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+/****************************************************************************
+**
+** Copyright (C) 2014 NVIDIA Corporation.
+** Copyright (C) 2017 The Qt Company Ltd.
+** Contact: https://www.qt.io/licensing/
+**
+** This file is part of Qt 3D Studio.
+**
+** $QT_BEGIN_LICENSE:GPL$
+** Commercial License Usage
+** Licensees holding valid commercial Qt licenses may use this file in
+** accordance with the commercial license agreement provided with the
+** Software or, alternatively, in accordance with the terms contained in
+** a written agreement between you and The Qt Company. For licensing terms
+** and conditions see https://www.qt.io/terms-conditions. For further
+** information use the contact form at https://www.qt.io/contact-us.
+**
+** GNU General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU
+** General Public License version 3 or (at your option) any later version
+** approved by the KDE Free Qt Foundation. The licenses are as published by
+** the Free Software Foundation and appearing in the file LICENSE.GPL3
+** included in the packaging of this file. Please review the following
+** information to ensure the GNU General Public License requirements will
+** be met: https://www.gnu.org/licenses/gpl-3.0.html.
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+float calculateRoughness( in vec3 N, in float roughnessU, in float roughnessV, in vec3 tangentU )
+{
+ float roughness = roughnessU;
+ if ( abs(roughnessU - roughnessV) > 0.00001)
+ {
+ // determine major and minor radii a and b, and the vector along the major axis
+ float a = roughnessU;
+ float b = roughnessV;
+
+ // we need the angle between the major axis and the projection of viewDir on the tangential plane
+ // the major axis is the orthonormalization of tangentU with respect to N
+ // the projection of viewDir is the orthonormalization of viewDir with respect to N
+ // as both vectors would be calculated by orthonormalize, we can as well leave the second cross
+ // product in those calculations away, as they don't change the angular relation.
+ vec3 minorAxis = normalize( cross( tangentU, N ) ); // crossing this with N would give the major axis
+ // which is equivalent to orthonormalizing tangentU with respect to N
+ if ( roughnessU < roughnessV )
+ {
+ a = roughnessV;
+ b = roughnessU;
+ minorAxis = cross( N, minorAxis );
+ }
+
+ vec3 po = normalize( cross( viewDir, N ) );
+ float cosPhi = dot( po, minorAxis );
+
+ // determine the polar coordinate of viewDir, take that radius as the roughness
+ float excentricitySquare = 1.0 - square( b / a );
+ roughness = b / sqrt( 1.0 - excentricitySquare * square( cosPhi ) );
+ }
+ return( roughness );
+}
+