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[C#, Unity3D] Quickly find the closest point on an ellipse centered on the origin.
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| using UnityEngine; | |
| using Math = System.Math; | |
| public static class NearestPointTo | |
| { | |
| /// <summary> | |
| /// Find the closest point on an ellipse centered on the origin. | |
| /// </summary> | |
| /// Credit: | |
| /// 2015-09 Original Paper by Luc. Maisonobe https://www.spaceroots.org/documents/distance/distance-to-ellipse.pdf | |
| /// 2017-08-27 Python Code by Carl Chatfield https://wet-robots.ghost.io/simple-method-for-distance-to-ellipse/ | |
| /// 2017-11-10 Trig-Free Optimization by Adrian Stephens https://github.com/0xfaded/ellipse_demo/issues/1 | |
| /// 2018-07-12 C# Code for Unity3D by Johannes Peter <this gist> | |
| public static Vector2 Ellipse(Vector2 point, double semiMajor, double semiMinor) | |
| { | |
| double px = Math.Abs(point.x); | |
| double py = Math.Abs(point.y); | |
| double tx = Math.PI / 4; | |
| double ty = Math.PI / 4; | |
| double x, y, ex, ey, rx, ry, qx, qy, r, q, t = 0; | |
| for (int i = 0; i < 3; ++i) | |
| { | |
| x = semiMajor * tx; | |
| y = semiMinor * ty; | |
| ex = (semiMajor * semiMajor - semiMinor * semiMinor) * (tx * tx * tx) / semiMajor; | |
| ey = (semiMinor * semiMinor - semiMajor * semiMajor) * (ty * ty * ty) / semiMinor; | |
| rx = x - ex; | |
| ry = y - ey; | |
| qx = px - ex; | |
| qy = py - ey; | |
| r = Math.Sqrt(rx * rx + ry * ry); | |
| q = Math.Sqrt(qy * qy + qx * qx); | |
| tx = (qx * r / q + ex) / semiMajor; | |
| ty = (qy * r / q + ey) / semiMinor; | |
| t = Math.Sqrt(tx * tx + ty * ty); | |
| tx /= t; | |
| ty /= t; | |
| } | |
| return new Vector2 | |
| { | |
| x = (float)(semiMajor * (point.x < 0 ? -tx : tx)), | |
| y = (float)(semiMinor * (point.y < 0 ? -ty : ty)) | |
| }; | |
| } | |
| } |
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