Question

我有一个有趣的数学问题，我无法弄清楚。

我正在建造一个用于安装磨损的表盘，需要根据时间计算出手的旋转角度。

通常情况下这很简单，但这里是踢球者：手不是时钟的核心。让我们说我的钟面尺寸为10,10 我的分针支点位于6,6（左下角为0,0），我的时针位于4,4。

如何在任何给定的分钟内计算出角度，使得该点始终指向正确的分钟？

由于

Answer 1

好的，在Nico的帮助下，我已经设法做出调整并得到一个有效的例子。

需要纳入的主要变化是改变输入的顺序以进行atan计算以及进行调整，因为android坚持将坐标系统颠倒过来。

请参阅下面的代码。

        //minutes hand rotation calculation
        int minute = mCalendar.get(Calendar.MINUTE);

        float minutePivotX = mCenterX+minuteOffsetX;
        //because of flipped coord system we take the y remainder of the full width instead
        float minutePivotY = mWidth - mCenterY - minuteOffsetY;

        //calculate target position
        double minuteTargetX = mCenterX + mRadius * Math.cos(ConvertToRadians(minute * 6));
        double minuteTargetY = mCenterY + mRadius * Math.sin(ConvertToRadians(minute * 6));

        //calculate the direction vector from the hand's pivot to the target
        double minuteDirectionX = minuteTargetX - minutePivotX;
        double minuteDirectionY = minuteTargetY - minutePivotY;

        //calculate the angle
        float minutesRotation = (float)Math.atan2(minuteDirectionY,minuteDirectionX );
        minutesRotation = (float)(minutesRotation * 360 / (2 * Math.PI));

        //do this because of flipped coord system
        minutesRotation = minutesRotation-180;

        //if less than 0 add 360 so the rotation is clockwise
        if (minutesRotation < 0)
        {
            minutesRotation = (minutesRotation+360);
        }


        //hours rotation calculations
        float hour = mCalendar.get(Calendar.HOUR);
        float minutePercentOfHour = (minute/60.0f);
        hour = hour+minutePercentOfHour;

        float hourPivotX = mCenterX+hourOffsetX;
        //because of flipped coord system we take the y remainder of the full width instead
        float hourPivotY = mWidth - mCenterY - hourOffsetY;

        //calculate target position
        double hourTargetX = mCenterX + mRadius * Math.cos(ConvertToRadians(hour * 30));
        double hourTargetY = mCenterY + mRadius * Math.sin(ConvertToRadians(hour * 30));

        //calculate the direction vector from the hand's pivot to the target
        double hourDirectionX = hourTargetX - hourPivotX;
        double hourDirectionY = hourTargetY - hourPivotY;

        //calculate the angle
        float hoursRotation = (float)Math.atan2(hourDirectionY,hourDirectionX );
        hoursRotation = (float)(hoursRotation * 360 / (2 * Math.PI));

        //do this because of flipped coord system
        hoursRotation = hoursRotation-180;

        //if less than 0 add 360 so the rotation is clockwise
        if (hoursRotation < 0)
        {
            hoursRotation = (hoursRotation+360);
        }

这还包括一个小辅助函数：

public double ConvertToRadians(double angle)
{
    return (Math.PI / 180) * angle;
}

感谢您的帮助

Answer 2

只需根据方向向量计算角度。

首先，计算目标位置。对于分针，这可能是：

targetX = radius * sin(2 * Pi / 60 * minutes)
targetY = radius * cos(2 * Pi / 60 * minutes)

然后计算从手的枢轴到目标的方向向量：

directionX = targetX - pivotX
directionY = targetY - pivotY

计算角度：

angle = atan2(directionX, directionY)

偏移时钟手角度计算

2 个答案: