Generating CSS 3D Mockups

// Original was CoffeeScript at https://codepen.io/fta/pen/ifnqH?editors=0010.
// This is ported back to plain JavaScript. It could be cleaned up!
{
  const $ = jQuery;

  function getTransform (from, to) {
    console.assert(from.length === to.length && to.length === 4);
      
    const A = []; // 8x8
    for (let i = 0; i < 4; i++) {
      A.push([from[i].x, from[i].y, 1, 0, 0, 0, -from[i].x * to[i].x, -from[i].y * to[i].x]);
      A.push([0, 0, 0, from[i].x, from[i].y, 1, -from[i].x * to[i].y, -from[i].y * to[i].y]);
    }
      
    const b = []; // 8x1
    for (let i = 0; i < 4; i++) {
      b.push(to[i].x);
      b.push(to[i].y);
    }
      
    // Solve A * h = b for h
    const h = numeric.solve(A, b);
    const H = [[h[0], h[1], 0, h[2]], [h[3], h[4], 0, h[5]], [0, 0, 1, 0], [h[6], h[7], 0, 1]];
      
// Sanity check that H actually maps `from` to `to`
    for (let i = 0; i < 4; i++) {
      const lhs = numeric.dot(H, [from[i].x, from[i].y, 0, 1]);
      const k_i = lhs[3];
      const rhs = numeric.dot(k_i, [to[i].x, to[i].y, 0, 1]);
      console.assert(numeric.norm2(numeric.sub(lhs, rhs)) < 1e-9, "Not equal:", lhs, rhs);
    }
      
    return H;
  };

   function applyTransform(element, originalPos, targetPos, callback) {    
    // All offsets were calculated relative to the document
    // Make them relative to (0, 0) of the element instead
    const from = (function() {
      const results = [];
      for (let k = 0, len = originalPos.length; k < len; k++) {
        const p = originalPos[k];
        results.push({
          x: p[0] - originalPos[0][0],
          y: p[1] - originalPos[0][1]
        });
      }
      return results;
    })();
       
    const to = (function() {
      const results = [];
      for (let k = 0, len = targetPos.length; k < len; k++) {
        const p = targetPos[k];
        results.push({
          x: p[0] - originalPos[0][0],
          y: p[1] - originalPos[0][1]
        });
      }
      return results;
    })();
       
    // Solve for the transform
    const H = getTransform(from, to);
    
    // Apply the matrix3d as H transposed because matrix3d is column major order
    // Also need use toFixed because css doesn't allow scientific notation
    $(element).css({
      'transform': `matrix3d(${((function() {
        const results = [];
        for (let i = 0; i < 4; i++) {
          results.push((function() {
            const results1 = [];
            for (let j = 0; j < 4; j++) {
              results1.push(H[j][i].toFixed(20));
            }
            return results1;
          })());
        }
        return results;
      })()).join(',')})`,
      'transform-origin': '0 0'
    });
       
    return typeof callback === "function" ? callback(element, H) : void 0;
  };

  function makeTransformable(selector, callback) {
    return $(selector).each(function(i, element) {
      $(element).css('transform', '');
      
      // Add four dots to corners of `element` as control points
      const controlPoints = (function() {
        const ref = ['left top', 'left bottom', 'right top', 'right bottom'];
        const results = [];
        for (let k = 0, len = ref.length; k < len; k++) {
          const position = ref[k];
          results.push($('<div>').css({
            border: '10px solid black',
            borderRadius: '10px',
            cursor: 'move',
            position: 'absolute',
            zIndex: 100000
          }).appendTo('body').position({
            at: position,
            of: element,
            collision: 'none'
          }));
        }
        return results;
      })();
        
      // Record the original positions of the dots
      const originalPos = (function() {
        const results = [];
        for (let k = 0, len = controlPoints.length; k < len; k++) {
          const p = controlPoints[k];
          results.push([p.offset().left, p.offset().top]);
        }
        return results;
      })();
      
      // Transform `element` to match the new positions of the dots whenever dragged
      $(controlPoints).draggable({
        start: () => {
          return $(element).css('pointer-events', 'none'); // makes dragging around iframes easier 
        },
        drag: () => {
          return applyTransform(element, originalPos, (function() {
            const results = [];
            for (let k = 0, len = controlPoints.length; k < len; k++) {
              const p = controlPoints[k];
              results.push([p.offset().left, p.offset().top]);
            }
            return results;
          })(), callback);
        },
        stop: () => {
          applyTransform(element, originalPos, (function() {
            const results = [];
            for (let k = 0, len = controlPoints.length; k < len; k++) {
              const p = controlPoints[k];
              results.push([p.offset().left, p.offset().top]);
            }
            return results;
          })(), callback);
            
          return $(element).css('pointer-events', 'auto');
        }
      });
        
      return element;
    });
  };

  makeTransformable('.box', function(element, H) {
    console.log($(element).css('transform'));
    return $(element).html($('<table>').append($('<tr>').html($('<td>').text('matrix3d('))).append((function() {
      const results = [];
      for (let i = 0; i < 4; i++) {
        results.push($('<tr>').append((function() {
          const results1 = [];
          for (let j = 0; j < 4; j++) {
            results1.push($('<td>').text(H[j][i] + ((i === j && j === 3) ? '' : ',')));
          }
          return results1;
        })()));
      }
      return results;
    })()).append($('<tr>').html($('<td>').text(')'))));
  });

}

.box {
  margin: 20px;
  padding: 10px;
  height: 150px;
  width: 500px;
  border: 1px solid black;
}

<div class="box">
    Drag the points to transform the box!
</div>

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.11.2/jquery-ui.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/numeric/1.2.6/numeric.min.js"></script>
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