| | | 1 | | using UnityEngine; |
| | | 2 | | |
| | | 3 | | // Utility functions for 2D coordinates. |
| | | 4 | | // In Cartesian coordinates, the x-axis points right, and the y-axis points up. The coordinates are |
| | | 5 | | // given by (x, y). |
| | | 6 | | // In polar coordinates, the angle is measured in degrees from the x-axis counterclockwise to the |
| | | 7 | | // y-axis. The coordinates are given by (r, theta). |
| | | 8 | | public class Coordinates2 { |
| | 3 | 9 | | public static Vector2 ConvertCartesianToPolar(in Vector2 cartesian) { |
| | 3 | 10 | | float r = cartesian.magnitude; |
| | 3 | 11 | | float theta = Mathf.Atan2(cartesian.y, cartesian.x) * Mathf.Rad2Deg; |
| | 3 | 12 | | return new Vector2(r, theta); |
| | 3 | 13 | | } |
| | 0 | 14 | | public static Vector2 ConvertCartesianToPolar(float x, float y) { |
| | 0 | 15 | | return ConvertCartesianToPolar(new Vector2(x, y)); |
| | 0 | 16 | | } |
| | | 17 | | |
| | 9 | 18 | | public static Vector2 ConvertPolarToCartesian(in Vector2 polar) { |
| | 9 | 19 | | float x = polar.x * Mathf.Cos(polar.y * Mathf.Deg2Rad); |
| | 9 | 20 | | float y = polar.x * Mathf.Sin(polar.y * Mathf.Deg2Rad); |
| | 9 | 21 | | return new Vector2(x, y); |
| | 9 | 22 | | } |
| | 0 | 23 | | public static Vector2 ConvertPolarToCartesian(float r, float theta) { |
| | 0 | 24 | | return ConvertPolarToCartesian(new Vector2(r, theta)); |
| | 0 | 25 | | } |
| | | 26 | | } |
| | | 27 | | |
| | | 28 | | // Utility functions for 3D coordinates. |
| | | 29 | | // In Cartesian coordinates, the x-axis points right, the y-axis points up, and the z-axis points |
| | | 30 | | // forward. The coordinates are given by (x, y, z). |
| | | 31 | | // In spherical coordinates, the azimuth is measured in degrees from the x-axis clockwise to the |
| | | 32 | | // z-axis, and elevation is measured in degrees from the x-z plane up to the y-axis. The coordinates |
| | | 33 | | // are given by (r, azimuth, elevation). |
| | | 34 | | public class Coordinates3 { |
| | | 35 | | public static Vector3 ConvertCartesianToSpherical(in Vector3 cartesian) { |
| | | 36 | | float r = cartesian.magnitude; |
| | | 37 | | float azimuth = Mathf.Atan2(cartesian.x, cartesian.z) * Mathf.Rad2Deg; |
| | | 38 | | float elevation = Mathf.Atan(cartesian.y / Mathf.Sqrt(cartesian.x * cartesian.x + |
| | | 39 | | cartesian.z * cartesian.z)) * |
| | | 40 | | Mathf.Rad2Deg; |
| | | 41 | | return new Vector3(r, azimuth, elevation); |
| | | 42 | | } |
| | | 43 | | public static Vector3 ConvertCartesianToSpherical(float x, float y, float z) { |
| | | 44 | | return ConvertCartesianToSpherical(new Vector3(x, y, z)); |
| | | 45 | | } |
| | | 46 | | |
| | | 47 | | public static Vector3 ConvertSphericalToCartesian(in Vector3 spherical) { |
| | | 48 | | float y = spherical.x * Mathf.Sin(spherical.z * Mathf.Deg2Rad); |
| | | 49 | | float x = spherical.x * Mathf.Cos(spherical.z * Mathf.Deg2Rad) * |
| | | 50 | | Mathf.Sin(spherical.y * Mathf.Deg2Rad); |
| | | 51 | | float z = spherical.x * Mathf.Cos(spherical.z * Mathf.Deg2Rad) * |
| | | 52 | | Mathf.Cos(spherical.y * Mathf.Deg2Rad); |
| | | 53 | | return new Vector3(x, y, z); |
| | | 54 | | } |
| | | 55 | | public static Vector3 ConvertSphericalToCartesian(float r, float azimuth, float elevation) { |
| | | 56 | | return ConvertSphericalToCartesian(new Vector3(r, azimuth, elevation)); |
| | | 57 | | } |
| | | 58 | | } |