MathUtilities.cs

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

public static class MathUtilities{
    public static Vector2[] LineBoxIntersect(Vector2 point1, Vector2 point2, Rect rect) {
        List<Vector2> intersect = new List<Vector2>(); //if this is ever greater than length 2 we have encountered a black hole
        //order is clockwise from bottom left -> left edge, top edge, right edge, bottom edge
        Vector2[] rectP1 = {
            new Vector2(rect.xMin, rect.yMin), //bottom left
            new Vector2(rect.xMin, rect.yMax), //top left
            new Vector2(rect.xMax, rect.yMax), //top right
            new Vector2(rect.xMax, rect.yMin) // bottom right
        };
        Vector2[] rectP2 = {
            new Vector2(rect.xMin, rect.yMax), //top left
            new Vector2(rect.xMax, rect.yMax), //top right
            new Vector2(rect.xMax, rect.yMin), //bottom right
            new Vector2(rect.xMin, rect.yMin)  //bottom left
        };
        for (int i = 0; i < 4; i++) {
            Vector2 test;
            if (LineIntersect(point1, point2, rectP1[i], rectP2[i], out test)) {
                intersect.Add(test);
            }
        }
        return intersect.ToArray();
    }
    public static bool LineIntersect(Vector2 a0, Vector2 a1, Vector2 b0, Vector2 b1, out Vector2 intersectionPoint) {
        intersectionPoint = Vector2.zero;
        if (a0 == b0 || a0 == b1 || a1 == b0 || a1 == b1)
            return false;
        float x1 = a0.x;
        float y1 = a0.y;
        float x2 = a1.x;
        float y2 = a1.y;
        float x3 = b0.x;
        float y3 = b0.y;
        float x4 = b1.x;
        float y4 = b1.y;
        //AABB early exit
        if (Mathf.Max(x1, x2) < Mathf.Min(x3, x4) || Mathf.Max(x3, x4) < Mathf.Min(x1, x2))
            return false;
        if (Mathf.Max(y1, y2) < Mathf.Min(y3, y4) || Mathf.Max(y3, y4) < Mathf.Min(y1, y2))
            return false;
        float ua = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3));
        float ub = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3));
        float denom = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1);
        if (Mathf.Abs(denom) < Mathf.Epsilon) {
            //Lines are too close to parallel to call
            return false;
        }
        ua /= denom;
        ub /= denom;
        if ((0 < ua) && (ua < 1) && (0 < ub) && (ub < 1)) {
            intersectionPoint.x = (x1 + ua * (x2 - x1));
            intersectionPoint.y = (y1 + ua * (y2 - y1));
            return true;
        }
        return false;
    }
    public static bool PointInRect(Vector2 point, Rect rect) {
        if(point.x > rect.min.x && 
            point.x < rect.max.x && 
            point.y < rect.min.y && 
            point.y > rect.max.y) {
            return true;
        }else {
            return false;
        }
    }
    
    public static bool CircleLineCheck(Vector2 point1, Vector2 point2, Vector2 circleOrigin, float circleRadius) {
        Vector2 localPoint1 = point1 - circleOrigin;
        Vector2 localPoint2 = point2 - circleOrigin;
        Vector2 lineOffset = localPoint2 - localPoint1;
        float a = (lineOffset.x * lineOffset.x) + (lineOffset.y * lineOffset.y);
        float b = 2f * ((lineOffset.x * localPoint1.x) + (lineOffset.y * localPoint1.y));
        float c = (localPoint1.x * localPoint1.x) + (localPoint1.y * localPoint1.y) - (circleRadius * circleRadius);
        float disc = (b * b) - (4f * a * c);
        return (disc > 0f);
    }
    
    public static Vector2[] CircleLineCheckPoints(Vector2 point1, Vector2 point2, Vector2 circleOrigin, float circleRadius) {
        Vector2 localPoint1 = point1 - circleOrigin;
        Vector2 localPoint2 = point2 - circleOrigin;
        Vector2 lineOffset = localPoint2 - localPoint1;
        float a = (lineOffset.x * lineOffset.x) + (lineOffset.y * lineOffset.y);
        float b = 2f * ((lineOffset.x * localPoint1.x) + (lineOffset.y * localPoint1.y));
        float c = (localPoint1.x * localPoint1.x) + (localPoint1.y * localPoint1.y) - (circleRadius * circleRadius);
        float disc = (b * b) - (4f * a * c);
        if(disc > 0f) {
            Vector2[] points;
            disc = Mathf.Sqrt(disc);
            float t1 = (-b - disc) / (2 * a);
            float t2 = (-b + disc) / (2 * a);
            if (t1 >= 0 && t2 >= 0) {
                //total intersection, populate both points
                points = new Vector2[2];
                points[0] = point1 + ((point2 - point1) * t1);
                points[1] = point1 + ((point2 - point1) * t2);
            } else {
                //Only one intersected, populate one point
                points = new Vector2[1];
                if (t1 >= 0) {
                    points[0] = point1 + ((point2 - point1) * t1);
                } else if (t2 >= 0) {
                    points[0] = point1 + ((point2 - point1) * t2);
                }
            }
            return points;
        }else {
            //no intersections
            return null;
        }
    }
}