如何檢查旋轉對象的平移點碰撞？

Question

我在WindowsForm上有兩個矩形，我想檢查它們是否碰撞。 對於簡單的非旋轉碰撞，它看起來像這樣：

Point newLocation; // upper-left corner of the object to check its collision
Size objectSize; // the object size
bool collision = false;

foreach (Object otherObject in otherObjects)
{
    if (newLocation.X >= otherObject.location.X && newLocation.X <= otherObject.location.X + otherObject.size.width)
        if (newLocation.Y >= otherObject.location.Y && newLocation.Y <= otherObject.location.Y + otherObject.size.height)
        {
            collision = true;
            break;
        }
}

但是現在我旋轉了兩個對象：

Matrix matrix = new Matrix();
matrix.RotateAt(angle, newLocation);
graphics.Transform = matrix;

如何檢查旋轉矩陣處的碰撞？ 我能以某種方式獲得平移的X，Y坐標嗎？

Answer 1

我有一些代碼可以將點從標准坐標系轉移到特定坐標系（但是在您的情況下，Y增加了屏幕上的顏色，因此進行了一些調整和注釋）。

在這里，double []代表一個點，其中索引0為X坐標，索引1為Y。請注意，新坐標系的角度是逆時針並以弧度為單位。 （乘以Pi / 180將度數轉換為弧度）。

    /// <summary>
    /// Implemented - Returns the point coordinates related to a new coordinate system
    /// Does not change original point
    /// </summary>
    /// <param name="Point">Point to be returned in new coordinate system</param>
    /// <param name="NewSystemCouterClockRotation">CounterClokWise Angle of rotation of the new coordinate system compared to the current, measured in radians</param>
    /// <param name="NewSystemOrigin">Location of the new origin point in the current coordinate system</param>
    /// <returns></returns>
    public double[] ChangeCoordinateSystem(double[] Point, double NewSystemCouterClockRotation, double[] NewSystemOrigin)
    {

        //first adjust: fix that winform downwards increasing Y before applying the method
        Point[1] = -Point[1];
        NewSystemOrigin[1] = -NewSystemOrigin[1]

        //end of first adjust


        //original method
        double[] Displacement = new double[2] { Point[0] - NewSystemOrigin[0], Point[1] - NewSystemOrigin[1] };


        double[] Result = new double[2]
        {
            + Displacement[0] * Math.Cos(NewSystemCouterClockRotation) + Displacement[1] * Math.Sin(NewSystemCouterClockRotation), 
            - Displacement[0] * Math.Sin(NewSystemCouterClockRotation) + Displacement[1] * Math.Cos(NewSystemCouterClockRotation) 
        }; 

        //second adjust: reset Y of the result
        Result[1] = - Result[1];

        return Result;
    }

但是，如果您的兩個對象的角度不同，則應當心，最好的方法是檢查all four corners of the first一個矩形中第一個矩形的all four corners of the first是否不在另一個對象內， the other object four corners是否不在the other object four corners內里面也一樣。

可以在此處找到一些算法來找出點是否在多邊形內： 點在多邊形中