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E. Brock, The Inertia Tensor for a Spherical Triangle,\n// J. 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Z0) / W0;\n}\n\nfunction centroidLineStart() {\n centroidStream.point = centroidLinePointFirst;\n}\n\nfunction centroidLinePointFirst(lambda, phi) {\n lambda *= radians, phi *= radians;\n var cosPhi = cos(phi);\n x0 = cosPhi * cos(lambda);\n y0 = cosPhi * sin(lambda);\n z0 = sin(phi);\n centroidStream.point = centroidLinePoint;\n centroidPointCartesian(x0, y0, z0);\n}\n\nfunction centroidLinePoint(lambda, phi) {\n lambda *= radians, phi *= radians;\n var cosPhi = cos(phi),\n x = cosPhi * cos(lambda),\n y = cosPhi * sin(lambda),\n z = sin(phi),\n w = atan2(sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z);\n W1 += w;\n X1 += w * (x0 + (x0 = x));\n Y1 += w * (y0 + (y0 = y));\n Z1 += w * (z0 + (z0 = z));\n centroidPointCartesian(x0, y0, z0);\n}\n\nfunction centroidLineEnd() {\n centroidStream.point = centroidPoint;\n}\n\n// See J. E. Brock, The Inertia Tensor for a Spherical Triangle,\n// J. Applied Mechanics 42, 239 (1975).\nfunction centroidRingStart() {\n centroidStream.point = centroidRingPointFirst;\n}\n\nfunction centroidRingEnd() {\n centroidRingPoint(lambda00, phi00);\n centroidStream.point = centroidPoint;\n}\n\nfunction centroidRingPointFirst(lambda, phi) {\n lambda00 = lambda, phi00 = phi;\n lambda *= radians, phi *= radians;\n centroidStream.point = centroidRingPoint;\n var cosPhi = cos(phi);\n x0 = cosPhi * cos(lambda);\n y0 = cosPhi * sin(lambda);\n z0 = sin(phi);\n centroidPointCartesian(x0, y0, z0);\n}\n\nfunction centroidRingPoint(lambda, phi) {\n lambda *= radians, phi *= radians;\n var cosPhi = cos(phi),\n x = cosPhi * cos(lambda),\n y = cosPhi * sin(lambda),\n z = sin(phi),\n cx = y0 * z - z0 * y,\n cy = z0 * x - x0 * z,\n cz = x0 * y - y0 * x,\n m = sqrt(cx * cx + cy * cy + cz * cz),\n w = asin(m), // line weight = angle\n v = m && -w / m; // area weight multiplier\n X2 += v * cx;\n Y2 += v * cy;\n Z2 += v * cz;\n W1 += w;\n X1 += w * (x0 + (x0 = x));\n Y1 += w * (y0 + (y0 = y));\n Z1 += w * (z0 + (z0 = z));\n centroidPointCartesian(x0, y0, z0);\n}\n\nexport default function(object) {\n W0 = W1 =\n X0 = Y0 = Z0 =\n X1 = Y1 = Z1 =\n X2 = Y2 = Z2 = 0;\n stream(object, centroidStream);\n\n var x = X2,\n y = Y2,\n z = Z2,\n m = x * x + y * y + z * z;\n\n // If the area-weighted ccentroid is undefined, fall back to length-weighted ccentroid.\n if (m < epsilon2) {\n x = X1, y = Y1, z = Z1;\n // If the feature has zero length, fall back to arithmetic mean of point vectors.\n if (W1 < epsilon) x = X0, y = Y0, z = Z0;\n m = x * x + y * y + z * z;\n // If the feature still has an undefined ccentroid, then return.\n if (m < epsilon2) return [NaN, NaN];\n }\n\n return [atan2(y, x) * degrees, asin(z / sqrt(m)) * degrees];\n}\n"},"lineCount":null}},"error":null,"hash":"de23b31d8430a51b57565f62412bec28","cacheData":{"env":{}}}