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id	title	challengeType
5a23c84252665b21eecc8045	Sutherland-Hodgman polygon clipping	5

Description

The Sutherland-Hodgman clipping algorithm finds the polygon that is the intersection between an arbitrary polygon (the “subject polygon”) and a convex polygon (the “clip polygon”). It is used in computer graphics (especially 2D graphics) to reduce the complexity of a scene being displayed by eliminating parts of a polygon that do not need to be displayed. Take the closed polygon defined by the points: $[(50, 150), (200, 50), (350, 150), (350, 300), (250, 300), (200, 250), (150, 350), (100, 250), (100, 200)]$ and clip it by the rectangle defined by the points: $[(100, 100), (300, 100), (300, 300), (100, 300)]$ Write a function that takes 2 arrays as parameters. The first array contains the points of the subject polygon and the second array contains the points of the clipping polygon. The function should return an array containing the points of the clipped polygon. Each number should be rounded to 3 decimal places.

Instructions

Tests

tests:
  - text: <code>clip</code> should be a function.
    testString: assert(typeof clip == 'function', '<code>clip</code> should be a function.');
  - text: <code>clip([[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]], [[100, 100], [300, 100], [300, 300], [100, 300]])</code> should return a array.
    testString: assert(Array.isArray(clip([[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]], [[100, 100], [300, 100], [300, 300], [100, 300]])), '<code>clip([[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]], [[100, 100], [300, 100], [300, 300], [100, 300]])</code> should return a array.');
  - text: <code>clip([[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]], [[100, 100], [300, 100], [300, 300], [100, 300]])</code> should return <code>[[100, 116.667], [125, 100], [275, 100], [300, 116.667], [300, 300], [250, 300], [200, 250], [175, 300], [125, 300], [100, 250]]</code>.
    testString: assert.deepEqual(clip([[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]], [[100, 100], [300, 100], [300, 300], [100, 300]]), [[100, 116.667], [125, 100], [275, 100], [300, 116.667], [300, 300], [250, 300], [200, 250], [175, 300], [125, 300], [100, 250]], '<code>clip([[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]], [[100, 100], [300, 100], [300, 300], [100, 300]])</code> should return <code>[[100, 116.667], [125, 100], [275, 100], [300, 116.667], [300, 300], [250, 300], [200, 250], [175, 300], [125, 300], [100, 250]]</code>.');
  - text: <code>clip([[150, 200], [400, 450], [30, 50]], [[10, 10], [300, 200], [400, 600], [100, 300]])</code> should return <code>[[150, 200], [350, 400], [348.611, 394.444], [30, 50]]</code>.
    testString: assert.deepEqual(clip([[150, 200], [400, 450], [30, 50]], [[10, 10], [300, 200], [400, 600], [100, 300]]), [[150, 200], [350, 400], [348.611, 394.444], [30, 50]], '<code>clip([[150, 200], [400, 450], [30, 50]], [[10, 10], [300, 200], [400, 600], [100, 300]])</code> should return <code>[[150, 200], [350, 400], [348.611, 394.444], [30, 50]]</code>.');
  - text: <code>clip([[250, 200], [100, 450], [130, 250]], [[50, 60], [100, 230], [400, 600], [100, 300]])</code> should return <code>[[129.167, 329.167], [119.565, 319.565], [121.854, 304.305]]</code>.
    testString: assert.deepEqual(clip([[250, 200], [100, 450], [130, 250]], [[50, 60], [100, 230], [400, 600], [100, 300]]), [[129.167, 329.167], [119.565, 319.565], [121.854, 304.305]], '<code>clip([[250, 200], [100, 450], [130, 250]], [[50, 60], [100, 230], [400, 600], [100, 300]])</code> should return <code>[[129.167, 329.167], [119.565, 319.565], [121.854, 304.305]]</code>.');

Challenge Seed

function clip (subjectPolygon, clipPolygon) {
  // Good luck!
}

Solution

function clip (subjectPolygon, clipPolygon) {
  var cp1, cp2, s, e, i, j;
  var inside = function(p) {
    return (cp2[0] - cp1[0]) * (p[1] - cp1[1]) > (cp2[1] - cp1[1]) * (p[0] - cp1[0]);
  };
  var intersection = function() {
    var dc = [cp1[0] - cp2[0], cp1[1] - cp2[1]],
      dp = [s[0] - e[0], s[1] - e[1]],
      n1 = cp1[0] * cp2[1] - cp1[1] * cp2[0],
      n2 = s[0] * e[1] - s[1] * e[0],
      n3 = 1.0 / (dc[0] * dp[1] - dc[1] * dp[0]);
    return [(n1 * dp[0] - n2 * dc[0]) * n3, (n1 * dp[1] - n2 * dc[1]) * n3];
  };
  var outputList = subjectPolygon;
  cp1 = clipPolygon[clipPolygon.length - 1];
  for (j in clipPolygon) {
    var cp2 = clipPolygon[j];
    var inputList = outputList;
    outputList = [];
    s = inputList[inputList.length - 1]; //last on the input list
    for (i in inputList) {
      var e = inputList[i];
      if (inside(e)) {
        if (!inside(s)) {
          outputList.push(intersection());
        }
        outputList.push(e);
      } else if (inside(s)) {
        outputList.push(intersection());
      }
      s = e;
    }
    cp1 = cp2;
  }
  return outputList.map(e => e.map(f => Math.round(f * 1000) / 1000));
}

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