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• Blend_SCREEN.jsl

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/*
 * Copyright (c) 2011, 2013, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

//res = 1 - (1-b)(1-t)
//res = 1 - (1-b-t+bt)
//res = 1 - 1+b+t-bt
//res = b+t-bt
// Note that when alpha is zero, then the values in t and b are 0.0 which
// means the values in the expressions (1-t) and (1-b) end up being 1.0.
// These values naturally cause smaller alphas to affect the result less
// and less without any adjustments:
// As t.a => 0:
//   res = 1 - (1-b)*1 = 1-1+b = b
//   res = b + 0 - b*0 = b
// And as b.a => 0:
//   res = 1 - 1*(1-t) = 1-1+t = t
//   res = 0 + t - 0*t = t
// Another way to prove this is that it is the application of the multiply
// equation (A) above on (t.a - t.rgb) and (b.a - b.rgb) and the result
// again inverted against res.a, thus we get:
//   res.C = res.a - [mul(bot.a - bot.C, top.a - top.C)]
//   res.C = res.a - (top.a-top.C)*((bot.a-bot.C) + 1 - bot.a)
//                 - (bot.a-bot.C)*(1 - top.a)
//   res.C = rA - (tA-tC)(bA-bC+1-bA) - (bA-bC)(1-tA)
//   res.C = rA - (tA-tC)(1-bC) - (bA-bC)(1-tA)
//   res.C = rA - tA + tC + tAbC - bCtC - bA + bC + bAtA - tAbC
//   res.C = rA - bA - tA + bAtA + bC + tC - bCtC
//   res.A = bA + tA - bAtA
//   res.C = bA+tA-bAtA - bA - tA + bAtA + bC + tC - bCtC
//   res.C = bC + tC - bCtC
float4 blend_screen(float4 bot, float4 top)
{
    return bot + top - bot * top;
}