path: root/basegfx/source/tools/gradienttools.cxx

/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
 * This file is part of the LibreOffice project.
 *
 * This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/.
 *
 * This file incorporates work covered by the following license notice:
 *
 *   Licensed to the Apache Software Foundation (ASF) under one or more
 *   contributor license agreements. See the NOTICE file distributed
 *   with this work for additional information regarding copyright
 *   ownership. The ASF licenses this file to you 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 .
 */

#include <basegfx/utils/gradienttools.hxx>
#include <basegfx/point/b2dpoint.hxx>
#include <basegfx/range/b2drange.hxx>
#include <basegfx/matrix/b2dhommatrixtools.hxx>
#include <com/sun/star/awt/Gradient2.hpp>
#include <osl/endian.h>

#include <algorithm>
#include <cmath>

namespace basegfx
{
    bool ODFGradientInfo::operator==(const ODFGradientInfo& rODFGradientInfo) const
    {
        return getTextureTransform() == rODFGradientInfo.getTextureTransform()
            && getAspectRatio() == rODFGradientInfo.getAspectRatio()
            && getRequestedSteps() == rODFGradientInfo.getRequestedSteps();
    }

    const B2DHomMatrix& ODFGradientInfo::getBackTextureTransform() const
    {
        if(maBackTextureTransform.isIdentity())
        {
            const_cast< ODFGradientInfo* >(this)->maBackTextureTransform = getTextureTransform();
            const_cast< ODFGradientInfo* >(this)->maBackTextureTransform.invert();
        }

        return maBackTextureTransform;
    }

    /** Most of the setup for linear & axial gradient is the same, except
        for the border treatment. Factored out here.
    */
    static ODFGradientInfo init1DGradientInfo(
        const B2DRange& rTargetRange,
        sal_uInt32 nSteps,
        double fBorder,
        double fAngle,
        bool bAxial)
    {
        B2DHomMatrix aTextureTransform;

        fAngle = -fAngle;

        double fTargetSizeX(rTargetRange.getWidth());
        double fTargetSizeY(rTargetRange.getHeight());
        double fTargetOffsetX(rTargetRange.getMinX());
        double fTargetOffsetY(rTargetRange.getMinY());

        // add object expansion
        const bool bAngleUsed(!fTools::equalZero(fAngle));

        if(bAngleUsed)
        {
            const double fAbsCos(fabs(cos(fAngle)));
            const double fAbsSin(fabs(sin(fAngle)));
            const double fNewX(fTargetSizeX * fAbsCos + fTargetSizeY * fAbsSin);
            const double fNewY(fTargetSizeY * fAbsCos + fTargetSizeX * fAbsSin);

            fTargetOffsetX -= (fNewX - fTargetSizeX) / 2.0;
            fTargetOffsetY -= (fNewY - fTargetSizeY) / 2.0;
            fTargetSizeX = fNewX;
            fTargetSizeY = fNewY;
        }

        const double fSizeWithoutBorder(1.0 - fBorder);

        if(bAxial)
        {
            aTextureTransform.scale(1.0, fSizeWithoutBorder * 0.5);
            aTextureTransform.translate(0.0, 0.5);
        }
        else
        {
            if(!fTools::equal(fSizeWithoutBorder, 1.0))
            {
                aTextureTransform.scale(1.0, fSizeWithoutBorder);
                aTextureTransform.translate(0.0, fBorder);
            }
        }

        aTextureTransform.scale(fTargetSizeX, fTargetSizeY);

        // add texture rotate after scale to keep perpendicular angles
        if(bAngleUsed)
        {
            const B2DPoint aCenter(0.5 * fTargetSizeX, 0.5 * fTargetSizeY);

            aTextureTransform *= basegfx::utils::createRotateAroundPoint(aCenter, fAngle);
        }

        // add object translate
        aTextureTransform.translate(fTargetOffsetX, fTargetOffsetY);

        // prepare aspect for texture
        const double fAspectRatio(fTools::equalZero(fTargetSizeY) ?  1.0 : fTargetSizeX / fTargetSizeY);

        return ODFGradientInfo(aTextureTransform, fAspectRatio, nSteps);
    }

    /** Most of the setup for radial & ellipsoidal gradient is the same,
        except for the border treatment. Factored out here.
    */
    static ODFGradientInfo initEllipticalGradientInfo(
        const B2DRange& rTargetRange,
        const B2DVector& rOffset,
        sal_uInt32 nSteps,
        double fBorder,
        double fAngle,
        bool bCircular)
    {
        B2DHomMatrix aTextureTransform;

        fAngle = -fAngle;

        double fTargetSizeX(rTargetRange.getWidth());
        double fTargetSizeY(rTargetRange.getHeight());
        double fTargetOffsetX(rTargetRange.getMinX());
        double fTargetOffsetY(rTargetRange.getMinY());

        // add object expansion
        if(bCircular)
        {
            const double fOriginalDiag(std::hypot(fTargetSizeX, fTargetSizeY));

            fTargetOffsetX -= (fOriginalDiag - fTargetSizeX) / 2.0;
            fTargetOffsetY -= (fOriginalDiag - fTargetSizeY) / 2.0;
            fTargetSizeX = fOriginalDiag;
            fTargetSizeY = fOriginalDiag;
        }
        else
        {
            fTargetOffsetX -= ((M_SQRT2 - 1) / 2.0 ) * fTargetSizeX;
            fTargetOffsetY -= ((M_SQRT2 - 1) / 2.0 ) * fTargetSizeY;
            fTargetSizeX = M_SQRT2 * fTargetSizeX;
            fTargetSizeY = M_SQRT2 * fTargetSizeY;
        }

        const double fHalfBorder((1.0 - fBorder) * 0.5);

        aTextureTransform.scale(fHalfBorder, fHalfBorder);
        aTextureTransform.translate(0.5, 0.5);
        aTextureTransform.scale(fTargetSizeX, fTargetSizeY);

        // add texture rotate after scale to keep perpendicular angles
        if(!bCircular && !fTools::equalZero(fAngle))
        {
            const B2DPoint aCenter(0.5 * fTargetSizeX, 0.5 * fTargetSizeY);

            aTextureTransform *= basegfx::utils::createRotateAroundPoint(aCenter, fAngle);
        }

        // add defined offsets after rotation
        if(!fTools::equal(0.5, rOffset.getX()) || !fTools::equal(0.5, rOffset.getY()))
        {
            // use original target size
            fTargetOffsetX += (rOffset.getX() - 0.5) * rTargetRange.getWidth();
            fTargetOffsetY += (rOffset.getY() - 0.5) * rTargetRange.getHeight();
        }

        // add object translate
        aTextureTransform.translate(fTargetOffsetX, fTargetOffsetY);

        // prepare aspect for texture
        const double fAspectRatio(fTargetSizeY == 0.0 ? 1.0 : (fTargetSizeX / fTargetSizeY));

        return ODFGradientInfo(aTextureTransform, fAspectRatio, nSteps);
    }

    /** Setup for rect & square gradient is exactly the same. Factored out
        here.
    */
    static ODFGradientInfo initRectGradientInfo(
        const B2DRange& rTargetRange,
        const B2DVector& rOffset,
        sal_uInt32 nSteps,
        double fBorder,
        double fAngle,
        bool bSquare)
    {
        B2DHomMatrix aTextureTransform;

        fAngle = -fAngle;

        double fTargetSizeX(rTargetRange.getWidth());
        double fTargetSizeY(rTargetRange.getHeight());
        double fTargetOffsetX(rTargetRange.getMinX());
        double fTargetOffsetY(rTargetRange.getMinY());

        // add object expansion
        if(bSquare)
        {
            const double fSquareWidth(std::max(fTargetSizeX, fTargetSizeY));

            fTargetOffsetX -= (fSquareWidth - fTargetSizeX) / 2.0;
            fTargetOffsetY -= (fSquareWidth - fTargetSizeY) / 2.0;
            fTargetSizeX = fTargetSizeY = fSquareWidth;
        }

        // add object expansion
        const bool bAngleUsed(!fTools::equalZero(fAngle));

        if(bAngleUsed)
        {
            const double fAbsCos(fabs(cos(fAngle)));
            const double fAbsSin(fabs(sin(fAngle)));
            const double fNewX(fTargetSizeX * fAbsCos + fTargetSizeY * fAbsSin);
            const double fNewY(fTargetSizeY * fAbsCos + fTargetSizeX * fAbsSin);

            fTargetOffsetX -= (fNewX - fTargetSizeX) / 2.0;
            fTargetOffsetY -= (fNewY - fTargetSizeY) / 2.0;
            fTargetSizeX = fNewX;
            fTargetSizeY = fNewY;
        }

        const double fHalfBorder((1.0 - fBorder) * 0.5);

        aTextureTransform.scale(fHalfBorder, fHalfBorder);
        aTextureTransform.translate(0.5, 0.5);
        aTextureTransform.scale(fTargetSizeX, fTargetSizeY);

        // add texture rotate after scale to keep perpendicular angles
        if(bAngleUsed)
        {
            const B2DPoint aCenter(0.5 * fTargetSizeX, 0.5 * fTargetSizeY);

            aTextureTransform *= basegfx::utils::createRotateAroundPoint(aCenter, fAngle);
        }

        // add defined offsets after rotation
        if(!fTools::equal(0.5, rOffset.getX()) || !fTools::equal(0.5, rOffset.getY()))
        {
            // use original target size
            fTargetOffsetX += (rOffset.getX() - 0.5) * rTargetRange.getWidth();
            fTargetOffsetY += (rOffset.getY() - 0.5) * rTargetRange.getHeight();
        }

        // add object translate
        aTextureTransform.translate(fTargetOffsetX, fTargetOffsetY);

        // prepare aspect for texture
        const double fAspectRatio(fTargetSizeY == 0.0 ? 1.0 : (fTargetSizeX / fTargetSizeY));

        return ODFGradientInfo(aTextureTransform, fAspectRatio, nSteps);
    }

    namespace utils
    {
        /* Tooling method to extract data from given BGradient
           to ColorStops, doing some corrections, partially based
           on given SingleColor */
        void prepareColorStops(
            const basegfx::BGradient& rGradient,
            BColorStops& rColorStops,
            BColor& rSingleColor)
        {
            if (rGradient.GetColorStops().isSingleColor(rSingleColor))
            {
                // when single color, preserve value in rSingleColor
                // and clear the ColorStops, done.
                rColorStops.clear();
                return;
            }

            const bool bAdaptStartEndIntensity(100 != rGradient.GetStartIntens() || 100 != rGradient.GetEndIntens());
            const bool bAdaptBorder(0 != rGradient.GetBorder());

            if (!bAdaptStartEndIntensity && !bAdaptBorder)
            {
                // copy unchanged ColorStops & done
                rColorStops = rGradient.GetColorStops();
                return;
            }

            // prepare a copy to work on
            basegfx::BGradient aWorkCopy(rGradient);

            if (bAdaptStartEndIntensity)
            {
                aWorkCopy.tryToApplyStartEndIntensity();

                // this can again lead to single color (e.g. both zero, so
                // all black), so check again for it
                if (aWorkCopy.GetColorStops().isSingleColor(rSingleColor))
                {
                    rColorStops.clear();
                    return;
                }
            }

            if (bAdaptBorder)
            {
                aWorkCopy.tryToApplyBorder();
            }

            // extract ColorStops, that's all we need here
            rColorStops = aWorkCopy.GetColorStops();
        }

        /* Tooling method to synchronize the given ColorStops.
           The intention is that a color GradientStops and an
           alpha/transparence GradientStops gets synchronized
           for export. */
        void synchronizeColorStops(
            BColorStops& rColorStops,
            BColorStops& rAlphaStops,
            const BColor& rSingleColor,
            const BColor& rSingleAlpha)
        {
            if (rColorStops.empty())
            {
                if (rAlphaStops.empty())
                {
                    // no AlphaStops and no ColorStops
                    // create two-stop fallbacks for both
                    rColorStops = BColorStops {
                        BColorStop(0.0, rSingleColor),
                        BColorStop(1.0, rSingleColor) };
                    rAlphaStops = BColorStops {
                        BColorStop(0.0, rSingleAlpha),
                        BColorStop(1.0, rSingleAlpha) };
                }
                else
                {
                    // AlphaStops but no ColorStops
                    // create fallback synched with existing AlphaStops
                    for (const auto& cand : rAlphaStops)
                    {
                        rColorStops.emplace_back(cand.getStopOffset(), rSingleColor);
                    }
                }

                // preparations complete, we are done
                return;
            }
            else if (rAlphaStops.empty())
            {
                // ColorStops but no AlphaStops
                // create fallback AlphaStops synched with existing ColorStops using SingleAlpha
                for (const auto& cand : rColorStops)
                {
                    rAlphaStops.emplace_back(cand.getStopOffset(), rSingleAlpha);
                }

                // preparations complete, we are done
                return;
            }

            // here we have ColorStops and AlphaStops not empty. Check if we need to
            // synchronize both or if they are already usable/in a synched state so
            // that they have same count and same StopOffsets
            bool bNeedToSyncronize(rColorStops.size() != rAlphaStops.size());

            if (!bNeedToSyncronize)
            {
                // check for same StopOffsets
                BColorStops::const_iterator aCurrColor(rColorStops.begin());
                BColorStops::const_iterator aCurrAlpha(rAlphaStops.begin());

                while (!bNeedToSyncronize &&
                    aCurrColor != rColorStops.end() &&
                    aCurrAlpha != rAlphaStops.end())
                {
                    if (fTools::equal(aCurrColor->getStopOffset(), aCurrAlpha->getStopOffset()))
                    {
                        aCurrColor++;
                        aCurrAlpha++;
                    }
                    else
                    {
                        bNeedToSyncronize = true;
                    }
                }
            }

            if (bNeedToSyncronize)
            {
                // synchronize sizes & StopOffsets
                BColorStops::const_iterator aCurrColor(rColorStops.begin());
                BColorStops::const_iterator aCurrAlpha(rAlphaStops.begin());
                BColorStops aNewColor;
                BColorStops aNewAlpha;
                BColorStops::BColorStopRange aColorStopRange;
                BColorStops::BColorStopRange aAlphaStopRange;
                bool bRealChange(false);

                do {
                    const bool bColor(aCurrColor != rColorStops.end());
                    const bool bAlpha(aCurrAlpha != rAlphaStops.end());

                    if (bColor && bAlpha)
                    {
                        const double fColorOff(aCurrColor->getStopOffset());
                        const double fAlphaOff(aCurrAlpha->getStopOffset());

                        if (fTools::less(fColorOff, fAlphaOff))
                        {
                            // copy color, create alpha
                            aNewColor.emplace_back(fColorOff, aCurrColor->getStopColor());
                            aNewAlpha.emplace_back(fColorOff, rAlphaStops.getInterpolatedBColor(fColorOff, 0, aAlphaStopRange));
                            bRealChange = true;
                            aCurrColor++;
                        }
                        else if (fTools::more(fColorOff, fAlphaOff))
                        {
                            // copy alpha, create color
                            aNewColor.emplace_back(fAlphaOff, rColorStops.getInterpolatedBColor(fAlphaOff, 0, aColorStopRange));
                            aNewAlpha.emplace_back(fAlphaOff, aCurrAlpha->getStopColor());
                            bRealChange = true;
                            aCurrAlpha++;
                        }
                        else
                        {
                            // equal: copy both, advance
                            aNewColor.emplace_back(fColorOff, aCurrColor->getStopColor());
                            aNewAlpha.emplace_back(fAlphaOff, aCurrAlpha->getStopColor());
                            aCurrColor++;
                            aCurrAlpha++;
                        }
                    }
                    else if (bColor)
                    {
                        const double fColorOff(aCurrColor->getStopOffset());
                        aNewAlpha.emplace_back(fColorOff, rAlphaStops.getInterpolatedBColor(fColorOff, 0, aAlphaStopRange));
                        aNewColor.emplace_back(fColorOff, aCurrColor->getStopColor());
                        bRealChange = true;
                        aCurrColor++;
                    }
                    else if (bAlpha)
                    {
                        const double fAlphaOff(aCurrAlpha->getStopOffset());
                        aNewColor.emplace_back(fAlphaOff, rColorStops.getInterpolatedBColor(fAlphaOff, 0, aColorStopRange));
                        aNewAlpha.emplace_back(fAlphaOff, aCurrAlpha->getStopColor());
                        bRealChange = true;
                        aCurrAlpha++;
                    }
                    else
                    {
                        // no more input, break do..while loop
                        break;
                    }
                }
                while(true);

                if (bRealChange)
                {
                    // copy on 'real' change, that means data was added.
                    // This should always be the cease and should have been
                    // detected as such above, see bNeedToSyncronize
                    rColorStops = aNewColor;
                    rAlphaStops = aNewAlpha; // MCGR: tdf#155537 used wrong result here
                }
            }
        }

        sal_uInt32 calculateNumberOfSteps(
            sal_uInt32 nRequestedSteps,
            const BColor& rStart,
            const BColor& rEnd)
        {
            const sal_uInt32 nMaxSteps(sal_uInt32((rStart.getMaximumDistance(rEnd) * 127.5) + 0.5));

            if (0 == nRequestedSteps)
            {
                nRequestedSteps = nMaxSteps;
            }

            if(nRequestedSteps > nMaxSteps)
            {
                nRequestedSteps = nMaxSteps;
            }

            return std::max(sal_uInt32(1), nRequestedSteps);
        }

        ODFGradientInfo createLinearODFGradientInfo(
            const B2DRange& rTargetArea,
            sal_uInt32 nSteps,
            double fBorder,
            double fAngle)
        {
            return init1DGradientInfo(
                rTargetArea,
                nSteps,
                fBorder,
                fAngle,
                false);
        }

        ODFGradientInfo createAxialODFGradientInfo(
            const B2DRange& rTargetArea,
            sal_uInt32 nSteps,
            double fBorder,
            double fAngle)
        {
            return init1DGradientInfo(
                rTargetArea,
                nSteps,
                fBorder,
                fAngle,
                true);
        }

        ODFGradientInfo createRadialODFGradientInfo(
            const B2DRange& rTargetArea,
            const B2DVector& rOffset,
            sal_uInt32 nSteps,
            double fBorder)
        {
            return initEllipticalGradientInfo(
                rTargetArea,
                rOffset,
                nSteps,
                fBorder,
                0.0,
                true);
        }

        ODFGradientInfo createEllipticalODFGradientInfo(
            const B2DRange& rTargetArea,
            const B2DVector& rOffset,
            sal_uInt32 nSteps,
            double fBorder,
            double fAngle)
        {
            return initEllipticalGradientInfo(
                rTargetArea,
                rOffset,
                nSteps,
                fBorder,
                fAngle,
                false);
        }

        ODFGradientInfo createSquareODFGradientInfo(
            const B2DRange& rTargetArea,
            const B2DVector& rOffset,
            sal_uInt32 nSteps,
            double fBorder,
            double fAngle)
        {
            return initRectGradientInfo(
                rTargetArea,
                rOffset,
                nSteps,
                fBorder,
                fAngle,
                true);
        }

        ODFGradientInfo createRectangularODFGradientInfo(
            const B2DRange& rTargetArea,
            const B2DVector& rOffset,
            sal_uInt32 nSteps,
            double fBorder,
            double fAngle)
        {
            return initRectGradientInfo(
                rTargetArea,
                rOffset,
                nSteps,
                fBorder,
                fAngle,
                false);
        }

        double getLinearGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
        {
            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);

            // Ignore X, this is not needed at all for Y-Oriented gradients
            // if(aCoor.getX() < 0.0 || aCoor.getX() > 1.0)
            // {
            //     return 0.0;
            // }

            if(aCoor.getY() <= 0.0)
            {
                return 0.0; // start value for inside
            }

            if(aCoor.getY() >= 1.0)
            {
                return 1.0; // end value for outside
            }

            return aCoor.getY();
        }

        double getAxialGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
        {
            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);

            // Ignore X, this is not needed at all for Y-Oriented gradients
            //if(aCoor.getX() < 0.0 || aCoor.getX() > 1.0)
            //{
            //    return 0.0;
            //}

            const double fAbsY(fabs(aCoor.getY()));

            if(fAbsY >= 1.0)
            {
                return 1.0; // use end value when outside in Y
            }

            return fAbsY;
        }

        double getRadialGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
        {
            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);

            if(aCoor.getX() < -1.0 || aCoor.getX() > 1.0 || aCoor.getY() < -1.0 || aCoor.getY() > 1.0)
            {
                return 0.0;
            }

            return 1.0 - std::hypot(aCoor.getX(), aCoor.getY());
        }

        double getEllipticalGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
        {
            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);

            if(aCoor.getX() < -1.0 || aCoor.getX() > 1.0 || aCoor.getY() < -1.0 || aCoor.getY() > 1.0)
            {
                return 0.0;
            }

            double fAspectRatio(rGradInfo.getAspectRatio());
            double t(1.0);

            // MCGR: Similar to getRectangularGradientAlpha (please
            // see there) we need to use aspect ratio here. Due to
            // initEllipticalGradientInfo using M_SQRT2 to make this
            // gradient look 'nicer' this correction seems not 100%
            // correct, but is close enough for now
            if(fAspectRatio > 1.0)
            {
                t = 1.0 - std::hypot(aCoor.getX() / fAspectRatio, aCoor.getY());
            }
            else if(fAspectRatio > 0.0)
            {
                t = 1.0 - std::hypot(aCoor.getX(), aCoor.getY() * fAspectRatio);
            }

            return t;
        }

        double getSquareGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
        {
            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
            const double fAbsX(fabs(aCoor.getX()));

            if(fAbsX >= 1.0)
            {
                return 0.0;
            }

            const double fAbsY(fabs(aCoor.getY()));

            if(fAbsY >= 1.0)
            {
                return 0.0;
            }

            return 1.0 - std::max(fAbsX, fAbsY);
        }

        double getRectangularGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
        {
            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
            double fAbsX(fabs(aCoor.getX()));

            if(fAbsX >= 1.0)
            {
                return 0.0;
            }

            double fAbsY(fabs(aCoor.getY()));

            if(fAbsY >= 1.0)
            {
                return 0.0;
            }

            // MCGR: Visualizations using the texturing method for
            // displaying gradients (getBackTextureTransform is
            // involved) show wrong results for GradientElliptical
            // and GradientRect, this can be best seen when using
            // less steps, e.g. just four. This thus has influence
            // on cppcanvas (slideshow) and 3D textures, so needs
            // to be corrected.
            // Missing is to use the aspect ratio of the object
            // in this [-1, -1, 1, 1] unified coordinate space
            // after getBackTextureTransform is applied. Optically
            // in the larger direction of the texturing the color
            // step distances are too big *because* we are in that
            // unit range now.
            // To correct that, a kind of 'limo stretching' needs to
            // be applied, adding space around the center
            // proportional to the aspect ratio, so the intuitive
            // idea would be to do
            //
            // fAbsX' = ((fAspectRatio - 1) + fAbsX) / fAspectRatio
            //
            // which scales from the center. This does not work, and
            // after some thoughts it's clear why: It's not the
            // position that needs to be moved (this cannot be
            // changed), but the position *before* that scale has
            // to be determined to get the correct, shifted color
            // for the already 'new' position. Thus, turn around
            // the expression as
            //
            // fAbsX' * fAspectRatio = fAspectRatio - 1 + fAbsX
            // fAbsX' * fAspectRatio - fAspectRatio + 1 = fAbsX
            // fAbsX = (fAbsX' - 1) * fAspectRatio + 1
            //
            // This works and can even be simply adapted for
            // fAspectRatio < 1.0 aka vertical is bigger.
            double fAspectRatio(rGradInfo.getAspectRatio());
            if(fAspectRatio > 1.0)
            {
                fAbsX = ((fAbsX - 1) * fAspectRatio) + 1;
            }
            else if(fAspectRatio > 0.0)
            {
                fAbsY = ((fAbsY - 1) / fAspectRatio) + 1;
            }

            return 1.0 - std::max(fAbsX, fAbsY);
        }
    } // namespace utils
} // namespace basegfx

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