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 // Copyright 2017 The Cobalt Authors. All Rights Reserved. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. // Calculate the normalized gaussian integral from (pos.x * k, pos.y * k) // where k = sqrt(2) * sigma and pos.x <= pos.y. This is just a 1D filter -- // the pos.x and pos.y values are expected to be on the same axis. float GaussianIntegral(vec2 pos) { // Approximation of the error function. // For x >= 0, // erf(x) = 1 - 1 / (1 + k1 * x + k2 * x^2 + k3 * x^3 + k4 * x^4)^4 // where k1 = 0.278393, k2 = 0.230389, k3 = 0.000972, k4 = 0.078108. // For y < 0, // erf(y) = -erf(-y). vec2 s = sign(pos); vec2 a = abs(pos); vec2 t = 1.0 + (0.278393 + (0.230389 + (0.000972 + 0.078108 * a) * a) * a) * a; vec2 t2 = t * t; vec2 erf = s - s / (t2 * t2); // erf(x) = the integral of the normalized gaussian from [-x * k, x * k], // where k = sqrt(2) * sigma. Find the integral from (pos.x * k, pos.y * k). return dot(erf, vec2(-0.5, 0.5)); }