hellbound/Assets/Scripts/Core/Extensions/MathfHelper.cs

using UnityEngine;

public static class MathfHelper
{
    public static bool QuadraticSolver(float a, float b, float c, out float t1, out float t2)
    {
        float D = Mathf.Pow(b, 2f) - 4f * a * c;
        if (D > 0 || D == 0)
        {
            t1 = (-b + Mathf.Sqrt(D)) / (2 * a);
            t2 = (-b - Mathf.Sqrt(D)) / (2 * a);

            return true;
        }

        t1 = -1;
        t2 = -1;
        return false;
    }

    #region HaunterRegion

    public static Vector3 CalculateTargetPositionForCatchUp(Vector3 startTargetPosition, Vector3 targetMoveDirection,
        float targetMoveSpeed, Vector3 hauntingPoint, float haunterSpeed)
    {
        float time = TimeForCatchUpToThePoint(startTargetPosition, targetMoveDirection, targetMoveSpeed, hauntingPoint,
            haunterSpeed);
        return startTargetPosition + targetMoveDirection * (targetMoveSpeed * time);
        ;
    }

    public static Vector3 CalculateMoveDirectionForCatchUp(Vector3 startTargetPosition, Vector3 targetMoveDirection,
        float targetMoveSpeed, Vector3 hauntingPoint, float haunterSpeed)
    {
        return CalculateTargetPositionForCatchUp(startTargetPosition, targetMoveDirection, targetMoveSpeed,
            hauntingPoint,
            haunterSpeed) - hauntingPoint;
    }

    public static bool CanCatchUpToThePoint(Vector3 targetPosition, Vector3 targetMoveDirection, float targetMoveSpeed,
        Vector3 hauntingPoint, float haunterSpeed)
    {
        return CanCatchUpToThePoint(targetPosition, targetMoveDirection, targetMoveSpeed, hauntingPoint, haunterSpeed,
            out float time);
    }

    public static bool CanCatchUpToThePoint(Vector3 targetPosition, Vector3 targetMoveDirection, float targetMoveSpeed,
        Vector3 hauntingPoint, float haunterSpeed, out float time)
    {
        time = TimeForCatchUpToThePoint(targetPosition, targetMoveDirection, targetMoveSpeed, hauntingPoint,
            haunterSpeed);
        return time >= 0;
    }

    public static bool CanCatchUpToThePoint(Vector3 targetPosition, Vector3 targetMoveDirection,
        float targetMoveSpeed, Vector3 hauntingPoint, float haunterSpeed, out Vector3 hitPoint)
    {
        CanCatchUpToThePoint(targetPosition, targetMoveDirection, targetMoveSpeed, hauntingPoint, haunterSpeed,
            out float time);
        hitPoint = (targetPosition + targetMoveDirection.normalized * time);
        return time >= 0;
    }

    public static float TimeForCatchUpToThePoint(Vector3 startTargetPosition, Vector3 targetMoveDirection,
        float targetMoveSpeed, Vector3 hauntingPoint, float haunterSpeed)
    {
        Vector3 targetToHaunter = hauntingPoint - startTargetPosition;
        //  float d = targetToHaunter.magnitude;

        float a = haunterSpeed * haunterSpeed - targetMoveSpeed * targetMoveSpeed;
        float b = 2 * Vector3.Dot(targetToHaunter, targetMoveDirection * targetMoveSpeed);
        float c = -targetToHaunter.sqrMagnitude;

        float time;
        if (QuadraticSolver(a, b, c, out float t1, out float t2))
        {
            if (t1 < 0 && t2 < 0)
                return -1;

            if (t1 > 0 && t2 > 0)
                time = Mathf.Min(t1, t2);
            else
                time = Mathf.Max(t1, t2);
        }
        else
            return -1;

        return time;
    }

    #endregion

    #region NearestPoints
    
    public static Vector3 NearestPointInRay(Vector3 position, Vector3 origin, Vector3 direction) =>
        origin + direction * GetUForIntersectPoint(position, origin, direction);
    
    public static Vector3 NearestPointInLineSegment(Vector3 position, Vector3 startPoint, Vector3 endPoint)
    {
        Vector3 startToEnd = endPoint - startPoint;
        float u = GetUForIntersectPoint(position, startPoint, endPoint - startPoint);

        return u < 0 ? startPoint : u > 1 ? endPoint : startPoint + startToEnd * u;
    }
    
    public static bool HasPerpendicularToLine(Vector3 position, Vector3 startPoint, Vector3 endPoint)
    {
        return TryGetPerpendicularPointInLineFromPosition(position, startPoint, endPoint, out Vector3 result);
    }
    
    public static bool TryGetPerpendicularPointInLineFromPosition(Vector3 position, Vector3 startPoint, Vector3 endPoint, out Vector3 result)
    {
        Vector3 startToEnd = endPoint - startPoint;
        float u = GetUForIntersectPoint(position, startPoint, startToEnd);
        
        bool isHas = IsCorrectUForPerpendicular(u);
        result = isHas ? startPoint + startToEnd * u : Vector3.zero;
        return isHas;
    }
    
    private static float GetUForIntersectPoint(Vector3 position, Vector3 origin, Vector3 direction) => Vector3.Dot(position - origin, direction) / direction.sqrMagnitude;
    private static bool IsCorrectUForPerpendicular(float u) => u >= 0 && u <= 1;
    
    #endregion
}