1 line
34 KiB
JSON
1 line
34 KiB
JSON
{"ast":null,"code":"import { create as v2Create, distSquare as v2DistSquare } from './vector.js';\nvar mathPow = Math.pow;\nvar mathSqrt = Math.sqrt;\nvar EPSILON = 1e-8;\nvar EPSILON_NUMERIC = 1e-4;\nvar THREE_SQRT = mathSqrt(3);\nvar ONE_THIRD = 1 / 3;\n\nvar _v0 = v2Create();\n\nvar _v1 = v2Create();\n\nvar _v2 = v2Create();\n\nfunction isAroundZero(val) {\n return val > -EPSILON && val < EPSILON;\n}\n\nfunction isNotAroundZero(val) {\n return val > EPSILON || val < -EPSILON;\n}\n\nexport function cubicAt(p0, p1, p2, p3, t) {\n var onet = 1 - t;\n return onet * onet * (onet * p0 + 3 * t * p1) + t * t * (t * p3 + 3 * onet * p2);\n}\nexport function cubicDerivativeAt(p0, p1, p2, p3, t) {\n var onet = 1 - t;\n return 3 * (((p1 - p0) * onet + 2 * (p2 - p1) * t) * onet + (p3 - p2) * t * t);\n}\nexport function cubicRootAt(p0, p1, p2, p3, val, roots) {\n var a = p3 + 3 * (p1 - p2) - p0;\n var b = 3 * (p2 - p1 * 2 + p0);\n var c = 3 * (p1 - p0);\n var d = p0 - val;\n var A = b * b - 3 * a * c;\n var B = b * c - 9 * a * d;\n var C = c * c - 3 * b * d;\n var n = 0;\n\n if (isAroundZero(A) && isAroundZero(B)) {\n if (isAroundZero(b)) {\n roots[0] = 0;\n } else {\n var t1 = -c / b;\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n }\n } else {\n var disc = B * B - 4 * A * C;\n\n if (isAroundZero(disc)) {\n var K = B / A;\n var t1 = -b / a + K;\n var t2 = -K / 2;\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n\n if (t2 >= 0 && t2 <= 1) {\n roots[n++] = t2;\n }\n } else if (disc > 0) {\n var discSqrt = mathSqrt(disc);\n var Y1 = A * b + 1.5 * a * (-B + discSqrt);\n var Y2 = A * b + 1.5 * a * (-B - discSqrt);\n\n if (Y1 < 0) {\n Y1 = -mathPow(-Y1, ONE_THIRD);\n } else {\n Y1 = mathPow(Y1, ONE_THIRD);\n }\n\n if (Y2 < 0) {\n Y2 = -mathPow(-Y2, ONE_THIRD);\n } else {\n Y2 = mathPow(Y2, ONE_THIRD);\n }\n\n var t1 = (-b - (Y1 + Y2)) / (3 * a);\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n } else {\n var T = (2 * A * b - 3 * a * B) / (2 * mathSqrt(A * A * A));\n var theta = Math.acos(T) / 3;\n var ASqrt = mathSqrt(A);\n var tmp = Math.cos(theta);\n var t1 = (-b - 2 * ASqrt * tmp) / (3 * a);\n var t2 = (-b + ASqrt * (tmp + THREE_SQRT * Math.sin(theta))) / (3 * a);\n var t3 = (-b + ASqrt * (tmp - THREE_SQRT * Math.sin(theta))) / (3 * a);\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n\n if (t2 >= 0 && t2 <= 1) {\n roots[n++] = t2;\n }\n\n if (t3 >= 0 && t3 <= 1) {\n roots[n++] = t3;\n }\n }\n }\n\n return n;\n}\nexport function cubicExtrema(p0, p1, p2, p3, extrema) {\n var b = 6 * p2 - 12 * p1 + 6 * p0;\n var a = 9 * p1 + 3 * p3 - 3 * p0 - 9 * p2;\n var c = 3 * p1 - 3 * p0;\n var n = 0;\n\n if (isAroundZero(a)) {\n if (isNotAroundZero(b)) {\n var t1 = -c / b;\n\n if (t1 >= 0 && t1 <= 1) {\n extrema[n++] = t1;\n }\n }\n } else {\n var disc = b * b - 4 * a * c;\n\n if (isAroundZero(disc)) {\n extrema[0] = -b / (2 * a);\n } else if (disc > 0) {\n var discSqrt = mathSqrt(disc);\n var t1 = (-b + discSqrt) / (2 * a);\n var t2 = (-b - discSqrt) / (2 * a);\n\n if (t1 >= 0 && t1 <= 1) {\n extrema[n++] = t1;\n }\n\n if (t2 >= 0 && t2 <= 1) {\n extrema[n++] = t2;\n }\n }\n }\n\n return n;\n}\nexport function cubicSubdivide(p0, p1, p2, p3, t, out) {\n var p01 = (p1 - p0) * t + p0;\n var p12 = (p2 - p1) * t + p1;\n var p23 = (p3 - p2) * t + p2;\n var p012 = (p12 - p01) * t + p01;\n var p123 = (p23 - p12) * t + p12;\n var p0123 = (p123 - p012) * t + p012;\n out[0] = p0;\n out[1] = p01;\n out[2] = p012;\n out[3] = p0123;\n out[4] = p0123;\n out[5] = p123;\n out[6] = p23;\n out[7] = p3;\n}\nexport function cubicProjectPoint(x0, y0, x1, y1, x2, y2, x3, y3, x, y, out) {\n var t;\n var interval = 0.005;\n var d = Infinity;\n var prev;\n var next;\n var d1;\n var d2;\n _v0[0] = x;\n _v0[1] = y;\n\n for (var _t = 0; _t < 1; _t += 0.05) {\n _v1[0] = cubicAt(x0, x1, x2, x3, _t);\n _v1[1] = cubicAt(y0, y1, y2, y3, _t);\n d1 = v2DistSquare(_v0, _v1);\n\n if (d1 < d) {\n t = _t;\n d = d1;\n }\n }\n\n d = Infinity;\n\n for (var i = 0; i < 32; i++) {\n if (interval < EPSILON_NUMERIC) {\n break;\n }\n\n prev = t - interval;\n next = t + interval;\n _v1[0] = cubicAt(x0, x1, x2, x3, prev);\n _v1[1] = cubicAt(y0, y1, y2, y3, prev);\n d1 = v2DistSquare(_v1, _v0);\n\n if (prev >= 0 && d1 < d) {\n t = prev;\n d = d1;\n } else {\n _v2[0] = cubicAt(x0, x1, x2, x3, next);\n _v2[1] = cubicAt(y0, y1, y2, y3, next);\n d2 = v2DistSquare(_v2, _v0);\n\n if (next <= 1 && d2 < d) {\n t = next;\n d = d2;\n } else {\n interval *= 0.5;\n }\n }\n }\n\n if (out) {\n out[0] = cubicAt(x0, x1, x2, x3, t);\n out[1] = cubicAt(y0, y1, y2, y3, t);\n }\n\n return mathSqrt(d);\n}\nexport function cubicLength(x0, y0, x1, y1, x2, y2, x3, y3, iteration) {\n var px = x0;\n var py = y0;\n var d = 0;\n var step = 1 / iteration;\n\n for (var i = 1; i <= iteration; i++) {\n var t = i * step;\n var x = cubicAt(x0, x1, x2, x3, t);\n var y = cubicAt(y0, y1, y2, y3, t);\n var dx = x - px;\n var dy = y - py;\n d += Math.sqrt(dx * dx + dy * dy);\n px = x;\n py = y;\n }\n\n return d;\n}\nexport function quadraticAt(p0, p1, p2, t) {\n var onet = 1 - t;\n return onet * (onet * p0 + 2 * t * p1) + t * t * p2;\n}\nexport function quadraticDerivativeAt(p0, p1, p2, t) {\n return 2 * ((1 - t) * (p1 - p0) + t * (p2 - p1));\n}\nexport function quadraticRootAt(p0, p1, p2, val, roots) {\n var a = p0 - 2 * p1 + p2;\n var b = 2 * (p1 - p0);\n var c = p0 - val;\n var n = 0;\n\n if (isAroundZero(a)) {\n if (isNotAroundZero(b)) {\n var t1 = -c / b;\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n }\n } else {\n var disc = b * b - 4 * a * c;\n\n if (isAroundZero(disc)) {\n var t1 = -b / (2 * a);\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n } else if (disc > 0) {\n var discSqrt = mathSqrt(disc);\n var t1 = (-b + discSqrt) / (2 * a);\n var t2 = (-b - discSqrt) / (2 * a);\n\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n\n if (t2 >= 0 && t2 <= 1) {\n roots[n++] = t2;\n }\n }\n }\n\n return n;\n}\nexport function quadraticExtremum(p0, p1, p2) 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{ create as v2Create, distSquare as v2DistSquare } from './vector.js';\nvar mathPow = Math.pow;\nvar mathSqrt = Math.sqrt;\nvar EPSILON = 1e-8;\nvar EPSILON_NUMERIC = 1e-4;\nvar THREE_SQRT = mathSqrt(3);\nvar ONE_THIRD = 1 / 3;\nvar _v0 = v2Create();\nvar _v1 = v2Create();\nvar _v2 = v2Create();\nfunction isAroundZero(val) {\n return val > -EPSILON && val < EPSILON;\n}\nfunction isNotAroundZero(val) {\n return val > EPSILON || val < -EPSILON;\n}\nexport function cubicAt(p0, p1, p2, p3, t) {\n var onet = 1 - t;\n return onet * onet * (onet * p0 + 3 * t * p1)\n + t * t * (t * p3 + 3 * onet * p2);\n}\nexport function cubicDerivativeAt(p0, p1, p2, p3, t) {\n var onet = 1 - t;\n return 3 * (((p1 - p0) * onet + 2 * (p2 - p1) * t) * onet\n + (p3 - p2) * t * t);\n}\nexport function cubicRootAt(p0, p1, p2, p3, val, roots) {\n var a = p3 + 3 * (p1 - p2) - p0;\n var b = 3 * (p2 - p1 * 2 + p0);\n var c = 3 * (p1 - p0);\n var d = p0 - val;\n var A = b * b - 3 * a * c;\n var B = b * c - 9 * a * d;\n var C = c * c - 3 * b * d;\n var n = 0;\n if (isAroundZero(A) && isAroundZero(B)) {\n if (isAroundZero(b)) {\n roots[0] = 0;\n }\n else {\n var t1 = -c / b;\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n }\n }\n else {\n var disc = B * B - 4 * A * C;\n if (isAroundZero(disc)) {\n var K = B / A;\n var t1 = -b / a + K;\n var t2 = -K / 2;\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n if (t2 >= 0 && t2 <= 1) {\n roots[n++] = t2;\n }\n }\n else if (disc > 0) {\n var discSqrt = mathSqrt(disc);\n var Y1 = A * b + 1.5 * a * (-B + discSqrt);\n var Y2 = A * b + 1.5 * a * (-B - discSqrt);\n if (Y1 < 0) {\n Y1 = -mathPow(-Y1, ONE_THIRD);\n }\n else {\n Y1 = mathPow(Y1, ONE_THIRD);\n }\n if (Y2 < 0) {\n Y2 = -mathPow(-Y2, ONE_THIRD);\n }\n else {\n Y2 = mathPow(Y2, ONE_THIRD);\n }\n var t1 = (-b - (Y1 + Y2)) / (3 * a);\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n }\n else {\n var T = (2 * A * b - 3 * a * B) / (2 * mathSqrt(A * A * A));\n var theta = Math.acos(T) / 3;\n var ASqrt = mathSqrt(A);\n var tmp = Math.cos(theta);\n var t1 = (-b - 2 * ASqrt * tmp) / (3 * a);\n var t2 = (-b + ASqrt * (tmp + THREE_SQRT * Math.sin(theta))) / (3 * a);\n var t3 = (-b + ASqrt * (tmp - THREE_SQRT * Math.sin(theta))) / (3 * a);\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n if (t2 >= 0 && t2 <= 1) {\n roots[n++] = t2;\n }\n if (t3 >= 0 && t3 <= 1) {\n roots[n++] = t3;\n }\n }\n }\n return n;\n}\nexport function cubicExtrema(p0, p1, p2, p3, extrema) {\n var b = 6 * p2 - 12 * p1 + 6 * p0;\n var a = 9 * p1 + 3 * p3 - 3 * p0 - 9 * p2;\n var c = 3 * p1 - 3 * p0;\n var n = 0;\n if (isAroundZero(a)) {\n if (isNotAroundZero(b)) {\n var t1 = -c / b;\n if (t1 >= 0 && t1 <= 1) {\n extrema[n++] = t1;\n }\n }\n }\n else {\n var disc = b * b - 4 * a * c;\n if (isAroundZero(disc)) {\n extrema[0] = -b / (2 * a);\n }\n else if (disc > 0) {\n var discSqrt = mathSqrt(disc);\n var t1 = (-b + discSqrt) / (2 * a);\n var t2 = (-b - discSqrt) / (2 * a);\n if (t1 >= 0 && t1 <= 1) {\n extrema[n++] = t1;\n }\n if (t2 >= 0 && t2 <= 1) {\n extrema[n++] = t2;\n }\n }\n }\n return n;\n}\nexport function cubicSubdivide(p0, p1, p2, p3, t, out) {\n var p01 = (p1 - p0) * t + p0;\n var p12 = (p2 - p1) * t + p1;\n var p23 = (p3 - p2) * t + p2;\n var p012 = (p12 - p01) * t + p01;\n var p123 = (p23 - p12) * t + p12;\n var p0123 = (p123 - p012) * t + p012;\n out[0] = p0;\n out[1] = p01;\n out[2] = p012;\n out[3] = p0123;\n out[4] = p0123;\n out[5] = p123;\n out[6] = p23;\n out[7] = p3;\n}\nexport function cubicProjectPoint(x0, y0, x1, y1, x2, y2, x3, y3, x, y, out) {\n var t;\n var interval = 0.005;\n var d = Infinity;\n var prev;\n var next;\n var d1;\n var d2;\n _v0[0] = x;\n _v0[1] = y;\n for (var _t = 0; _t < 1; _t += 0.05) {\n _v1[0] = cubicAt(x0, x1, x2, x3, _t);\n _v1[1] = cubicAt(y0, y1, y2, y3, _t);\n d1 = v2DistSquare(_v0, _v1);\n if (d1 < d) {\n t = _t;\n d = d1;\n }\n }\n d = Infinity;\n for (var i = 0; i < 32; i++) {\n if (interval < EPSILON_NUMERIC) {\n break;\n }\n prev = t - interval;\n next = t + interval;\n _v1[0] = cubicAt(x0, x1, x2, x3, prev);\n _v1[1] = cubicAt(y0, y1, y2, y3, prev);\n d1 = v2DistSquare(_v1, _v0);\n if (prev >= 0 && d1 < d) {\n t = prev;\n d = d1;\n }\n else {\n _v2[0] = cubicAt(x0, x1, x2, x3, next);\n _v2[1] = cubicAt(y0, y1, y2, y3, next);\n d2 = v2DistSquare(_v2, _v0);\n if (next <= 1 && d2 < d) {\n t = next;\n d = d2;\n }\n else {\n interval *= 0.5;\n }\n }\n }\n if (out) {\n out[0] = cubicAt(x0, x1, x2, x3, t);\n out[1] = cubicAt(y0, y1, y2, y3, t);\n }\n return mathSqrt(d);\n}\nexport function cubicLength(x0, y0, x1, y1, x2, y2, x3, y3, iteration) {\n var px = x0;\n var py = y0;\n var d = 0;\n var step = 1 / iteration;\n for (var i = 1; i <= iteration; i++) {\n var t = i * step;\n var x = cubicAt(x0, x1, x2, x3, t);\n var y = cubicAt(y0, y1, y2, y3, t);\n var dx = x - px;\n var dy = y - py;\n d += Math.sqrt(dx * dx + dy * dy);\n px = x;\n py = y;\n }\n return d;\n}\nexport function quadraticAt(p0, p1, p2, t) {\n var onet = 1 - t;\n return onet * (onet * p0 + 2 * t * p1) + t * t * p2;\n}\nexport function quadraticDerivativeAt(p0, p1, p2, t) {\n return 2 * ((1 - t) * (p1 - p0) + t * (p2 - p1));\n}\nexport function quadraticRootAt(p0, p1, p2, val, roots) {\n var a = p0 - 2 * p1 + p2;\n var b = 2 * (p1 - p0);\n var c = p0 - val;\n var n = 0;\n if (isAroundZero(a)) {\n if (isNotAroundZero(b)) {\n var t1 = -c / b;\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n }\n }\n else {\n var disc = b * b - 4 * a * c;\n if (isAroundZero(disc)) {\n var t1 = -b / (2 * a);\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n }\n else if (disc > 0) {\n var discSqrt = mathSqrt(disc);\n var t1 = (-b + discSqrt) / (2 * a);\n var t2 = (-b - discSqrt) / (2 * a);\n if (t1 >= 0 && t1 <= 1) {\n roots[n++] = t1;\n }\n if (t2 >= 0 && t2 <= 1) {\n roots[n++] = t2;\n }\n }\n }\n return n;\n}\nexport function quadraticExtremum(p0, p1, p2) {\n var divider = p0 + p2 - 2 * p1;\n if (divider === 0) {\n return 0.5;\n }\n else {\n return (p0 - p1) / divider;\n }\n}\nexport function quadraticSubdivide(p0, p1, p2, t, out) {\n var p01 = (p1 - p0) * t + p0;\n var p12 = (p2 - p1) * t + p1;\n var p012 = (p12 - p01) * t + p01;\n out[0] = p0;\n out[1] = p01;\n out[2] = p012;\n out[3] = p012;\n out[4] = p12;\n out[5] = p2;\n}\nexport function quadraticProjectPoint(x0, y0, x1, y1, x2, y2, x, y, out) {\n var t;\n var interval = 0.005;\n var d = Infinity;\n _v0[0] = x;\n _v0[1] = y;\n for (var _t = 0; _t < 1; _t += 0.05) {\n _v1[0] = quadraticAt(x0, x1, x2, _t);\n _v1[1] = quadraticAt(y0, y1, y2, _t);\n var d1 = v2DistSquare(_v0, _v1);\n if (d1 < d) {\n t = _t;\n d = d1;\n }\n }\n d = Infinity;\n for (var i = 0; i < 32; i++) {\n if (interval < EPSILON_NUMERIC) {\n break;\n }\n var prev = t - interval;\n var next = t + interval;\n _v1[0] = quadraticAt(x0, x1, x2, prev);\n _v1[1] = quadraticAt(y0, y1, y2, prev);\n var d1 = v2DistSquare(_v1, _v0);\n if (prev >= 0 && d1 < d) {\n t = prev;\n d = d1;\n }\n else {\n _v2[0] = quadraticAt(x0, x1, x2, next);\n _v2[1] = quadraticAt(y0, y1, y2, next);\n var d2 = v2DistSquare(_v2, _v0);\n if (next <= 1 && d2 < d) {\n t = next;\n d = d2;\n }\n else {\n interval *= 0.5;\n }\n }\n }\n if (out) {\n out[0] = quadraticAt(x0, x1, x2, t);\n out[1] = quadraticAt(y0, y1, y2, t);\n }\n return mathSqrt(d);\n}\nexport function quadraticLength(x0, y0, x1, y1, x2, y2, iteration) {\n var px = x0;\n var py = y0;\n var d = 0;\n var step = 1 / iteration;\n for (var i = 1; i <= iteration; i++) {\n var t = i * step;\n var x = quadraticAt(x0, x1, x2, t);\n var y = quadraticAt(y0, y1, y2, t);\n var dx = x - px;\n var dy = y - py;\n d += Math.sqrt(dx * dx + dy * dy);\n px = x;\n py = y;\n }\n return d;\n}\n"]},"metadata":{},"sourceType":"module"} |