如何根据中心单元旋转对象

时间:2016-01-19 13:44:20

标签: javascript

我有一个网格,我在其中放置一个对象,我想围绕一个固定的单元格(cell3)旋转。该对象包含坐标,如:

activeObject = {
    coords: {
        cell1: {
             x: 0,
             y: 0
        },
        cell2: {
             x: 1,
             y: 1
        },
        cell3: {
             x: 2,
             y: 2
        },
        cell4: {
             x: 2,
             y: 3
        },
        cell5: {
             x: 3,
             y: 3
        },
    }
}

输出:

我想围绕cell3旋转此对象,例如使用x:2,y:2,不使用某种(基本)三角函数对每个单元格位置进行硬编码。我意识到我必须检查每个细胞与细胞3的距离以及方向。但是我不知道如何进行计算,因为我对三角学不太了解。新的活动对象将是:

activeObject = {
    coords: {
        cell1: {
             x: 4,
             y: 0
        },
        cell2: {
             x: 4,
             y: 1
        },
        cell3: {
             x: 2,
             y: 2
        },
        cell4: {
             x: 1,
             y: 2
        },
        cell5: {
             x: 1,
             y: 3
        },
    }
}

输出:

enter image description here

1 个答案:

答案 0 :(得分:3)

一些基本想法

  • 如果枢轴不是原点,则必须对变换进行一些修正。
  • 如果点位于(1,2),则围绕原点旋转
    • 90°CW:变为(2,-1)
    • 90°CCW:变为(-2,1)
  • 点(x,y)的结论
    • 90°CW:变为(y,-x)
    • 90°CCW:变为(-y,x)
  • 至少应用枢轴修正

找到了一些数学here

function Point(x, y) {
    this.x = x;
    this.y = y;
}

Point.prototype.rotateCW = function (c) {
    // x' =  x cos phi + y sin phi \ formula with pivot at (0, 0)
    // y' = -x sin phi + y cos phi /
    // phi = 90°                   insert phi
    // cos 90° = 0   sin 90° = 1   calculate cos and sin 
    // x' =  y                     \ formula with pivot at (0, 0)
    // y' = -x                     /
    // x' =  (cy - y) + cx         \ formula with different pivot needs correction 
    // y' = -(cx - x) + cy         /
    // y' = -cx + x + cy          /
    return new Point(
        c.x + c.y - this.y,
        c.y - c.x + this.x
    );
}

Point.prototype.rotateCCW = function (c) {
    // source: https://en.wikipedia.org/wiki/Rotation_(mathematics)#Two_dimensions
    // x' =  x cos phi + y sin phi  \ formula with pivot at (0, 0)
    // y' = -x sin phi + y cos phi  /
    // phi = -90°
    // cos -90° = 0   sin -90° = -1
    // x' = -y                      \ formula with pivot at (0, 0)
    // y' =  x                      /
    // x' = -(cy - y) + cx          \ formula with different pivot needs correction 
    // x' = -cy + y + cx            /
    // y' =  (cx - x) + cy         /
    return new Point(
        c.x - c.y + this.y,
        c.y + c.x - this.x
    );
}

var activeObject = {
        coords: {
            cell1: new Point(0, 0),
            cell2: new Point(1, 1),
            cell3: new Point(2, 2),
            cell4: new Point(2, 3),
            cell5: new Point(3, 3),
        }
    },
    pivot = new Point(2, 2),
    rotated = { coords: {} };

Object.keys(activeObject.coords).forEach(function (k) {
    rotated.coords[k] = activeObject.coords[k].rotateCW(pivot);
});

document.write('<pre>' + JSON.stringify(rotated, 0, 4) + '</pre>');