| // 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)); | |
| } |