发射弹丸以击中移动目标时如何计算极角？

Question

我是 java 的初学者，正在为这个问题而苦苦挣扎。这是假设射弹的发射点是 (0,0) 并且它会一直保持相同的速度。

现在，这就是我所拥有的：

public static void main( String[] args )
{
    // Testing data
     System.out.println(calculateShotAngle(5, 0, 1, 0, 2));
     System.out.println(calculateShotAngle(0, 5, 0, 1, 2));
     System.out.println(calculateShotAngle(0, -5, 0, -1, 2));
     System.out.println(calculateShotAngle(5, 5, 1, 1, 2));
     System.out.println(calculateShotAngle(5, -5, 1, -1, 2));
     System.out.println(calculateShotAngle(-5, 5, -1, 1, 2));
     System.out.println(calculateShotAngle(-5, -5, -1, -1, 2));
     System.out.println(calculateShotAngle(5, 0, 1, 1, 2));
     System.out.println(calculateShotAngle(-5, 0, 0, -1, 2));
     System.out.println(calculateShotAngle(0, 5, 1, 0, 2));
}
public static float calculateShotAngle(float xPosition, float yPosition, float xVelocity,                  
float yVelocity, float projectileSpeed) 
{
    // Find the distance to the target
    float distance = (float) Math.sqrt(Math.pow(xPosition, 2) + Math.pow(yPosition, 2));

    // Find the time it takes to reach target
    float t = distance / projectileSpeed;

    // Find the position of the target when the projectile reaches it
    float xTarget = (xPosition + xVelocity * t);
    float yTarget = (yPosition + yVelocity * t);

    // Calculate the angle
    float angle = (float) Math.atan2(yTarget - yPosition, xTarget - xPosition);


    return angle;
}

这些是返回的值：

0.0 1.5707964 -1.5707964 0.7853982 -0.7853982 2.3561945 -2.3561945 0.7853982 -1.5707964 0.0

这些是我应该得到的值：

0.00000000 1.57079633 -1.57079633 0.78539816 -0.78539816 2.35619449 0.78539816 0.54041950 -2.60117315 1.03037683

如有任何帮助，我将不胜感激。

Answer 1

你有耦合方程，其解保证命中：

x0 + vx * t = V cos(alpha) t; y0 + vy * t = V sin(alpha) t;

要求解系统，可以将两个方程都提高到 2 的幂并将它们相加。然后，找到 t 和角度。看代码：

public static float calculateShotAngle(float xPosition, float yPosition, float xVelocity,
                                       float yVelocity, float projectileSpeed)
{
    float a = xVelocity * xVelocity + yVelocity * yVelocity - projectileSpeed * projectileSpeed;
    float b = 2 * (xPosition * xVelocity + yPosition * yVelocity);
    float c = xPosition * xPosition + yPosition * yPosition;
    float t = solveQuadraticEquation(a, b, c);
    float tan = (yPosition + yVelocity * t) / (xPosition + xVelocity * t);
    return (float) Math.atan(tan);
}

public static float solveQuadraticEquation(float a, float b, float c) throws ArithmeticException{
    float disc = b * b - 4 * a * c;
    if(disc < 0){
        throw new ArithmeticException("Complex roots!");
    }
    float root1 = (float)(- b + Math.sqrt(disc)) / (2 * a);
    float root2 = (float)(- b - Math.sqrt(disc)) / (2 * a);
    return (root1 >= 0) ? root1 : root2;
}