To find what the movements were, I created a spreadsheet which computed the ratio of X and Y to the length of the arc at every half of a degree. Therefore, if you know the circumference of the circle that arc you want is a segment of, then you can calculate how far you need to move X and Y for that half degree.
To use the chart I calculate the circumference of the circle (2r*pi) the arc is a segment of and divide it by 720 to get the length of each half degree of circumference. I then imagine a circle on the table, with angle 0* parallel with the Y axis, and find what angle relative to 0* I want to start the arc at. I'll first multiply the X ratio by the length of the half degree and move my X that amount. Then I multiply the Y ratio by the length of the half degree and move my Y that amount. I then step to the next half degree and repeat the process until I've reached the angle I want to finish my arc at.
As you probably noticed the chart doesn't tell you which direction to move, just the amount needed to move.
The spreadsheet I use:
Circle.xlsx
Angle | Ratio X | Ratio Y |
0 | ||
0.5 | 87 | 0 |
1 | 76.39 | 0.01 |
1.5 | 45.83 | 0.02 |
2 | 32.73 | 0.03 |
2.5 | 25.45 | 0.04 |
3 | 20.82 | 0.05 |
3.5 | 17.61 | 0.06 |
4 | 15.26 | 0.07 |
4.5 | 13.46 | 0.07 |
5 | 12.03 | 0.08 |
5.5 | 10.88 | 0.09 |
6 | 9.93 | 0.1 |
6.5 | 9.13 | 0.11 |
7 | 8.45 | 0.12 |
7.5 | 7.86 | 0.13 |
8 | 7.35 | 0.14 |
8.5 | 6.9 | 0.14 |
9 | 6.5 | 0.15 |
9.5 | 6.14 | 0.16 |
10 | 5.82 | 0.17 |
10.5 | 5.53 | 0.18 |
11 | 5.27 | 0.19 |
11.5 | 5.03 | 0.2 |
12 | 4.81 | 0.21 |
12.5 | 4.61 | 0.22 |
13 | 4.42 | 0.23 |
13.5 | 4.25 | 0.24 |
14 | 4.09 | 0.24 |
14.5 | 3.94 | 0.25 |
15 | 3.8 | 0.26 |
15.5 | 3.67 | 0.27 |
16 | 3.55 | 0.28 |
16.5 | 3.43 | 0.29 |
17 | 3.32 | 0.3 |
17.5 | 3.22 | 0.31 |
18 | 3.12 | 0.32 |
18.5 | 3.03 | 0.33 |
19 | 2.95 | 0.34 |
19.5 | 2.86 | 0.35 |
20 | 2.79 | 0.36 |
20.5 | 2.71 | 0.37 |
21 | 2.64 | 0.38 |
21.5 | 2.57 | 0.39 |
22 | 2.51 | 0.4 |
22.5 | 2.44 | 0.41 |
23 | 2.38 | 0.42 |
23.5 | 2.33 | 0.43 |
24 | 2.27 | 0.44 |
24.5 | 2.22 | 0.45 |
25 | 2.17 | 0.46 |
25.5 | 2.12 | 0.47 |
26 | 2.07 | 0.48 |
26.5 | 2.03 | 0.49 |
27 | 1.98 | 0.5 |
27.5 | 1.94 | 0.52 |
28 | 1.9 | 0.53 |
28.5 | 1.86 | 0.54 |
29 | 1.82 | 0.55 |
29.5 | 1.79 | 0.56 |
30 | 1.75 | 0.57 |
30.5 | 1.71 | 0.58 |
31 | 1.68 | 0.59 |
31.5 | 1.65 | 0.61 |
32 | 1.62 | 0.62 |
32.5 | 1.58 | 0.63 |
33 | 1.55 | 0.64 |
33.5 | 1.53 | 0.66 |
34 | 1.5 | 0.67 |
34.5 | 1.47 | 0.68 |
35 | 1.44 | 0.69 |
35.5 | 1.41 | 0.71 |
36 | 1.39 | 0.72 |
36.5 | 1.36 | 0.73 |
37 | 1.34 | 0.75 |
37.5 | 1.32 | 0.76 |
38 | 1.29 | 0.77 |
38.5 | 1.27 | 0.79 |
39 | 1.25 | 0.8 |
39.5 | 1.22 | 0.82 |
40 | 1.2 | 0.83 |
40.5 | 1.18 | 0.85 |
41 | 1.16 | 0.86 |
41.5 | 1.14 | 0.88 |
42 | 1.12 | 0.89 |
42.5 | 1.1 | 0.91 |
43 | 1.08 | 0.92 |
43.5 | 1.06 | 0.94 |
44 | 1.04 | 0.96 |
44.5 | 1.03 | 0.97 |
45 | 1.01 | 0.99 |
45.5 | 0.99 | 1.01 |
46 | 0.97 | 1.03 |
46.5 | 0.96 | 1.04 |
47 | 0.94 | 1.06 |
47.5 | 0.92 | 1.08 |
48 | 0.91 | 1.1 |
48.5 | 0.89 | 1.12 |
49 | 0.88 | 1.14 |
49.5 | 0.86 | 1.16 |
50 | 0.85 | 1.18 |
50.5 | 0.83 | 1.2 |
51 | 0.82 | 1.22 |
51.5 | 0.8 | 1.25 |
52 | 0.79 | 1.27 |
52.5 | 0.77 | 1.29 |
53 | 0.76 | 1.32 |
53.5 | 0.75 | 1.34 |
54 | 0.73 | 1.36 |
54.5 | 0.72 | 1.39 |
55 | 0.71 | 1.41 |
55.5 | 0.69 | 1.44 |
56 | 0.68 | 1.47 |
56.5 | 0.67 | 1.5 |
57 | 0.66 | 1.53 |
57.5 | 0.64 | 1.55 |
58 | 0.63 | 1.58 |
58.5 | 0.62 | 1.62 |
59 | 0.61 | 1.65 |
59.5 | 0.59 | 1.68 |
60 | 0.58 | 1.71 |
60.5 | 0.57 | 1.75 |
61 | 0.56 | 1.79 |
61.5 | 0.55 | 1.82 |
62 | 0.54 | 1.86 |
62.5 | 0.53 | 1.9 |
63 | 0.52 | 1.94 |
63.5 | 0.5 | 1.98 |
64 | 0.49 | 2.03 |
64.5 | 0.48 | 2.07 |
65 | 0.47 | 2.12 |
65.5 | 0.46 | 2.17 |
66 | 0.45 | 2.22 |
66.5 | 0.44 | 2.27 |
67 | 0.43 | 2.33 |
67.5 | 0.42 | 2.38 |
68 | 0.41 | 2.44 |
68.5 | 0.4 | 2.51 |
69 | 0.39 | 2.57 |
69.5 | 0.38 | 2.64 |
70 | 0.37 | 2.71 |
70.5 | 0.36 | 2.79 |
71 | 0.35 | 2.86 |
71.5 | 0.34 | 2.95 |
72 | 0.33 | 3.03 |
72.5 | 0.32 | 3.12 |
73 | 0.31 | 3.22 |
73.5 | 0.3 | 3.32 |
74 | 0.29 | 3.43 |
74.5 | 0.28 | 3.55 |
75 | 0.27 | 3.67 |
75.5 | 0.26 | 3.8 |
76 | 0.25 | 3.94 |
76.5 | 0.24 | 4.09 |
77 | 0.24 | 4.25 |
77.5 | 0.23 | 4.42 |
78 | 0.22 | 4.61 |
78.5 | 0.21 | 4.81 |
79 | 0.2 | 5.03 |
79.5 | 0.19 | 5.27 |
80 | 0.18 | 5.53 |
80.5 | 0.17 | 5.82 |
81 | 0.16 | 6.14 |
81.5 | 0.15 | 6.5 |
82 | 0.14 | 6.9 |
82.5 | 0.14 | 7.35 |
83 | 0.13 | 7.86 |
83.5 | 0.12 | 8.45 |
84 | 0.11 | 9.13 |
84.5 | 0.1 | 9.93 |
85 | 0.09 | 10.88 |
85.5 | 0.08 | 12.03 |
86 | 0.07 | 13.46 |
86.5 | 0.07 | 15.26 |
87 | 0.06 | 17.61 |
87.5 | 0.05 | 20.82 |
88 | 0.04 | 25.45 |
88.5 | 0.03 | 32.73 |
89 | 0.02 | 45.83 |
89.5 | 0.01 | 76.39 |
90 | 0 | 1 |