 # JS version of multi-line time step function

Apr 15th, 2021 (edited)
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1. // points: array of {x, y}
2. // position: relative position within the line, between 0 and 1
3. // speeding_distance: distance required to go from no speed to max and vice-versa
4. function compute_point (points, position, speeding_distance) {
5.   "use strict";
6.   let count = points.length;
7.   if (!count) return {x: 0, y: 0};
8.   if (!-- count) return points;
9.   if (position <= 0) return points;
10.   if (position >= 1) return points[count];
11.   if (speeding_distance < 0.01) speeding_distance = 0.01;
12.   let acceleration = 4 / speeding_distance;
13.   let p, segment_length = [];
14.   for (p = 0; p < count; p ++)
15.     segment_length[p] = Math.sqrt((points[p + 1].x - points[p].x) * (points[p + 1].x - points[p].x) +
16.                                   (points[p + 1].y - points[p].y) * (points[p + 1].y - points[p].y));
17.   let corner_speed = ;
18.   corner_speed[count] = 0;
19.   // speed at each corner: 1 - cos(angle). Easy to calculate using a dot product, without any actual trigonometry.
20.   for (p = 1; p < count; p ++)
21.     corner_speed[p] = 1 - ((points[p + 1].x - points[p].x) * (points[p - 1].x - points[p].x) +
22.                            (points[p + 1].y - points[p].y) * (points[p - 1].y - points[p].y)) /
23.                           (segment_length[p] * segment_length[p - 1]);
24.   let segment_time = [], segment_type = [], total_time = 0;
25.   let initial, final, peak, time, length; // work with local variables for simplicity
26.   for (p = 0; p < count; p ++) {
27.     initial = corner_speed[p];
28.     final = corner_speed[p + 1];
29.     length = segment_length[p];
30.     peak = Math.sqrt((initial * initial + final * final) / 2 + length * acceleration);
31.     if (peak >= 2) {
32.       // speed capped at 2; the peak value is just a calculation aid now
33.       segment_type[p] = 0;
34.       time = (peak * peak - 2 * (initial + final) + 4) / (acceleration * 2);
35.     } else if ((peak >= initial) && (peak >= final)) {
36.       segment_type[p] = 1;
37.       time = (peak * 2 - initial - final) / acceleration;
38.     } else if (initial <= final) {
39.       // not enough distance to reach the final speed, so we lower it
40.       segment_type[p] = 2;
41.       final = Math.sqrt(initial * initial + 2 * acceleration * length);
42.       corner_speed[p + 1] = final;
43.       time = length * 2 / (initial + final);
44.     } else {
45.       // not enough distance to stop this time, but we must stop faster or we'll overrun the segment
46.       segment_type[p] = 3;
47.       time = length * 2 / (initial + final); // same as above
48.     }
49.     segment_time[p] = time;
50.     total_time += time;
51.   }
52.   position *= total_time;
53.   for (p = 0; (p < count) && (segment_time[p] <= position); position -= segment_time[p ++]);
54.   let type = 4;
55.   if (p < count) {
56.     initial = corner_speed[p];
57.     final = corner_speed[p + 1];
58.     time = segment_time[p];
59.     length = segment_length[p];
60.     type = segment_type[p];
61.     position /= time;
62.   }
63.   let first_split, second_split;
64.   switch (type) {
65.     case 0:
66.       // two splits: when peak speed is reached and when slowdown begins
67.       first_split = (2 - initial) / acceleration;
68.       second_split = time - (2 - final) / acceleration;
69.       break;
70.     case 1:
71.       // only one split
72.       first_split = ((final - initial) / acceleration + time) / 2;
73.       second_split = first_split;
74.       break;
75.     case 2:
76.       // no splits (the split would come after the end point); assign an arbitrary large value
77.       first_split = time * 16;
78.       second_split = first_split;
79.       break;
80.     case 3:
81.       // uses a different formula, so compute the position directly (and avoid recomputing later)
82.       position *= (2 * initial + position * (final - initial)) / (initial + final);
83.       break;
84.     default:
85.       // only possible if position >= 1 due to rounding errors; just stay at the line's end point
86.       return points[count];
87.   }
88.   if (type < 3)
89.     if (position <= (first_split / time))
90.       position *= time * (initial + time * position * acceleration / 2) / length;
91.     else if (position >= (second_split / time))
92.       position = 1 + (position - 1) * time * (final - time * acceleration * (position - 1) / 2) / length;
93.     else
94.       position = (2 * (time * position - first_split) + (4 - initial * initial) / (2 * acceleration)) / length;
95.   return {
96.     x: Math.round(points[p].x * (1 - position) + points[p + 1].x * position),
97.     y: Math.round(points[p].y * (1 - position) + points[p + 1].y * position)
98.   };
99. }
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