cesium_nxmap/_cesium@1.72.0@cesium/Build/CesiumUnminified/Workers/IntersectionTests-afc38163.js.map

{"version":3,"file":"IntersectionTests-afc38163.js","sources":["../../../../Source/Core/QuadraticRealPolynomial.js","../../../../Source/Core/CubicRealPolynomial.js","../../../../Source/Core/QuarticRealPolynomial.js","../../../../Source/Core/Ray.js","../../../../Source/Core/IntersectionTests.js"],"sourcesContent":["import DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\n\n/**\n * Defines functions for 2nd order polynomial functions of one variable with only real coefficients.\n *\n * @namespace QuadraticRealPolynomial\n */\nvar QuadraticRealPolynomial = {};\n\n/**\n * Provides the discriminant of the quadratic equation from the supplied coefficients.\n *\n * @param {Number} a The coefficient of the 2nd order monomial.\n * @param {Number} b The coefficient of the 1st order monomial.\n * @param {Number} c The coefficient of the 0th order monomial.\n * @returns {Number} The value of the discriminant.\n */\nQuadraticRealPolynomial.computeDiscriminant = function (a, b, c) {\n  //>>includeStart('debug', pragmas.debug);\n  if (typeof a !== \"number\") {\n    throw new DeveloperError(\"a is a required number.\");\n  }\n  if (typeof b !== \"number\") {\n    throw new DeveloperError(\"b is a required number.\");\n  }\n  if (typeof c !== \"number\") {\n    throw new DeveloperError(\"c is a required number.\");\n  }\n  //>>includeEnd('debug');\n\n  var discriminant = b * b - 4.0 * a * c;\n  return discriminant;\n};\n\nfunction addWithCancellationCheck(left, right, tolerance) {\n  var difference = left + right;\n  if (\n    CesiumMath.sign(left) !== CesiumMath.sign(right) &&\n    Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance\n  ) {\n    return 0.0;\n  }\n\n  return difference;\n}\n\n/**\n * Provides the real valued roots of the quadratic polynomial with the provided coefficients.\n *\n * @param {Number} a The coefficient of the 2nd order monomial.\n * @param {Number} b The coefficient of the 1st order monomial.\n * @param {Number} c The coefficient of the 0th order monomial.\n * @returns {Number[]} The real valued roots.\n */\nQuadraticRealPolynomial.computeRealRoots = function (a, b, c) {\n  //>>includeStart('debug', pragmas.debug);\n  if (typeof a !== \"number\") {\n    throw new DeveloperError(\"a is a required number.\");\n  }\n  if (typeof b !== \"number\") {\n    throw new DeveloperError(\"b is a required number.\");\n  }\n  if (typeof c !== \"number\") {\n    throw new DeveloperError(\"c is a required number.\");\n  }\n  //>>includeEnd('debug');\n\n  var ratio;\n  if (a === 0.0) {\n    if (b === 0.0) {\n      // Constant function: c = 0.\n      return [];\n    }\n\n    // Linear function: b * x + c = 0.\n    return [-c / b];\n  } else if (b === 0.0) {\n    if (c === 0.0) {\n      // 2nd order monomial: a * x^2 = 0.\n      return [0.0, 0.0];\n    }\n\n    var cMagnitude = Math.abs(c);\n    var aMagnitude = Math.abs(a);\n\n    if (\n      cMagnitude < aMagnitude &&\n      cMagnitude / aMagnitude < CesiumMath.EPSILON14\n    ) {\n      // c ~= 0.0.\n      // 2nd order monomial: a * x^2 = 0.\n      return [0.0, 0.0];\n    } else if (\n      cMagnitude > aMagnitude &&\n      aMagnitude / cMagnitude < CesiumMath.EPSILON14\n    ) {\n      // a ~= 0.0.\n      // Constant function: c = 0.\n      return [];\n    }\n\n    // a * x^2 + c = 0\n    ratio = -c / a;\n\n    if (ratio < 0.0) {\n      // Both roots are complex.\n      return [];\n    }\n\n    // Both roots are real.\n    var root = Math.sqrt(ratio);\n    return [-root, root];\n  } else if (c === 0.0) {\n    // a * x^2 + b * x = 0\n    ratio = -b / a;\n    if (ratio < 0.0) {\n      return [ratio, 0.0];\n    }\n\n    return [0.0, ratio];\n  }\n\n  // a * x^2 + b * x + c = 0\n  var b2 = b * b;\n  var four_ac = 4.0 * a * c;\n  var radicand = addWithCancellationCheck(b2, -four_ac, CesiumMath.EPSILON14);\n\n  if (radicand < 0.0) {\n    // Both roots are complex.\n    return [];\n  }\n\n  var q =\n    -0.5 *\n    addWithCancellationCheck(\n      b,\n      CesiumMath.sign(b) * Math.sqrt(radicand),\n      CesiumMath.EPSILON14\n    );\n  if (b > 0.0) {\n    return [q / a, c / q];\n  }\n\n  return [c / q, q / a];\n};\nexport default QuadraticRealPolynomial;\n","import DeveloperError from \"./DeveloperError.js\";\nimport QuadraticRealPolynomial from \"./QuadraticRealPolynomial.js\";\n\n/**\n * Defines functions for 3rd order polynomial functions of one variable with only real coefficients.\n *\n * @namespace CubicRealPolynomial\n */\nvar CubicRealPolynomial = {};\n\n/**\n * Provides the discriminant of the cubic equation from the supplied coefficients.\n *\n * @param {Number} a The coefficient of the 3rd order monomial.\n * @param {Number} b The coefficient of the 2nd order monomial.\n * @param {Number} c The coefficient of the 1st order monomial.\n * @param {Number} d The coefficient of the 0th order monomial.\n * @returns {Number} The value of the discriminant.\n */\nCubicRealPolynomial.computeDiscriminant = function (a, b, c, d) {\n  //>>includeStart('debug', pragmas.debug);\n  if (typeof a !== \"number\") {\n    throw new DeveloperError(\"a is a required number.\");\n  }\n  if (typeof b !== \"number\") {\n    throw new DeveloperError(\"b is a required number.\");\n  }\n  if (typeof c !== \"number\") {\n    throw new DeveloperError(\"c is a required number.\");\n  }\n  if (typeof d !== \"number\") {\n    throw new DeveloperError(\"d is a required number.\");\n  }\n  //>>includeEnd('debug');\n\n  var a2 = a * a;\n  var b2 = b * b;\n  var c2 = c * c;\n  var d2 = d * d;\n\n  var discriminant =\n    18.0 * a * b * c * d +\n    b2 * c2 -\n    27.0 * a2 * d2 -\n    4.0 * (a * c2 * c + b2 * b * d);\n  return discriminant;\n};\n\nfunction computeRealRoots(a, b, c, d) {\n  var A = a;\n  var B = b / 3.0;\n  var C = c / 3.0;\n  var D = d;\n\n  var AC = A * C;\n  var BD = B * D;\n  var B2 = B * B;\n  var C2 = C * C;\n  var delta1 = A * C - B2;\n  var delta2 = A * D - B * C;\n  var delta3 = B * D - C2;\n\n  var discriminant = 4.0 * delta1 * delta3 - delta2 * delta2;\n  var temp;\n  var temp1;\n\n  if (discriminant < 0.0) {\n    var ABar;\n    var CBar;\n    var DBar;\n\n    if (B2 * BD >= AC * C2) {\n      ABar = A;\n      CBar = delta1;\n      DBar = -2.0 * B * delta1 + A * delta2;\n    } else {\n      ABar = D;\n      CBar = delta3;\n      DBar = -D * delta2 + 2.0 * C * delta3;\n    }\n\n    var s = DBar < 0.0 ? -1.0 : 1.0; // This is not Math.Sign()!\n    var temp0 = -s * Math.abs(ABar) * Math.sqrt(-discriminant);\n    temp1 = -DBar + temp0;\n\n    var x = temp1 / 2.0;\n    var p = x < 0.0 ? -Math.pow(-x, 1.0 / 3.0) : Math.pow(x, 1.0 / 3.0);\n    var q = temp1 === temp0 ? -p : -CBar / p;\n\n    temp = CBar <= 0.0 ? p + q : -DBar / (p * p + q * q + CBar);\n\n    if (B2 * BD >= AC * C2) {\n      return [(temp - B) / A];\n    }\n\n    return [-D / (temp + C)];\n  }\n\n  var CBarA = delta1;\n  var DBarA = -2.0 * B * delta1 + A * delta2;\n\n  var CBarD = delta3;\n  var DBarD = -D * delta2 + 2.0 * C * delta3;\n\n  var squareRootOfDiscriminant = Math.sqrt(discriminant);\n  var halfSquareRootOf3 = Math.sqrt(3.0) / 2.0;\n\n  var theta = Math.abs(Math.atan2(A * squareRootOfDiscriminant, -DBarA) / 3.0);\n  temp = 2.0 * Math.sqrt(-CBarA);\n  var cosine = Math.cos(theta);\n  temp1 = temp * cosine;\n  var temp3 = temp * (-cosine / 2.0 - halfSquareRootOf3 * Math.sin(theta));\n\n  var numeratorLarge = temp1 + temp3 > 2.0 * B ? temp1 - B : temp3 - B;\n  var denominatorLarge = A;\n\n  var root1 = numeratorLarge / denominatorLarge;\n\n  theta = Math.abs(Math.atan2(D * squareRootOfDiscriminant, -DBarD) / 3.0);\n  temp = 2.0 * Math.sqrt(-CBarD);\n  cosine = Math.cos(theta);\n  temp1 = temp * cosine;\n  temp3 = temp * (-cosine / 2.0 - halfSquareRootOf3 * Math.sin(theta));\n\n  var numeratorSmall = -D;\n  var denominatorSmall = temp1 + temp3 < 2.0 * C ? temp1 + C : temp3 + C;\n\n  var root3 = numeratorSmall / denominatorSmall;\n\n  var E = denominatorLarge * denominatorSmall;\n  var F =\n    -numeratorLarge * denominatorSmall - denominatorLarge * numeratorSmall;\n  var G = numeratorLarge * numeratorSmall;\n\n  var root2 = (C * F - B * G) / (-B * F + C * E);\n\n  if (root1 <= root2) {\n    if (root1 <= root3) {\n      if (root2 <= root3) {\n        return [root1, root2, root3];\n      }\n      return [root1, root3, root2];\n    }\n    return [root3, root1, root2];\n  }\n  if (root1 <= root3) {\n    return [root2, root1, root3];\n  }\n  if (root2 <= root3) {\n    return [root2, root3, root1];\n  }\n  return [root3, root2, root1];\n}\n\n/**\n * Provides the real valued roots of the cubic polynomial with the provided coefficients.\n *\n * @param {Number} a The coefficient of the 3rd order monomial.\n * @param {Number} b The coefficient of the 2nd order monomial.\n * @param {Number} c The coefficient of the 1st order monomial.\n * @param {Number} d The coefficient of the 0th order monomial.\n * @returns {Number[]} The real valued roots.\n */\nCubicRealPolynomial.computeRealRoots = function (a, b, c, d) {\n  //>>includeStart('debug', pragmas.debug);\n  if (typeof a !== \"number\") {\n    throw new DeveloperError(\"a is a required number.\");\n  }\n  if (typeof b !== \"number\") {\n    throw new DeveloperError(\"b is a required number.\");\n  }\n  if (typeof c !== \"number\") {\n    throw new DeveloperError(\"c is a required number.\");\n  }\n  if (typeof d !== \"number\") {\n    throw new DeveloperError(\"d is a required number.\");\n  }\n  //>>includeEnd('debug');\n\n  var roots;\n  var ratio;\n  if (a === 0.0) {\n    // Quadratic function: b * x^2 + c * x + d = 0.\n    return QuadraticRealPolynomial.computeRealRoots(b, c, d);\n  } else if (b === 0.0) {\n    if (c === 0.0) {\n      if (d === 0.0) {\n        // 3rd order monomial: a * x^3 = 0.\n        return [0.0, 0.0, 0.0];\n      }\n\n      // a * x^3 + d = 0\n      ratio = -d / a;\n      var root =\n        ratio < 0.0 ? -Math.pow(-ratio, 1.0 / 3.0) : Math.pow(ratio, 1.0 / 3.0);\n      return [root, root, root];\n    } else if (d === 0.0) {\n      // x * (a * x^2 + c) = 0.\n      roots = QuadraticRealPolynomial.computeRealRoots(a, 0, c);\n\n      // Return the roots in ascending order.\n      if (roots.Length === 0) {\n        return [0.0];\n      }\n      return [roots[0], 0.0, roots[1]];\n    }\n\n    // Deflated cubic polynomial: a * x^3 + c * x + d= 0.\n    return computeRealRoots(a, 0, c, d);\n  } else if (c === 0.0) {\n    if (d === 0.0) {\n      // x^2 * (a * x + b) = 0.\n      ratio = -b / a;\n      if (ratio < 0.0) {\n        return [ratio, 0.0, 0.0];\n      }\n      return [0.0, 0.0, ratio];\n    }\n    // a * x^3 + b * x^2 + d = 0.\n    return computeRealRoots(a, b, 0, d);\n  } else if (d === 0.0) {\n    // x * (a * x^2 + b * x + c) = 0\n    roots = QuadraticRealPolynomial.computeRealRoots(a, b, c);\n\n    // Return the roots in ascending order.\n    if (roots.length === 0) {\n      return [0.0];\n    } else if (roots[1] <= 0.0) {\n      return [roots[0], roots[1], 0.0];\n    } else if (roots[0] >= 0.0) {\n      return [0.0, roots[0], roots[1]];\n    }\n    return [roots[0], 0.0, roots[1]];\n  }\n\n  return computeRealRoots(a, b, c, d);\n};\nexport default CubicRealPolynomial;\n","import CubicRealPolynomial from \"./CubicRealPolynomial.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport CesiumMath from \"./Math.js\";\nimport QuadraticRealPolynomial from \"./QuadraticRealPolynomial.js\";\n\n/**\n * Defines functions for 4th order polynomial functions of one variable with only real coefficients.\n *\n * @namespace QuarticRealPolynomial\n */\nvar QuarticRealPolynomial = {};\n\n/**\n * Provides the discriminant of the quartic equation from the supplied coefficients.\n *\n * @param {Number} a The coefficient of the 4th order monomial.\n * @param {Number} b The coefficient of the 3rd order monomial.\n * @param {Number} c The coefficient of the 2nd order monomial.\n * @param {Number} d The coefficient of the 1st order monomial.\n * @param {Number} e The coefficient of the 0th order monomial.\n * @returns {Number} The value of the discriminant.\n */\nQuarticRealPolynomial.computeDiscriminant = function (a, b, c, d, e) {\n  //>>includeStart('debug', pragmas.debug);\n  if (typeof a !== \"number\") {\n    throw new DeveloperError(\"a is a required number.\");\n  }\n  if (typeof b !== \"number\") {\n    throw new DeveloperError(\"b is a required number.\");\n  }\n  if (typeof c !== \"number\") {\n    throw new DeveloperError(\"c is a required number.\");\n  }\n  if (typeof d !== \"number\") {\n    throw new DeveloperError(\"d is a required number.\");\n  }\n  if (typeof e !== \"number\") {\n    throw new DeveloperError(\"e is a required number.\");\n  }\n  //>>includeEnd('debug');\n\n  var a2 = a * a;\n  var a3 = a2 * a;\n  var b2 = b * b;\n  var b3 = b2 * b;\n  var c2 = c * c;\n  var c3 = c2 * c;\n  var d2 = d * d;\n  var d3 = d2 * d;\n  var e2 = e * e;\n  var e3 = e2 * e;\n\n  var discriminant =\n    b2 * c2 * d2 -\n    4.0 * b3 * d3 -\n    4.0 * a * c3 * d2 +\n    18 * a * b * c * d3 -\n    27.0 * a2 * d2 * d2 +\n    256.0 * a3 * e3 +\n    e *\n      (18.0 * b3 * c * d -\n        4.0 * b2 * c3 +\n        16.0 * a * c2 * c2 -\n        80.0 * a * b * c2 * d -\n        6.0 * a * b2 * d2 +\n        144.0 * a2 * c * d2) +\n    e2 *\n      (144.0 * a * b2 * c -\n        27.0 * b2 * b2 -\n        128.0 * a2 * c2 -\n        192.0 * a2 * b * d);\n  return discriminant;\n};\n\nfunction original(a3, a2, a1, a0) {\n  var a3Squared = a3 * a3;\n\n  var p = a2 - (3.0 * a3Squared) / 8.0;\n  var q = a1 - (a2 * a3) / 2.0 + (a3Squared * a3) / 8.0;\n  var r =\n    a0 -\n    (a1 * a3) / 4.0 +\n    (a2 * a3Squared) / 16.0 -\n    (3.0 * a3Squared * a3Squared) / 256.0;\n\n  // Find the roots of the cubic equations:  h^6 + 2 p h^4 + (p^2 - 4 r) h^2 - q^2 = 0.\n  var cubicRoots = CubicRealPolynomial.computeRealRoots(\n    1.0,\n    2.0 * p,\n    p * p - 4.0 * r,\n    -q * q\n  );\n\n  if (cubicRoots.length > 0) {\n    var temp = -a3 / 4.0;\n\n    // Use the largest positive root.\n    var hSquared = cubicRoots[cubicRoots.length - 1];\n\n    if (Math.abs(hSquared) < CesiumMath.EPSILON14) {\n      // y^4 + p y^2 + r = 0.\n      var roots = QuadraticRealPolynomial.computeRealRoots(1.0, p, r);\n\n      if (roots.length === 2) {\n        var root0 = roots[0];\n        var root1 = roots[1];\n\n        var y;\n        if (root0 >= 0.0 && root1 >= 0.0) {\n          var y0 = Math.sqrt(root0);\n          var y1 = Math.sqrt(root1);\n\n          return [temp - y1, temp - y0, temp + y0, temp + y1];\n        } else if (root0 >= 0.0 && root1 < 0.0) {\n          y = Math.sqrt(root0);\n          return [temp - y, temp + y];\n        } else if (root0 < 0.0 && root1 >= 0.0) {\n          y = Math.sqrt(root1);\n          return [temp - y, temp + y];\n        }\n      }\n      return [];\n    } else if (hSquared > 0.0) {\n      var h = Math.sqrt(hSquared);\n\n      var m = (p + hSquared - q / h) / 2.0;\n      var n = (p + hSquared + q / h) / 2.0;\n\n      // Now solve the two quadratic factors:  (y^2 + h y + m)(y^2 - h y + n);\n      var roots1 = QuadraticRealPolynomial.computeRealRoots(1.0, h, m);\n      var roots2 = QuadraticRealPolynomial.computeRealRoots(1.0, -h, n);\n\n      if (roots1.length !== 0) {\n        roots1[0] += temp;\n        roots1[1] += temp;\n\n        if (roots2.length !== 0) {\n          roots2[0] += temp;\n          roots2[1] += temp;\n\n          if (roots1[1] <= roots2[0]) {\n            return [roots1[0], roots1[1], roots2[0], roots2[1]];\n          } else if (roots2[1] <= roots1[0]) {\n            return [roots2[0], roots2[1], roots1[0], roots1[1]];\n          } else if (roots1[0] >= roots2[0] && roots1[1] <= roots2[1]) {\n            return [roots2[0], roots1[0], roots1[1], roots2[1]];\n          } else if (roots2[0] >= roots1[0] && roots2[1] <= roots1[1]) {\n            return [roots1[0], roots2[0], roots2[1], roots1[1]];\n          } else if (roots1[0] > roots2[0] && roots1[0] < roots2[1]) {\n            return [roots2[0], roots1[0], roots2[1], roots1[1]];\n          }\n          return [roots1[0], roots2[0], roots1[1], roots2[1]];\n        }\n        return roots1;\n      }\n\n      if (roots2.length !== 0) {\n        roots2[0] += temp;\n        roots2[1] += temp;\n\n        return roots2;\n      }\n      return [];\n    }\n  }\n  return [];\n}\n\nfunction neumark(a3, a2, a1, a0) {\n  var a1Squared = a1 * a1;\n  var a2Squared = a2 * a2;\n  var a3Squared = a3 * a3;\n\n  var p = -2.0 * a2;\n  var q = a1 * a3 + a2Squared - 4.0 * a0;\n  var r = a3Squared * a0 - a1 * a2 * a3 + a1Squared;\n\n  var cubicRoots = CubicRealPolynomial.computeRealRoots(1.0, p, q, r);\n\n  if (cubicRoots.length > 0) {\n    // Use the most positive root\n    var y = cubicRoots[0];\n\n    var temp = a2 - y;\n    var tempSquared = temp * temp;\n\n    var g1 = a3 / 2.0;\n    var h1 = temp / 2.0;\n\n    var m = tempSquared - 4.0 * a0;\n    var mError = tempSquared + 4.0 * Math.abs(a0);\n\n    var n = a3Squared - 4.0 * y;\n    var nError = a3Squared + 4.0 * Math.abs(y);\n\n    var g2;\n    var h2;\n\n    if (y < 0.0 || m * nError < n * mError) {\n      var squareRootOfN = Math.sqrt(n);\n      g2 = squareRootOfN / 2.0;\n      h2 = squareRootOfN === 0.0 ? 0.0 : (a3 * h1 - a1) / squareRootOfN;\n    } else {\n      var squareRootOfM = Math.sqrt(m);\n      g2 = squareRootOfM === 0.0 ? 0.0 : (a3 * h1 - a1) / squareRootOfM;\n      h2 = squareRootOfM / 2.0;\n    }\n\n    var G;\n    var g;\n    if (g1 === 0.0 && g2 === 0.0) {\n      G = 0.0;\n      g = 0.0;\n    } else if (CesiumMath.sign(g1) === CesiumMath.sign(g2)) {\n      G = g1 + g2;\n      g = y / G;\n    } else {\n      g = g1 - g2;\n      G = y / g;\n    }\n\n    var H;\n    var h;\n    if (h1 === 0.0 && h2 === 0.0) {\n      H = 0.0;\n      h = 0.0;\n    } else if (CesiumMath.sign(h1) === CesiumMath.sign(h2)) {\n      H = h1 + h2;\n      h = a0 / H;\n    } else {\n      h = h1 - h2;\n      H = a0 / h;\n    }\n\n    // Now solve the two quadratic factors:  (y^2 + G y + H)(y^2 + g y + h);\n    var roots1 = QuadraticRealPolynomial.computeRealRoots(1.0, G, H);\n    var roots2 = QuadraticRealPolynomial.computeRealRoots(1.0, g, h);\n\n    if (roots1.length !== 0) {\n      if (roots2.length !== 0) {\n        if (roots1[1] <= roots2[0]) {\n          return [roots1[0], roots1[1], roots2[0], roots2[1]];\n        } else if (roots2[1] <= roots1[0]) {\n          return [roots2[0], roots2[1], roots1[0], roots1[1]];\n        } else if (roots1[0] >= roots2[0] && roots1[1] <= roots2[1]) {\n          return [roots2[0], roots1[0], roots1[1], roots2[1]];\n        } else if (roots2[0] >= roots1[0] && roots2[1] <= roots1[1]) {\n          return [roots1[0], roots2[0], roots2[1], roots1[1]];\n        } else if (roots1[0] > roots2[0] && roots1[0] < roots2[1]) {\n          return [roots2[0], roots1[0], roots2[1], roots1[1]];\n        }\n        return [roots1[0], roots2[0], roots1[1], roots2[1]];\n      }\n      return roots1;\n    }\n    if (roots2.length !== 0) {\n      return roots2;\n    }\n  }\n  return [];\n}\n\n/**\n * Provides the real valued roots of the quartic polynomial with the provided coefficients.\n *\n * @param {Number} a The coefficient of the 4th order monomial.\n * @param {Number} b The coefficient of the 3rd order monomial.\n * @param {Number} c The coefficient of the 2nd order monomial.\n * @param {Number} d The coefficient of the 1st order monomial.\n * @param {Number} e The coefficient of the 0th order monomial.\n * @returns {Number[]} The real valued roots.\n */\nQuarticRealPolynomial.computeRealRoots = function (a, b, c, d, e) {\n  //>>includeStart('debug', pragmas.debug);\n  if (typeof a !== \"number\") {\n    throw new DeveloperError(\"a is a required number.\");\n  }\n  if (typeof b !== \"number\") {\n    throw new DeveloperError(\"b is a required number.\");\n  }\n  if (typeof c !== \"number\") {\n    throw new DeveloperError(\"c is a required number.\");\n  }\n  if (typeof d !== \"number\") {\n    throw new DeveloperError(\"d is a required number.\");\n  }\n  if (typeof e !== \"number\") {\n    throw new DeveloperError(\"e is a required number.\");\n  }\n  //>>includeEnd('debug');\n\n  if (Math.abs(a) < CesiumMath.EPSILON15) {\n    return CubicRealPolynomial.computeRealRoots(b, c, d, e);\n  }\n  var a3 = b / a;\n  var a2 = c / a;\n  var a1 = d / a;\n  var a0 = e / a;\n\n  var k = a3 < 0.0 ? 1 : 0;\n  k += a2 < 0.0 ? k + 1 : k;\n  k += a1 < 0.0 ? k + 1 : k;\n  k += a0 < 0.0 ? k + 1 : k;\n\n  switch (k) {\n    case 0:\n      return original(a3, a2, a1, a0);\n    case 1:\n      return neumark(a3, a2, a1, a0);\n    case 2:\n      return neumark(a3, a2, a1, a0);\n    case 3:\n      return original(a3, a2, a1, a0);\n    case 4:\n      return original(a3, a2, a1, a0);\n    case 5:\n      return neumark(a3, a2, a1, a0);\n    case 6:\n      return original(a3, a2, a1, a0);\n    case 7:\n      return original(a3, a2, a1, a0);\n    case 8:\n      return neumark(a3, a2, a1, a0);\n    case 9:\n      return original(a3, a2, a1, a0);\n    case 10:\n      return original(a3, a2, a1, a0);\n    case 11:\n      return neumark(a3, a2, a1, a0);\n    case 12:\n      return original(a3, a2, a1, a0);\n    case 13:\n      return original(a3, a2, a1, a0);\n    case 14:\n      return original(a3, a2, a1, a0);\n    case 15:\n      return original(a3, a2, a1, a0);\n    default:\n      return undefined;\n  }\n};\nexport default QuarticRealPolynomial;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\n\n/**\n * Represents a ray that extends infinitely from the provided origin in the provided direction.\n * @alias Ray\n * @constructor\n *\n * @param {Cartesian3} [origin=Cartesian3.ZERO] The origin of the ray.\n * @param {Cartesian3} [direction=Cartesian3.ZERO] The direction of the ray.\n */\nfunction Ray(origin, direction) {\n  direction = Cartesian3.clone(defaultValue(direction, Cartesian3.ZERO));\n  if (!Cartesian3.equals(direction, Cartesian3.ZERO)) {\n    Cartesian3.normalize(direction, direction);\n  }\n\n  /**\n   * The origin of the ray.\n   * @type {Cartesian3}\n   * @default {@link Cartesian3.ZERO}\n   */\n  this.origin = Cartesian3.clone(defaultValue(origin, Cartesian3.ZERO));\n\n  /**\n   * The direction of the ray.\n   * @type {Cartesian3}\n   */\n  this.direction = direction;\n}\n\n/**\n * Duplicates a Ray instance.\n *\n * @param {Ray} ray The ray to duplicate.\n * @param {Ray} [result] The object onto which to store the result.\n * @returns {Ray} The modified result parameter or a new Ray instance if one was not provided. (Returns undefined if ray is undefined)\n */\nRay.clone = function (ray, result) {\n  if (!defined(ray)) {\n    return undefined;\n  }\n  if (!defined(result)) {\n    return new Ray(ray.origin, ray.direction);\n  }\n  result.origin = Cartesian3.clone(ray.origin);\n  result.direction = Cartesian3.clone(ray.direction);\n  return result;\n};\n\n/**\n * Computes the point along the ray given by r(t) = o + t*d,\n * where o is the origin of the ray and d is the direction.\n *\n * @param {Ray} ray The ray.\n * @param {Number} t A scalar value.\n * @param {Cartesian3} [result] The object in which the result will be stored.\n * @returns {Cartesian3} The modified result parameter, or a new instance if none was provided.\n *\n * @example\n * //Get the first intersection point of a ray and an ellipsoid.\n * var intersection = Cesium.IntersectionTests.rayEllipsoid(ray, ellipsoid);\n * var point = Cesium.Ray.getPoint(ray, intersection.start);\n */\nRay.getPoint = function (ray, t, result) {\n  //>>includeStart('debug', pragmas.debug);\n  Check.typeOf.object(\"ray\", ray);\n  Check.typeOf.number(\"t\", t);\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    result = new Cartesian3();\n  }\n\n  result = Cartesian3.multiplyByScalar(ray.direction, t, result);\n  return Cartesian3.add(ray.origin, result, result);\n};\nexport default Ray;\n","import Cartesian3 from \"./Cartesian3.js\";\nimport Cartographic from \"./Cartographic.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport Interval from \"./Interval.js\";\nimport CesiumMath from \"./Math.js\";\nimport Matrix3 from \"./Matrix3.js\";\nimport QuadraticRealPolynomial from \"./QuadraticRealPolynomial.js\";\nimport QuarticRealPolynomial from \"./QuarticRealPolynomial.js\";\nimport Ray from \"./Ray.js\";\n\n/**\n * Functions for computing the intersection between geometries such as rays, planes, triangles, and ellipsoids.\n *\n * @namespace IntersectionTests\n */\nvar IntersectionTests = {};\n\n/**\n * Computes the intersection of a ray and a plane.\n *\n * @param {Ray} ray The ray.\n * @param {Plane} plane The plane.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The intersection point or undefined if there is no intersections.\n */\nIntersectionTests.rayPlane = function (ray, plane, result) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(ray)) {\n    throw new DeveloperError(\"ray is required.\");\n  }\n  if (!defined(plane)) {\n    throw new DeveloperError(\"plane is required.\");\n  }\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    result = new Cartesian3();\n  }\n\n  var origin = ray.origin;\n  var direction = ray.direction;\n  var normal = plane.normal;\n  var denominator = Cartesian3.dot(normal, direction);\n\n  if (Math.abs(denominator) < CesiumMath.EPSILON15) {\n    // Ray is parallel to plane.  The ray may be in the polygon's plane.\n    return undefined;\n  }\n\n  var t = (-plane.distance - Cartesian3.dot(normal, origin)) / denominator;\n\n  if (t < 0) {\n    return undefined;\n  }\n\n  result = Cartesian3.multiplyByScalar(direction, t, result);\n  return Cartesian3.add(origin, result, result);\n};\n\nvar scratchEdge0 = new Cartesian3();\nvar scratchEdge1 = new Cartesian3();\nvar scratchPVec = new Cartesian3();\nvar scratchTVec = new Cartesian3();\nvar scratchQVec = new Cartesian3();\n\n/**\n * Computes the intersection of a ray and a triangle as a parametric distance along the input ray. The result is negative when the triangle is behind the ray.\n *\n * Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|\n * Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.\n *\n * @memberof IntersectionTests\n *\n * @param {Ray} ray The ray.\n * @param {Cartesian3} p0 The first vertex of the triangle.\n * @param {Cartesian3} p1 The second vertex of the triangle.\n * @param {Cartesian3} p2 The third vertex of the triangle.\n * @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle\n *                  and return undefined for intersections with the back face.\n * @returns {Number} The intersection as a parametric distance along the ray, or undefined if there is no intersection.\n */\nIntersectionTests.rayTriangleParametric = function (\n  ray,\n  p0,\n  p1,\n  p2,\n  cullBackFaces\n) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(ray)) {\n    throw new DeveloperError(\"ray is required.\");\n  }\n  if (!defined(p0)) {\n    throw new DeveloperError(\"p0 is required.\");\n  }\n  if (!defined(p1)) {\n    throw new DeveloperError(\"p1 is required.\");\n  }\n  if (!defined(p2)) {\n    throw new DeveloperError(\"p2 is required.\");\n  }\n  //>>includeEnd('debug');\n\n  cullBackFaces = defaultValue(cullBackFaces, false);\n\n  var origin = ray.origin;\n  var direction = ray.direction;\n\n  var edge0 = Cartesian3.subtract(p1, p0, scratchEdge0);\n  var edge1 = Cartesian3.subtract(p2, p0, scratchEdge1);\n\n  var p = Cartesian3.cross(direction, edge1, scratchPVec);\n  var det = Cartesian3.dot(edge0, p);\n\n  var tvec;\n  var q;\n\n  var u;\n  var v;\n  var t;\n\n  if (cullBackFaces) {\n    if (det < CesiumMath.EPSILON6) {\n      return undefined;\n    }\n\n    tvec = Cartesian3.subtract(origin, p0, scratchTVec);\n    u = Cartesian3.dot(tvec, p);\n    if (u < 0.0 || u > det) {\n      return undefined;\n    }\n\n    q = Cartesian3.cross(tvec, edge0, scratchQVec);\n\n    v = Cartesian3.dot(direction, q);\n    if (v < 0.0 || u + v > det) {\n      return undefined;\n    }\n\n    t = Cartesian3.dot(edge1, q) / det;\n  } else {\n    if (Math.abs(det) < CesiumMath.EPSILON6) {\n      return undefined;\n    }\n    var invDet = 1.0 / det;\n\n    tvec = Cartesian3.subtract(origin, p0, scratchTVec);\n    u = Cartesian3.dot(tvec, p) * invDet;\n    if (u < 0.0 || u > 1.0) {\n      return undefined;\n    }\n\n    q = Cartesian3.cross(tvec, edge0, scratchQVec);\n\n    v = Cartesian3.dot(direction, q) * invDet;\n    if (v < 0.0 || u + v > 1.0) {\n      return undefined;\n    }\n\n    t = Cartesian3.dot(edge1, q) * invDet;\n  }\n\n  return t;\n};\n\n/**\n * Computes the intersection of a ray and a triangle as a Cartesian3 coordinate.\n *\n * Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|\n * Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.\n *\n * @memberof IntersectionTests\n *\n * @param {Ray} ray The ray.\n * @param {Cartesian3} p0 The first vertex of the triangle.\n * @param {Cartesian3} p1 The second vertex of the triangle.\n * @param {Cartesian3} p2 The third vertex of the triangle.\n * @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle\n *                  and return undefined for intersections with the back face.\n * @param {Cartesian3} [result] The <code>Cartesian3</code> onto which to store the result.\n * @returns {Cartesian3} The intersection point or undefined if there is no intersections.\n */\nIntersectionTests.rayTriangle = function (\n  ray,\n  p0,\n  p1,\n  p2,\n  cullBackFaces,\n  result\n) {\n  var t = IntersectionTests.rayTriangleParametric(\n    ray,\n    p0,\n    p1,\n    p2,\n    cullBackFaces\n  );\n  if (!defined(t) || t < 0.0) {\n    return undefined;\n  }\n\n  if (!defined(result)) {\n    result = new Cartesian3();\n  }\n\n  Cartesian3.multiplyByScalar(ray.direction, t, result);\n  return Cartesian3.add(ray.origin, result, result);\n};\n\nvar scratchLineSegmentTriangleRay = new Ray();\n\n/**\n * Computes the intersection of a line segment and a triangle.\n * @memberof IntersectionTests\n *\n * @param {Cartesian3} v0 The an end point of the line segment.\n * @param {Cartesian3} v1 The other end point of the line segment.\n * @param {Cartesian3} p0 The first vertex of the triangle.\n * @param {Cartesian3} p1 The second vertex of the triangle.\n * @param {Cartesian3} p2 The third vertex of the triangle.\n * @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle\n *                  and return undefined for intersections with the back face.\n * @param {Cartesian3} [result] The <code>Cartesian3</code> onto which to store the result.\n * @returns {Cartesian3} The intersection point or undefined if there is no intersections.\n */\nIntersectionTests.lineSegmentTriangle = function (\n  v0,\n  v1,\n  p0,\n  p1,\n  p2,\n  cullBackFaces,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(v0)) {\n    throw new DeveloperError(\"v0 is required.\");\n  }\n  if (!defined(v1)) {\n    throw new DeveloperError(\"v1 is required.\");\n  }\n  if (!defined(p0)) {\n    throw new DeveloperError(\"p0 is required.\");\n  }\n  if (!defined(p1)) {\n    throw new DeveloperError(\"p1 is required.\");\n  }\n  if (!defined(p2)) {\n    throw new DeveloperError(\"p2 is required.\");\n  }\n  //>>includeEnd('debug');\n\n  var ray = scratchLineSegmentTriangleRay;\n  Cartesian3.clone(v0, ray.origin);\n  Cartesian3.subtract(v1, v0, ray.direction);\n  Cartesian3.normalize(ray.direction, ray.direction);\n\n  var t = IntersectionTests.rayTriangleParametric(\n    ray,\n    p0,\n    p1,\n    p2,\n    cullBackFaces\n  );\n  if (!defined(t) || t < 0.0 || t > Cartesian3.distance(v0, v1)) {\n    return undefined;\n  }\n\n  if (!defined(result)) {\n    result = new Cartesian3();\n  }\n\n  Cartesian3.multiplyByScalar(ray.direction, t, result);\n  return Cartesian3.add(ray.origin, result, result);\n};\n\nfunction solveQuadratic(a, b, c, result) {\n  var det = b * b - 4.0 * a * c;\n  if (det < 0.0) {\n    return undefined;\n  } else if (det > 0.0) {\n    var denom = 1.0 / (2.0 * a);\n    var disc = Math.sqrt(det);\n    var root0 = (-b + disc) * denom;\n    var root1 = (-b - disc) * denom;\n\n    if (root0 < root1) {\n      result.root0 = root0;\n      result.root1 = root1;\n    } else {\n      result.root0 = root1;\n      result.root1 = root0;\n    }\n\n    return result;\n  }\n\n  var root = -b / (2.0 * a);\n  if (root === 0.0) {\n    return undefined;\n  }\n\n  result.root0 = result.root1 = root;\n  return result;\n}\n\nvar raySphereRoots = {\n  root0: 0.0,\n  root1: 0.0,\n};\n\nfunction raySphere(ray, sphere, result) {\n  if (!defined(result)) {\n    result = new Interval();\n  }\n\n  var origin = ray.origin;\n  var direction = ray.direction;\n\n  var center = sphere.center;\n  var radiusSquared = sphere.radius * sphere.radius;\n\n  var diff = Cartesian3.subtract(origin, center, scratchPVec);\n\n  var a = Cartesian3.dot(direction, direction);\n  var b = 2.0 * Cartesian3.dot(direction, diff);\n  var c = Cartesian3.magnitudeSquared(diff) - radiusSquared;\n\n  var roots = solveQuadratic(a, b, c, raySphereRoots);\n  if (!defined(roots)) {\n    return undefined;\n  }\n\n  result.start = roots.root0;\n  result.stop = roots.root1;\n  return result;\n}\n\n/**\n * Computes the intersection points of a ray with a sphere.\n * @memberof IntersectionTests\n *\n * @param {Ray} ray The ray.\n * @param {BoundingSphere} sphere The sphere.\n * @param {Interval} [result] The result onto which to store the result.\n * @returns {Interval} The interval containing scalar points along the ray or undefined if there are no intersections.\n */\nIntersectionTests.raySphere = function (ray, sphere, result) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(ray)) {\n    throw new DeveloperError(\"ray is required.\");\n  }\n  if (!defined(sphere)) {\n    throw new DeveloperError(\"sphere is required.\");\n  }\n  //>>includeEnd('debug');\n\n  result = raySphere(ray, sphere, result);\n  if (!defined(result) || result.stop < 0.0) {\n    return undefined;\n  }\n\n  result.start = Math.max(result.start, 0.0);\n  return result;\n};\n\nvar scratchLineSegmentRay = new Ray();\n\n/**\n * Computes the intersection points of a line segment with a sphere.\n * @memberof IntersectionTests\n *\n * @param {Cartesian3} p0 An end point of the line segment.\n * @param {Cartesian3} p1 The other end point of the line segment.\n * @param {BoundingSphere} sphere The sphere.\n * @param {Interval} [result] The result onto which to store the result.\n * @returns {Interval} The interval containing scalar points along the ray or undefined if there are no intersections.\n */\nIntersectionTests.lineSegmentSphere = function (p0, p1, sphere, result) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(p0)) {\n    throw new DeveloperError(\"p0 is required.\");\n  }\n  if (!defined(p1)) {\n    throw new DeveloperError(\"p1 is required.\");\n  }\n  if (!defined(sphere)) {\n    throw new DeveloperError(\"sphere is required.\");\n  }\n  //>>includeEnd('debug');\n\n  var ray = scratchLineSegmentRay;\n  Cartesian3.clone(p0, ray.origin);\n  var direction = Cartesian3.subtract(p1, p0, ray.direction);\n\n  var maxT = Cartesian3.magnitude(direction);\n  Cartesian3.normalize(direction, direction);\n\n  result = raySphere(ray, sphere, result);\n  if (!defined(result) || result.stop < 0.0 || result.start > maxT) {\n    return undefined;\n  }\n\n  result.start = Math.max(result.start, 0.0);\n  result.stop = Math.min(result.stop, maxT);\n  return result;\n};\n\nvar scratchQ = new Cartesian3();\nvar scratchW = new Cartesian3();\n\n/**\n * Computes the intersection points of a ray with an ellipsoid.\n *\n * @param {Ray} ray The ray.\n * @param {Ellipsoid} ellipsoid The ellipsoid.\n * @returns {Interval} The interval containing scalar points along the ray or undefined if there are no intersections.\n */\nIntersectionTests.rayEllipsoid = function (ray, ellipsoid) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(ray)) {\n    throw new DeveloperError(\"ray is required.\");\n  }\n  if (!defined(ellipsoid)) {\n    throw new DeveloperError(\"ellipsoid is required.\");\n  }\n  //>>includeEnd('debug');\n\n  var inverseRadii = ellipsoid.oneOverRadii;\n  var q = Cartesian3.multiplyComponents(inverseRadii, ray.origin, scratchQ);\n  var w = Cartesian3.multiplyComponents(inverseRadii, ray.direction, scratchW);\n\n  var q2 = Cartesian3.magnitudeSquared(q);\n  var qw = Cartesian3.dot(q, w);\n\n  var difference, w2, product, discriminant, temp;\n\n  if (q2 > 1.0) {\n    // Outside ellipsoid.\n    if (qw >= 0.0) {\n      // Looking outward or tangent (0 intersections).\n      return undefined;\n    }\n\n    // qw < 0.0.\n    var qw2 = qw * qw;\n    difference = q2 - 1.0; // Positively valued.\n    w2 = Cartesian3.magnitudeSquared(w);\n    product = w2 * difference;\n\n    if (qw2 < product) {\n      // Imaginary roots (0 intersections).\n      return undefined;\n    } else if (qw2 > product) {\n      // Distinct roots (2 intersections).\n      discriminant = qw * qw - product;\n      temp = -qw + Math.sqrt(discriminant); // Avoid cancellation.\n      var root0 = temp / w2;\n      var root1 = difference / temp;\n      if (root0 < root1) {\n        return new Interval(root0, root1);\n      }\n\n      return {\n        start: root1,\n        stop: root0,\n      };\n    }\n    // qw2 == product.  Repeated roots (2 intersections).\n    var root = Math.sqrt(difference / w2);\n    return new Interval(root, root);\n  } else if (q2 < 1.0) {\n    // Inside ellipsoid (2 intersections).\n    difference = q2 - 1.0; // Negatively valued.\n    w2 = Cartesian3.magnitudeSquared(w);\n    product = w2 * difference; // Negatively valued.\n\n    discriminant = qw * qw - product;\n    temp = -qw + Math.sqrt(discriminant); // Positively valued.\n    return new Interval(0.0, temp / w2);\n  }\n  // q2 == 1.0. On ellipsoid.\n  if (qw < 0.0) {\n    // Looking inward.\n    w2 = Cartesian3.magnitudeSquared(w);\n    return new Interval(0.0, -qw / w2);\n  }\n\n  // qw >= 0.0.  Looking outward or tangent.\n  return undefined;\n};\n\nfunction addWithCancellationCheck(left, right, tolerance) {\n  var difference = left + right;\n  if (\n    CesiumMath.sign(left) !== CesiumMath.sign(right) &&\n    Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance\n  ) {\n    return 0.0;\n  }\n\n  return difference;\n}\n\nfunction quadraticVectorExpression(A, b, c, x, w) {\n  var xSquared = x * x;\n  var wSquared = w * w;\n\n  var l2 = (A[Matrix3.COLUMN1ROW1] - A[Matrix3.COLUMN2ROW2]) * wSquared;\n  var l1 =\n    w *\n    (x *\n      addWithCancellationCheck(\n        A[Matrix3.COLUMN1ROW0],\n        A[Matrix3.COLUMN0ROW1],\n        CesiumMath.EPSILON15\n      ) +\n      b.y);\n  var l0 =\n    A[Matrix3.COLUMN0ROW0] * xSquared +\n    A[Matrix3.COLUMN2ROW2] * wSquared +\n    x * b.x +\n    c;\n\n  var r1 =\n    wSquared *\n    addWithCancellationCheck(\n      A[Matrix3.COLUMN2ROW1],\n      A[Matrix3.COLUMN1ROW2],\n      CesiumMath.EPSILON15\n    );\n  var r0 =\n    w *\n    (x *\n      addWithCancellationCheck(A[Matrix3.COLUMN2ROW0], A[Matrix3.COLUMN0ROW2]) +\n      b.z);\n\n  var cosines;\n  var solutions = [];\n  if (r0 === 0.0 && r1 === 0.0) {\n    cosines = QuadraticRealPolynomial.computeRealRoots(l2, l1, l0);\n    if (cosines.length === 0) {\n      return solutions;\n    }\n\n    var cosine0 = cosines[0];\n    var sine0 = Math.sqrt(Math.max(1.0 - cosine0 * cosine0, 0.0));\n    solutions.push(new Cartesian3(x, w * cosine0, w * -sine0));\n    solutions.push(new Cartesian3(x, w * cosine0, w * sine0));\n\n    if (cosines.length === 2) {\n      var cosine1 = cosines[1];\n      var sine1 = Math.sqrt(Math.max(1.0 - cosine1 * cosine1, 0.0));\n      solutions.push(new Cartesian3(x, w * cosine1, w * -sine1));\n      solutions.push(new Cartesian3(x, w * cosine1, w * sine1));\n    }\n\n    return solutions;\n  }\n\n  var r0Squared = r0 * r0;\n  var r1Squared = r1 * r1;\n  var l2Squared = l2 * l2;\n  var r0r1 = r0 * r1;\n\n  var c4 = l2Squared + r1Squared;\n  var c3 = 2.0 * (l1 * l2 + r0r1);\n  var c2 = 2.0 * l0 * l2 + l1 * l1 - r1Squared + r0Squared;\n  var c1 = 2.0 * (l0 * l1 - r0r1);\n  var c0 = l0 * l0 - r0Squared;\n\n  if (c4 === 0.0 && c3 === 0.0 && c2 === 0.0 && c1 === 0.0) {\n    return solutions;\n  }\n\n  cosines = QuarticRealPolynomial.computeRealRoots(c4, c3, c2, c1, c0);\n  var length = cosines.length;\n  if (length === 0) {\n    return solutions;\n  }\n\n  for (var i = 0; i < length; ++i) {\n    var cosine = cosines[i];\n    var cosineSquared = cosine * cosine;\n    var sineSquared = Math.max(1.0 - cosineSquared, 0.0);\n    var sine = Math.sqrt(sineSquared);\n\n    //var left = l2 * cosineSquared + l1 * cosine + l0;\n    var left;\n    if (CesiumMath.sign(l2) === CesiumMath.sign(l0)) {\n      left = addWithCancellationCheck(\n        l2 * cosineSquared + l0,\n        l1 * cosine,\n        CesiumMath.EPSILON12\n      );\n    } else if (CesiumMath.sign(l0) === CesiumMath.sign(l1 * cosine)) {\n      left = addWithCancellationCheck(\n        l2 * cosineSquared,\n        l1 * cosine + l0,\n        CesiumMath.EPSILON12\n      );\n    } else {\n      left = addWithCancellationCheck(\n        l2 * cosineSquared + l1 * cosine,\n        l0,\n        CesiumMath.EPSILON12\n      );\n    }\n\n    var right = addWithCancellationCheck(r1 * cosine, r0, CesiumMath.EPSILON15);\n    var product = left * right;\n\n    if (product < 0.0) {\n      solutions.push(new Cartesian3(x, w * cosine, w * sine));\n    } else if (product > 0.0) {\n      solutions.push(new Cartesian3(x, w * cosine, w * -sine));\n    } else if (sine !== 0.0) {\n      solutions.push(new Cartesian3(x, w * cosine, w * -sine));\n      solutions.push(new Cartesian3(x, w * cosine, w * sine));\n      ++i;\n    } else {\n      solutions.push(new Cartesian3(x, w * cosine, w * sine));\n    }\n  }\n\n  return solutions;\n}\n\nvar firstAxisScratch = new Cartesian3();\nvar secondAxisScratch = new Cartesian3();\nvar thirdAxisScratch = new Cartesian3();\nvar referenceScratch = new Cartesian3();\nvar bCart = new Cartesian3();\nvar bScratch = new Matrix3();\nvar btScratch = new Matrix3();\nvar diScratch = new Matrix3();\nvar dScratch = new Matrix3();\nvar cScratch = new Matrix3();\nvar tempMatrix = new Matrix3();\nvar aScratch = new Matrix3();\nvar sScratch = new Cartesian3();\nvar closestScratch = new Cartesian3();\nvar surfPointScratch = new Cartographic();\n\n/**\n * Provides the point along the ray which is nearest to the ellipsoid.\n *\n * @param {Ray} ray The ray.\n * @param {Ellipsoid} ellipsoid The ellipsoid.\n * @returns {Cartesian3} The nearest planetodetic point on the ray.\n */\nIntersectionTests.grazingAltitudeLocation = function (ray, ellipsoid) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(ray)) {\n    throw new DeveloperError(\"ray is required.\");\n  }\n  if (!defined(ellipsoid)) {\n    throw new DeveloperError(\"ellipsoid is required.\");\n  }\n  //>>includeEnd('debug');\n\n  var position = ray.origin;\n  var direction = ray.direction;\n\n  if (!Cartesian3.equals(position, Cartesian3.ZERO)) {\n    var normal = ellipsoid.geodeticSurfaceNormal(position, firstAxisScratch);\n    if (Cartesian3.dot(direction, normal) >= 0.0) {\n      // The location provided is the closest point in altitude\n      return position;\n    }\n  }\n\n  var intersects = defined(this.rayEllipsoid(ray, ellipsoid));\n\n  // Compute the scaled direction vector.\n  var f = ellipsoid.transformPositionToScaledSpace(direction, firstAxisScratch);\n\n  // Constructs a basis from the unit scaled direction vector. Construct its rotation and transpose.\n  var firstAxis = Cartesian3.normalize(f, f);\n  var reference = Cartesian3.mostOrthogonalAxis(f, referenceScratch);\n  var secondAxis = Cartesian3.normalize(\n    Cartesian3.cross(reference, firstAxis, secondAxisScratch),\n    secondAxisScratch\n  );\n  var thirdAxis = Cartesian3.normalize(\n    Cartesian3.cross(firstAxis, secondAxis, thirdAxisScratch),\n    thirdAxisScratch\n  );\n  var B = bScratch;\n  B[0] = firstAxis.x;\n  B[1] = firstAxis.y;\n  B[2] = firstAxis.z;\n  B[3] = secondAxis.x;\n  B[4] = secondAxis.y;\n  B[5] = secondAxis.z;\n  B[6] = thirdAxis.x;\n  B[7] = thirdAxis.y;\n  B[8] = thirdAxis.z;\n\n  var B_T = Matrix3.transpose(B, btScratch);\n\n  // Get the scaling matrix and its inverse.\n  var D_I = Matrix3.fromScale(ellipsoid.radii, diScratch);\n  var D = Matrix3.fromScale(ellipsoid.oneOverRadii, dScratch);\n\n  var C = cScratch;\n  C[0] = 0.0;\n  C[1] = -direction.z;\n  C[2] = direction.y;\n  C[3] = direction.z;\n  C[4] = 0.0;\n  C[5] = -direction.x;\n  C[6] = -direction.y;\n  C[7] = direction.x;\n  C[8] = 0.0;\n\n  var temp = Matrix3.multiply(\n    Matrix3.multiply(B_T, D, tempMatrix),\n    C,\n    tempMatrix\n  );\n  var A = Matrix3.multiply(Matrix3.multiply(temp, D_I, aScratch), B, aScratch);\n  var b = Matrix3.multiplyByVector(temp, position, bCart);\n\n  // Solve for the solutions to the expression in standard form:\n  var solutions = quadraticVectorExpression(\n    A,\n    Cartesian3.negate(b, firstAxisScratch),\n    0.0,\n    0.0,\n    1.0\n  );\n\n  var s;\n  var altitude;\n  var length = solutions.length;\n  if (length > 0) {\n    var closest = Cartesian3.clone(Cartesian3.ZERO, closestScratch);\n    var maximumValue = Number.NEGATIVE_INFINITY;\n\n    for (var i = 0; i < length; ++i) {\n      s = Matrix3.multiplyByVector(\n        D_I,\n        Matrix3.multiplyByVector(B, solutions[i], sScratch),\n        sScratch\n      );\n      var v = Cartesian3.normalize(\n        Cartesian3.subtract(s, position, referenceScratch),\n        referenceScratch\n      );\n      var dotProduct = Cartesian3.dot(v, direction);\n\n      if (dotProduct > maximumValue) {\n        maximumValue = dotProduct;\n        closest = Cartesian3.clone(s, closest);\n      }\n    }\n\n    var surfacePoint = ellipsoid.cartesianToCartographic(\n      closest,\n      surfPointScratch\n    );\n    maximumValue = CesiumMath.clamp(maximumValue, 0.0, 1.0);\n    altitude =\n      Cartesian3.magnitude(\n        Cartesian3.subtract(closest, position, referenceScratch)\n      ) * Math.sqrt(1.0 - maximumValue * maximumValue);\n    altitude = intersects ? -altitude : altitude;\n    surfacePoint.height = altitude;\n    return ellipsoid.cartographicToCartesian(surfacePoint, new Cartesian3());\n  }\n\n  return undefined;\n};\n\nvar lineSegmentPlaneDifference = new Cartesian3();\n\n/**\n * Computes the intersection of a line segment and a plane.\n *\n * @param {Cartesian3} endPoint0 An end point of the line segment.\n * @param {Cartesian3} endPoint1 The other end point of the line segment.\n * @param {Plane} plane The plane.\n * @param {Cartesian3} [result] The object onto which to store the result.\n * @returns {Cartesian3} The intersection point or undefined if there is no intersection.\n *\n * @example\n * var origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);\n * var normal = ellipsoid.geodeticSurfaceNormal(origin);\n * var plane = Cesium.Plane.fromPointNormal(origin, normal);\n *\n * var p0 = new Cesium.Cartesian3(...);\n * var p1 = new Cesium.Cartesian3(...);\n *\n * // find the intersection of the line segment from p0 to p1 and the tangent plane at origin.\n * var intersection = Cesium.IntersectionTests.lineSegmentPlane(p0, p1, plane);\n */\nIntersectionTests.lineSegmentPlane = function (\n  endPoint0,\n  endPoint1,\n  plane,\n  result\n) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(endPoint0)) {\n    throw new DeveloperError(\"endPoint0 is required.\");\n  }\n  if (!defined(endPoint1)) {\n    throw new DeveloperError(\"endPoint1 is required.\");\n  }\n  if (!defined(plane)) {\n    throw new DeveloperError(\"plane is required.\");\n  }\n  //>>includeEnd('debug');\n\n  if (!defined(result)) {\n    result = new Cartesian3();\n  }\n\n  var difference = Cartesian3.subtract(\n    endPoint1,\n    endPoint0,\n    lineSegmentPlaneDifference\n  );\n  var normal = plane.normal;\n  var nDotDiff = Cartesian3.dot(normal, difference);\n\n  // check if the segment and plane are parallel\n  if (Math.abs(nDotDiff) < CesiumMath.EPSILON6) {\n    return undefined;\n  }\n\n  var nDotP0 = Cartesian3.dot(normal, endPoint0);\n  var t = -(plane.distance + nDotP0) / nDotDiff;\n\n  // intersection only if t is in [0, 1]\n  if (t < 0.0 || t > 1.0) {\n    return undefined;\n  }\n\n  // intersection is endPoint0 + t * (endPoint1 - endPoint0)\n  Cartesian3.multiplyByScalar(difference, t, result);\n  Cartesian3.add(endPoint0, result, result);\n  return result;\n};\n\n/**\n * Computes the intersection of a triangle and a plane\n *\n * @param {Cartesian3} p0 First point of the triangle\n * @param {Cartesian3} p1 Second point of the triangle\n * @param {Cartesian3} p2 Third point of the triangle\n * @param {Plane} plane Intersection plane\n * @returns {Object} An object with properties <code>positions</code> and <code>indices</code>, which are arrays that represent three triangles that do not cross the plane. (Undefined if no intersection exists)\n *\n * @example\n * var origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);\n * var normal = ellipsoid.geodeticSurfaceNormal(origin);\n * var plane = Cesium.Plane.fromPointNormal(origin, normal);\n *\n * var p0 = new Cesium.Cartesian3(...);\n * var p1 = new Cesium.Cartesian3(...);\n * var p2 = new Cesium.Cartesian3(...);\n *\n * // convert the triangle composed of points (p0, p1, p2) to three triangles that don't cross the plane\n * var triangles = Cesium.IntersectionTests.trianglePlaneIntersection(p0, p1, p2, plane);\n */\nIntersectionTests.trianglePlaneIntersection = function (p0, p1, p2, plane) {\n  //>>includeStart('debug', pragmas.debug);\n  if (!defined(p0) || !defined(p1) || !defined(p2) || !defined(plane)) {\n    throw new DeveloperError(\"p0, p1, p2, and plane are required.\");\n  }\n  //>>includeEnd('debug');\n\n  var planeNormal = plane.normal;\n  var planeD = plane.distance;\n  var p0Behind = Cartesian3.dot(planeNormal, p0) + planeD < 0.0;\n  var p1Behind = Cartesian3.dot(planeNormal, p1) + planeD < 0.0;\n  var p2Behind = Cartesian3.dot(planeNormal, p2) + planeD < 0.0;\n  // Given these dots products, the calls to lineSegmentPlaneIntersection\n  // always have defined results.\n\n  var numBehind = 0;\n  numBehind += p0Behind ? 1 : 0;\n  numBehind += p1Behind ? 1 : 0;\n  numBehind += p2Behind ? 1 : 0;\n\n  var u1, u2;\n  if (numBehind === 1 || numBehind === 2) {\n    u1 = new Cartesian3();\n    u2 = new Cartesian3();\n  }\n\n  if (numBehind === 1) {\n    if (p0Behind) {\n      IntersectionTests.lineSegmentPlane(p0, p1, plane, u1);\n      IntersectionTests.lineSegmentPlane(p0, p2, plane, u2);\n\n      return {\n        positions: [p0, p1, p2, u1, u2],\n        indices: [\n          // Behind\n          0,\n          3,\n          4,\n\n          // In front\n          1,\n          2,\n          4,\n          1,\n          4,\n          3,\n        ],\n      };\n    } else if (p1Behind) {\n      IntersectionTests.lineSegmentPlane(p1, p2, plane, u1);\n      IntersectionTests.lineSegmentPlane(p1, p0, plane, u2);\n\n      return {\n        positions: [p0, p1, p2, u1, u2],\n        indices: [\n          // Behind\n          1,\n          3,\n          4,\n\n          // In front\n          2,\n          0,\n          4,\n          2,\n          4,\n          3,\n        ],\n      };\n    } else if (p2Behind) {\n      IntersectionTests.lineSegmentPlane(p2, p0, plane, u1);\n      IntersectionTests.lineSegmentPlane(p2, p1, plane, u2);\n\n      return {\n        positions: [p0, p1, p2, u1, u2],\n        indices: [\n          // Behind\n          2,\n          3,\n          4,\n\n          // In front\n          0,\n          1,\n          4,\n          0,\n          4,\n          3,\n        ],\n      };\n    }\n  } else if (numBehind === 2) {\n    if (!p0Behind) {\n      IntersectionTests.lineSegmentPlane(p1, p0, plane, u1);\n      IntersectionTests.lineSegmentPlane(p2, p0, plane, u2);\n\n      return {\n        positions: [p0, p1, p2, u1, u2],\n        indices: [\n          // Behind\n          1,\n          2,\n          4,\n          1,\n          4,\n          3,\n\n          // In front\n          0,\n          3,\n          4,\n        ],\n      };\n    } else if (!p1Behind) {\n      IntersectionTests.lineSegmentPlane(p2, p1, plane, u1);\n      IntersectionTests.lineSegmentPlane(p0, p1, plane, u2);\n\n      return {\n        positions: [p0, p1, p2, u1, u2],\n        indices: [\n          // Behind\n          2,\n          0,\n          4,\n          2,\n          4,\n          3,\n\n          // In front\n          1,\n          3,\n          4,\n        ],\n      };\n    } else if (!p2Behind) {\n      IntersectionTests.lineSegmentPlane(p0, p2, plane, u1);\n      IntersectionTests.lineSegmentPlane(p1, p2, plane, u2);\n\n      return {\n        positions: [p0, p1, p2, u1, u2],\n        indices: [\n          // Behind\n          0,\n          1,\n          4,\n          0,\n          4,\n          3,\n\n          // In front\n          2,\n          3,\n          4,\n        ],\n      };\n    }\n  }\n\n  // if numBehind is 3, the triangle is completely behind the plane;\n  // otherwise, it is completely in front (numBehind is 0).\n  return undefined;\n};\nexport default 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