如何使用点积找出旋转角度

Question

我正在尝试使用 HTML 页面上的 mousemove 事件来旋转 DIV 元素。我想使用点积找到一个旋转角度。我知道也可以使用 Math.atan2，但我想在我的示例中使用点积。

到目前为止，我尝试实现以下公式：

cos(角度) = 点(a, b) / (长度(a) * 长度(b))

但是下面的实现效果不好。 可能是什么问题？

谢谢

代码笔： https://codepen.io/1rosehip/pen/qBrLYLo

const $box = document.getElementById('box');
const shapeRect = $box.getBoundingClientRect();

const shapeCenterX = shapeRect.x + shapeRect.width / 2;
const shapeCenterY = shapeRect.y + shapeRect.height / 2;

/**
 * get vector magnitude
 * @param {Array.<number>} v
 * @return {number}
 */
const length = v => {
  return Math.sqrt(v[0] ** 2 + v[1] ** 2);
};

/**
 * dot product
 * @param {Array.<number>} v1
 * @param {Array.<number>} v2
 * @return {number}
 */
const dot = (v1, v2) => {
  return v1[0] * v2[0] + v1[1] * v2[1];
};

/**
 * handle rotation
 */
document.addEventListener('mousemove', (evt) => {

  // vector #1 - shape center
  const centerVector = [shapeCenterX, shapeCenterY];
  const centerVectorLength = length(centerVector);

  // vector #2 - mouse position
  const mouseVector = [evt.pageX, evt.pageY];
  const mouseVectorLength = length(mouseVector);

  // cos(angle) = dot(a, b) / (length(a) * length(b))
  const radians = Math.acos(dot(centerVector, mouseVector) / (centerVectorLength * mouseVectorLength));
  
  const degrees = radians * (180 / Math.PI);
  const angle = (degrees + 360) % 360;

  $box.style.transform = `rotate(${degrees}deg)`;
});

#box{
  position: absolute;
  background: #111;
  left: 100px;
  top: 100px;
  width: 100px;
  height: 100px;
}

<div id="box"></div>

Answer 1

我找到了问题。

(1) 向量是从错误的原点（页面左上角而不是形状中心）定义的。

(2) Math.acos 返回范围 [0,pi] 而不是 [0,2*pi] 的结果。 当鼠标向左移动并经过形状中心时，它应该固定（360-度）。

固定版本的codepen： https://codepen.io/1rosehip/pen/JjWwaYE

const $box = document.getElementById('box');
const shapeRect = $box.getBoundingClientRect();

const shapeCenterX = shapeRect.x + shapeRect.width / 2;
const shapeCenterY = shapeRect.y + shapeRect.height / 2;

/**
 * get vector magnitude
 * @param {Array.<number>} v
 * @return {number}
 */
const length = v => {
  return Math.sqrt(v[0] ** 2 + v[1] ** 2);
};

/**
 * dot product
 * @param {Array.<number>} v1
 * @param {Array.<number>} v2
 * @return {number}
 */
const dot = (v1, v2) => {
  return v1[0] * v2[0] + v1[1] * v2[1];
};

/**
 * handle rotation
 */
document.addEventListener('mousemove', (evt) => {

  // vector #1 - shape center
  const centerVector = [evt.pageX - shapeCenterX, 0 - shapeCenterY];
  const centerVectorLength = length(centerVector);

  // vector #2 - mouse position
  const mouseVector = [evt.pageX - shapeCenterX, evt.pageY - shapeCenterY];
  const mouseVectorLength = length(mouseVector);

  // cos(angle) = dot(a, b) / (length(a) * length(b))
  const radians = Math.acos(dot(centerVector, mouseVector) / (centerVectorLength * mouseVectorLength));
  
  let degrees = radians * (180 / Math.PI);
  // const angle = (degrees + 360) % 360;
  
  if(evt.pageX < shapeCenterX){
     degrees = 360 - degrees;
  }

  $box.style.transform = `rotate(${degrees}deg)`;
});

#box{
  position: absolute;
  background: #111;
  left: 100px;
  top: 100px;
  width: 100px;
  height: 100px;
}

<div id="box"></div>