1.00 0.00 0.00 0.00 1.00 | 1.05 0.00 0.52 1.30 0.00 0.00 0.25 1.32
1.05 0.52 0.00 0.87 0.22 0.13 0.43 1.00 | 1.05 0.52 0.52 1.13 0.40 0.23 0.59 1.35
1.05 1.05 0.00 0.50 0.38 0.22 0.75 1.00 | 1.05 1.05 0.52 0.65 0.70 0.40 0.77 1.29
1.05 1.57 0.00 0.00 0.43 0.25 0.87 1.00 | 1.05 1.57 0.52 0.00 0.81 0.47 0.75 1.20
1.05 2.09 0.00 -0.50 0.38 0.22 0.75 1.00 | 1.05 2.09 0.52 -0.65 0.70 0.40 0.52 1.16
1.05 2.62 0.00 -0.87 0.22 0.13 0.43 1.00 | 1.05 2.62 0.52 -1.13 0.40 0.23 0.16 1.23
1.05 3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 1.05 3.14 0.52 -1.30 0.00 0.00 -0.25 1.32
----------------------------------------------------------------|-------------------------------------------------------------
u v t w x y z r | u v t w x y z r
1.57 -3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 1.57 -3.14 0.52 -1.22 0.00 0.00 -0.35 1.27
1.57 -2.62 0.00 -0.87 -0.35 0.00 -0.35 1.00 | 1.57 -2.62 0.52 -1.06 -0.56 0.00 -0.61 1.34
1.57 -2.09 0.00 -0.50 -0.61 0.00 -0.61 1.00 | 1.57 -2.09 0.52 -0.61 -0.96 0.00 -0.71 1.34
1.57 -1.57 0.00 0.00 -0.71 0.00 -0.71 1.00 | 1.57 -1.57 0.52 0.00 -1.11 0.00 -0.61 1.27
1.57 -1.05 0.00 0.50 -0.61 0.00 -0.61 1.00 | 1.57 -1.05 0.52 0.61 -0.96 0.00 -0.35 1.19
1.57 -0.52 0.00 0.87 -0.35 0.00 -0.35 1.00 | 1.57 -0.52 0.52 1.06 -0.56 0.00 0.00 1.19
1.57 0.00 0.00 1.00 0.00 0.00 0.00 1.00 | 1.57 0.00 0.52 1.22 0.00 0.00 0.35 1.27
1.57 0.52 0.00 0.87 0.35 0.00 0.35 1.00 | 1.57 0.52 0.52 1.06 0.56 0.00 0.61 1.34
1.57 1.05 0.00 0.50 0.61 0.00 0.61 1.00 | 1.57 1.05 0.52 0.61 0.96 0.00 0.71 1.34
1.57 1.57 0.00 0.00 0.71 0.00 0.71 1.00 | 1.57 1.57 0.52 0.00 1.11 0.00 0.61 1.27
1.57 2.09 0.00 -0.50 0.61 0.00 0.61 1.00 | 1.57 2.09 0.52 -0.61 0.96 0.00 0.35 1.19
1.57 2.62 0.00 -0.87 0.35 0.00 0.35 1.00 | 1.57 2.62 0.52 -1.06 0.56 0.00 0.00 1.19
1.57 3.14 0.00 -1.00 0.00 0.00 0.00 1.00 | 1.57 3.14 0.52 -1.22 0.00 0.00 -0.35 1.27
Hope that helps? If more example data will assist just let me know.