Aetheria/Assets/Plugins/Celestial Body/Scripts/Script Utilities/MathUtility.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public static class MathUtility {
    public static bool RaySphere (Vector3 centre, float radius, Vector3 rayOrigin, Vector3 rayDir, out Vector3 intersectionPoint) {
        // See: http://viclw17.github.io/2018/07/16/raytracing-ray-sphere-intersection/
        Vector3 offset = rayOrigin - centre;
        float a = Vector3.Dot (rayDir, rayDir); // sqr ray length (in case of non-normalized rayDir)
        float b = 2 * Vector3.Dot (offset, rayDir);
        float c = Vector3.Dot (offset, offset) - radius * radius;
        float discriminant = b * b - 4 * a * c;

        // No intersections: discriminant < 0
        // 1 intersection: discriminant == 0
        // 2 intersections: discriminant > 0
        if (discriminant >= 0) {
            float t = (-b - Mathf.Sqrt (discriminant)) / (2 * a);
            //float t2 = (-b + Mathf.Sqrt (discriminant)) / (2 * a); // The further away intersection point

            // If t is negative, the intersection was in negative ray direction so ignore it
            if (t >= 0) {
                intersectionPoint = rayOrigin + rayDir * t;
                return true;
            }
        }

        intersectionPoint = Vector3.zero;
        return false;
    }

    public static bool LineSegmentsIntersect (Vector2 a1, Vector2 a2, Vector2 b1, Vector2 b2) {
        float d = (b2.x - b1.x) * (a1.y - a2.y) - (a1.x - a2.x) * (b2.y - b1.y);
        if (d == 0)
            return false;
        float t = ((b1.y - b2.y) * (a1.x - b1.x) + (b2.x - b1.x) * (a1.y - b1.y)) / d;
        float u = ((a1.y - a2.y) * (a1.x - b1.x) + (a2.x - a1.x) * (a1.y - b1.y)) / d;

        return t >= 0 && t <= 1 && u >= 0 && u <= 1;
    }

    public static bool LinesIntersect (Vector2 a1, Vector2 a2, Vector2 a3, Vector2 a4) {
        return (a1.x - a2.x) * (a3.y - a4.y) - (a1.y - a2.y) * (a3.x - a4.x) != 0;
    }

    public static Vector2 PointOfLineLineIntersection (Vector2 a1, Vector2 a2, Vector2 a3, Vector2 a4) {
        float d = (a1.x - a2.x) * (a3.y - a4.y) - (a1.y - a2.y) * (a3.x - a4.x);
        if (d == 0) {
            Debug.LogError ("Lines are parallel, please check that this is not the case before calling line intersection method");
            return Vector2.zero;
        } else {
            float n = (a1.x - a3.x) * (a3.y - a4.y) - (a1.y - a3.y) * (a3.x - a4.x);
            float t = n / d;
            return a1 + (a2 - a1) * t;
        }
    }

    public static Vector2 ClosestPointOnLineSegment (Vector2 p, Vector2 a, Vector2 b) {
        Vector2 aB = b - a;
        Vector2 aP = p - a;
        float sqrLenAB = aB.sqrMagnitude;

        if (sqrLenAB == 0)
            return a;

        float t = Mathf.Clamp01 (Vector2.Dot (aP, aB) / sqrLenAB);
        return a + aB * t;
    }

    public static Vector3 ClosestPointOnLineSegment (Vector3 p, Vector3 a, Vector3 b) {
        Vector3 aB = b - a;
        Vector3 aP = p - a;
        float sqrLenAB = aB.sqrMagnitude;

        if (sqrLenAB == 0)
            return a;

        float t = Mathf.Clamp01 (Vector3.Dot (aP, aB) / sqrLenAB);
        return a + aB * t;
    }

    public static int SideOfLine (Vector2 a, Vector2 b, Vector2 c) {
        return (int) Mathf.Sign ((c.x - a.x) * (-b.y + a.y) + (c.y - a.y) * (b.x - a.x));
    }

    /// returns the smallest angle between ABC. Never greater than 180
    public static float MinAngle (Vector3 a, Vector3 b, Vector3 c) {
        return Vector3.Angle ((a - b), (c - b));
    }

    public static bool PointInTriangle (Vector2 a, Vector2 b, Vector2 c, Vector2 p) {
        float area = 0.5f * (-b.y * c.x + a.y * (-b.x + c.x) + a.x * (b.y - c.y) + b.x * c.y);
        float s = 1 / (2 * area) * (a.y * c.x - a.x * c.y + (c.y - a.y) * p.x + (a.x - c.x) * p.y);
        float t = 1 / (2 * area) * (a.x * b.y - a.y * b.x + (a.y - b.y) * p.x + (b.x - a.x) * p.y);
        return s >= 0 && t >= 0 && (s + t) <= 1;
    }

    public static bool PointsAreClockwise (Vector2[] points) {
        float signedArea = 0;
        for (int i = 0; i < points.Length; i++) {
            int nextIndex = (i + 1) % points.Length;
            signedArea += (points[nextIndex].x - points[i].x) * (points[nextIndex].y + points[i].y);
        }

        return signedArea >= 0;
    }

    public static Vector2 V3ToXZ (Vector3 v3) {
        return new Vector2 (v3.x, v3.z);
    }

    public static Vector3 V2ToXYZ (Vector2 v2, float yValue) {
        return new Vector3 (v2.x, yValue, v2.y);
    }

}