juce_PathStrokeType.cpp

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 /*
  ==============================================================================
 
   This file is part of the JUCE library.
   Copyright (c) 2022 - Raw Material Software Limited
 
   JUCE is an open source library subject to commercial or open-source
   licensing.
 
   By using JUCE, you agree to the terms of both the JUCE 7 End-User License
   Agreement and JUCE Privacy Policy.
 
   End User License Agreement: www.juce.com/juce-7-licence
   Privacy Policy: www.juce.com/juce-privacy-policy
 
   Or: You may also use this code under the terms of the GPL v3 (see
   www.gnu.org/licenses).
 
   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
   DISCLAIMED.
 
  ==============================================================================
*/
 
namespace juce
{
 
PathStrokeType::PathStrokeType (float strokeThickness) noexcept
    : thickness (strokeThickness), jointStyle (mitered), endStyle (butt)
{
}
 
PathStrokeType::PathStrokeType (float strokeThickness, JointStyle joint, EndCapStyle end) noexcept
    : thickness (strokeThickness), jointStyle (joint), endStyle (end)
{
}
 
PathStrokeType::PathStrokeType (const PathStrokeType& other) noexcept
    : thickness (other.thickness),
      jointStyle (other.jointStyle),
      endStyle (other.endStyle)
{
}
 
PathStrokeType& PathStrokeType::operator= (const PathStrokeType& other) noexcept
{
    thickness = other.thickness;
    jointStyle = other.jointStyle;
    endStyle = other.endStyle;
    return *this;
}
 
PathStrokeType::~PathStrokeType() noexcept
{
}
 
bool PathStrokeType::operator== (const PathStrokeType& other) const noexcept
{
    const auto tie = [] (const PathStrokeType& p) { return std::tie (p.thickness, p.jointStyle, p.endStyle); };
    return tie (*this) == tie (other);
}
 
bool PathStrokeType::operator!= (const PathStrokeType& other) const noexcept
{
    return ! operator== (other);
}
 
//==============================================================================
namespace PathStrokeHelpers
{
    struct LineIntersection
    {
        Point<float> point;
        float distanceBeyondLine1EndSquared;
        bool intersects;
    };
 
    static LineIntersection lineIntersection (const float x1, const float y1,
                                              const float x2, const float y2,
                                              const float x3, const float y3,
                                              const float x4, const float y4)
    {
        if (! approximatelyEqual (x2, x3) || ! approximatelyEqual (y2, y3))
        {
            const auto dx1 = x2 - x1;
            const auto dy1 = y2 - y1;
            const auto dx2 = x4 - x3;
            const auto dy2 = y4 - y3;
            const auto divisor = dx1 * dy2 - dx2 * dy1;
 
            if (approximatelyEqual (divisor, 0.0f))
            {
                if (! ((approximatelyEqual (dx1, 0.0f) && approximatelyEqual (dy1, 0.0f))
                       || (approximatelyEqual (dx2, 0.0f) && approximatelyEqual (dy2, 0.0f))))
                {
                    if (approximatelyEqual (dy1, 0.0f) && ! approximatelyEqual (dy2, 0.0f))
                    {
                        const auto along = (y1 - y3) / dy2;
                        const auto intersectionX = x3 + along * dx2;
                        const auto intersectionY = y1;
 
                        const auto distance = square (intersectionX - x2);
                        const auto distanceBeyondLine1EndSquared = (x2 > x1) == (intersectionX < x2)
                                                                 ? -distance
                                                                 : distance;
 
                        return { { intersectionX, intersectionY },
                                 distanceBeyondLine1EndSquared,
                                 along >= 0 && along <= 1.0f };
                    }
 
                    if (approximatelyEqual (dy2, 0.0f) && ! approximatelyEqual (dy1, 0.0f))
                    {
                        const auto along = (y3 - y1) / dy1;
                        const auto intersectionX = x1 + along * dx1;
                        const auto intersectionY = y3;
 
                        const auto distance = square ((along - 1.0f) * dx1);
                        const auto distanceBeyondLine1EndSquared = along < 1.0f ? -distance : distance;
 
                        return { { intersectionX, intersectionY },
                                 distanceBeyondLine1EndSquared,
                                 along >= 0 && along <= 1.0f };
                    }
 
                    if (approximatelyEqual (dx1, 0.0f) && ! approximatelyEqual (dx2, 0.0f))
                    {
                        const auto along = (x1 - x3) / dx2;
                        const auto intersectionX = x1;
                        const auto intersectionY = y3 + along * dy2;
 
                        const auto distance = square (intersectionY - y2);
                        const auto distanceBeyondLine1EndSquared = (y2 > y1) == (intersectionY < y2)
                                                                 ? -distance
                                                                 : distance;
 
                        return { { intersectionX, intersectionY },
                                 distanceBeyondLine1EndSquared,
                                 along >= 0 && along <= 1.0f };
                    }
 
                    if (approximatelyEqual (dx2, 0.0f) && ! approximatelyEqual (dx1, 0.0f))
                    {
                        const auto along = (x3 - x1) / dx1;
                        const auto intersectionX = x3;
                        const auto intersectionY = y1 + along * dy1;
 
                        const auto distance = square ((along - 1.0f) * dy1);
                        const auto distanceBeyondLine1EndSquared = along < 1.0f ? -distance : distance;
 
                        return { { intersectionX, intersectionY },
                                 distanceBeyondLine1EndSquared,
                                 along >= 0 && along <= 1.0f };
                    }
                }
 
                const auto intersectionX = 0.5f * (x2 + x3);
                const auto intersectionY = 0.5f * (y2 + y3);
 
                const auto distanceBeyondLine1EndSquared = 0.0f;
 
                return { { intersectionX, intersectionY },
                         distanceBeyondLine1EndSquared,
                         false };
            }
 
            const auto along = ((y1 - y3) * dx2 - (x1 - x3) * dy2) / divisor;
 
            const auto intersectionX = x1 + along * dx1;
            const auto intersectionY = y1 + along * dy1;
 
            if (along >= 0 && along <= 1.0f)
            {
                const auto along2 = ((y1 - y3) * dx1 - (x1 - x3) * dy1) / divisor;
 
                if (along2 >= 0 && along2 <= 1.0f)
                {
                    return { { intersectionX, intersectionY },
                             0.0f,
                             true };
                }
            }
 
            const auto distance = square (along - 1.0f) * (dx1 * dx1 + dy1 * dy1);
            const auto distanceBeyondLine1EndSquared = along < 1.0f ? -distance : distance;
 
            return { { intersectionX, intersectionY },
                     distanceBeyondLine1EndSquared,
                     false };
        }
 
        return { Point { x2, y2 }, 0.0f, true };
    }
 
    static void addEdgeAndJoint (Path& destPath,
                                 const PathStrokeType::JointStyle style,
                                 const float maxMiterExtensionSquared, const float width,
                                 const float x1, const float y1,
                                 const float x2, const float y2,
                                 const float x3, const float y3,
                                 const float x4, const float y4,
                                 const float midX, const float midY)
    {
        if (style == PathStrokeType::beveled
            || (approximatelyEqual (x3, x4) && approximatelyEqual (y3, y4))
            || (approximatelyEqual (x1, x2) && approximatelyEqual (y1, y2)))
        {
            destPath.lineTo (x2, y2);
            destPath.lineTo (x3, y3);
        }
        else
        {
            const auto intersection = lineIntersection (x1, y1, x2, y2, x3, y3, x4, y4);
 
            // if they intersect, use this point..
            if (intersection.intersects)
            {
                destPath.lineTo (intersection.point);
            }
            else
            {
                if (style == PathStrokeType::mitered)
                {
                    if (0.0f < intersection.distanceBeyondLine1EndSquared
                        && intersection.distanceBeyondLine1EndSquared < maxMiterExtensionSquared)
                    {
                        destPath.lineTo (intersection.point);
                    }
                    else
                    {
                        // the end sticks out too far, so just use a blunt joint
                        destPath.lineTo (x2, y2);
                        destPath.lineTo (x3, y3);
                    }
                }
                else
                {
                    // curved joints
                    float angle1 = std::atan2 (x2 - midX, y2 - midY);
                    float angle2 = std::atan2 (x3 - midX, y3 - midY);
                    const float angleIncrement = 0.1f;
 
                    destPath.lineTo (x2, y2);
 
                    if (std::abs (angle1 - angle2) > angleIncrement)
                    {
                        if (angle2 > angle1 + MathConstants<float>::pi
                             || (angle2 < angle1 && angle2 >= angle1 - MathConstants<float>::pi))
                        {
                            if (angle2 > angle1)
                                angle2 -= MathConstants<float>::twoPi;
 
                            jassert (angle1 <= angle2 + MathConstants<float>::pi);
 
                            angle1 -= angleIncrement;
                            while (angle1 > angle2)
                            {
                                destPath.lineTo (midX + width * std::sin (angle1),
                                                 midY + width * std::cos (angle1));
 
                                angle1 -= angleIncrement;
                            }
                        }
                        else
                        {
                            if (angle1 > angle2)
                                angle1 -= MathConstants<float>::twoPi;
 
                            jassert (angle1 >= angle2 - MathConstants<float>::pi);
 
                            angle1 += angleIncrement;
                            while (angle1 < angle2)
                            {
                                destPath.lineTo (midX + width * std::sin (angle1),
                                                 midY + width * std::cos (angle1));
 
                                angle1 += angleIncrement;
                            }
                        }
                    }
 
                    destPath.lineTo (x3, y3);
                }
            }
        }
    }
 
    static void addLineEnd (Path& destPath,
                            const PathStrokeType::EndCapStyle style,
                            const float x1, const float y1,
                            const float x2, const float y2,
                            const float width)
    {
        if (style == PathStrokeType::butt)
        {
            destPath.lineTo (x2, y2);
        }
        else
        {
            float offx1, offy1, offx2, offy2;
 
            auto dx = x2 - x1;
            auto dy = y2 - y1;
            auto len = juce_hypot (dx, dy);
 
            if (approximatelyEqual (len, 0.0f))
            {
                offx1 = offx2 = x1;
                offy1 = offy2 = y1;
            }
            else
            {
                auto offset = width / len;
                dx *= offset;
                dy *= offset;
 
                offx1 = x1 + dy;
                offy1 = y1 - dx;
                offx2 = x2 + dy;
                offy2 = y2 - dx;
            }
 
            if (style == PathStrokeType::square)
            {
                // square ends
                destPath.lineTo (offx1, offy1);
                destPath.lineTo (offx2, offy2);
                destPath.lineTo (x2, y2);
            }
            else
            {
                // rounded ends
                auto midx = (offx1 + offx2) * 0.5f;
                auto midy = (offy1 + offy2) * 0.5f;
 
                destPath.cubicTo (x1 + (offx1 - x1) * 0.55f, y1 + (offy1 - y1) * 0.55f,
                                  offx1 + (midx - offx1) * 0.45f, offy1 + (midy - offy1) * 0.45f,
                                  midx, midy);
 
                destPath.cubicTo (midx + (offx2 - midx) * 0.55f, midy + (offy2 - midy) * 0.55f,
                                  offx2 + (x2 - offx2) * 0.45f, offy2 + (y2 - offy2) * 0.45f,
                                  x2, y2);
            }
        }
    }
 
    struct Arrowhead
    {
        float startWidth, startLength;
        float endWidth, endLength;
    };
 
    static void addArrowhead (Path& destPath,
                              const float x1, const float y1,
                              const float x2, const float y2,
                              const float tipX, const float tipY,
                              const float width,
                              const float arrowheadWidth)
    {
        Line<float> line (x1, y1, x2, y2);
        destPath.lineTo (line.getPointAlongLine (-(arrowheadWidth / 2.0f - width), 0));
        destPath.lineTo (tipX, tipY);
        destPath.lineTo (line.getPointAlongLine (arrowheadWidth - (arrowheadWidth / 2.0f - width), 0));
        destPath.lineTo (x2, y2);
    }
 
    struct LineSection
    {
        float x1, y1, x2, y2;      // original line
        float lx1, ly1, lx2, ly2;  // the left-hand stroke
        float rx1, ry1, rx2, ry2;  // the right-hand stroke
    };
 
    static void shortenSubPath (Array<LineSection>& subPath, float amountAtStart, float amountAtEnd)
    {
        while (amountAtEnd > 0 && subPath.size() > 0)
        {
            auto& l = subPath.getReference (subPath.size() - 1);
            auto dx = l.rx2 - l.rx1;
            auto dy = l.ry2 - l.ry1;
            auto len = juce_hypot (dx, dy);
 
            if (len <= amountAtEnd && subPath.size() > 1)
            {
                LineSection& prev = subPath.getReference (subPath.size() - 2);
                prev.x2 = l.x2;
                prev.y2 = l.y2;
                subPath.removeLast();
                amountAtEnd -= len;
            }
            else
            {
                auto prop = jmin (0.9999f, amountAtEnd / len);
                dx *= prop;
                dy *= prop;
                l.rx1 += dx;
                l.ry1 += dy;
                l.lx2 += dx;
                l.ly2 += dy;
                break;
            }
        }
 
        while (amountAtStart > 0 && subPath.size() > 0)
        {
            auto& l = subPath.getReference (0);
            auto dx = l.rx2 - l.rx1;
            auto dy = l.ry2 - l.ry1;
            auto len = juce_hypot (dx, dy);
 
            if (len <= amountAtStart && subPath.size() > 1)
            {
                LineSection& next = subPath.getReference (1);
                next.x1 = l.x1;
                next.y1 = l.y1;
                subPath.remove (0);
                amountAtStart -= len;
            }
            else
            {
                auto prop = jmin (0.9999f, amountAtStart / len);
                dx *= prop;
                dy *= prop;
                l.rx2 -= dx;
                l.ry2 -= dy;
                l.lx1 -= dx;
                l.ly1 -= dy;
                break;
            }
        }
    }
 
    static void addSubPath (Path& destPath, Array<LineSection>& subPath,
                            const bool isClosed, const float width, const float maxMiterExtensionSquared,
                            const PathStrokeType::JointStyle jointStyle, const PathStrokeType::EndCapStyle endStyle,
                            const Arrowhead* const arrowhead)
    {
        jassert (subPath.size() > 0);
 
        if (arrowhead != nullptr)
            shortenSubPath (subPath, arrowhead->startLength, arrowhead->endLength);
 
        auto& firstLine = subPath.getReference (0);
 
        auto lastX1 = firstLine.lx1;
        auto lastY1 = firstLine.ly1;
        auto lastX2 = firstLine.lx2;
        auto lastY2 = firstLine.ly2;
 
        if (isClosed)
        {
            destPath.startNewSubPath (lastX1, lastY1);
        }
        else
        {
            destPath.startNewSubPath (firstLine.rx2, firstLine.ry2);
 
            if (arrowhead != nullptr && arrowhead->startWidth > 0.0f)
                addArrowhead (destPath, firstLine.rx2, firstLine.ry2, lastX1, lastY1, firstLine.x1, firstLine.y1,
                              width, arrowhead->startWidth);
            else
                addLineEnd (destPath, endStyle, firstLine.rx2, firstLine.ry2, lastX1, lastY1, width);
        }
 
        for (int i = 1; i < subPath.size(); ++i)
        {
            const LineSection& l = subPath.getReference (i);
 
            addEdgeAndJoint (destPath, jointStyle,
                             maxMiterExtensionSquared, width,
                             lastX1, lastY1, lastX2, lastY2,
                             l.lx1, l.ly1, l.lx2, l.ly2,
                             l.x1, l.y1);
 
            lastX1 = l.lx1;
            lastY1 = l.ly1;
            lastX2 = l.lx2;
            lastY2 = l.ly2;
        }
 
        auto& lastLine = subPath.getReference (subPath.size() - 1);
 
        if (isClosed)
        {
            auto& l = subPath.getReference (0);
 
            addEdgeAndJoint (destPath, jointStyle,
                             maxMiterExtensionSquared, width,
                             lastX1, lastY1, lastX2, lastY2,
                             l.lx1, l.ly1, l.lx2, l.ly2,
                             l.x1, l.y1);
 
            destPath.closeSubPath();
            destPath.startNewSubPath (lastLine.rx1, lastLine.ry1);
        }
        else
        {
            destPath.lineTo (lastX2, lastY2);
 
            if (arrowhead != nullptr && arrowhead->endWidth > 0.0f)
                addArrowhead (destPath, lastX2, lastY2, lastLine.rx1, lastLine.ry1, lastLine.x2, lastLine.y2,
                              width, arrowhead->endWidth);
            else
                addLineEnd (destPath, endStyle, lastX2, lastY2, lastLine.rx1, lastLine.ry1, width);
        }
 
        lastX1 = lastLine.rx1;
        lastY1 = lastLine.ry1;
        lastX2 = lastLine.rx2;
        lastY2 = lastLine.ry2;
 
        for (int i = subPath.size() - 1; --i >= 0;)
        {
            auto& l = subPath.getReference (i);
 
            addEdgeAndJoint (destPath, jointStyle,
                             maxMiterExtensionSquared, width,
                             lastX1, lastY1, lastX2, lastY2,
                             l.rx1, l.ry1, l.rx2, l.ry2,
                             l.x2, l.y2);
 
            lastX1 = l.rx1;
            lastY1 = l.ry1;
            lastX2 = l.rx2;
            lastY2 = l.ry2;
        }
 
        if (isClosed)
        {
            addEdgeAndJoint (destPath, jointStyle,
                             maxMiterExtensionSquared, width,
                             lastX1, lastY1, lastX2, lastY2,
                             lastLine.rx1, lastLine.ry1, lastLine.rx2, lastLine.ry2,
                             lastLine.x2, lastLine.y2);
        }
        else
        {
            // do the last line
            destPath.lineTo (lastX2, lastY2);
        }
 
        destPath.closeSubPath();
    }
 
    static void createStroke (const float thickness, const PathStrokeType::JointStyle jointStyle,
                              const PathStrokeType::EndCapStyle endStyle,
                              Path& destPath, const Path& source,
                              const AffineTransform& transform,
                              const float extraAccuracy, const Arrowhead* const arrowhead)
    {
        jassert (extraAccuracy > 0);
 
        if (thickness <= 0)
        {
            destPath.clear();
            return;
        }
 
        const Path* sourcePath = &source;
        Path temp;
 
        if (sourcePath == &destPath)
        {
            destPath.swapWithPath (temp);
            sourcePath = &temp;
        }
        else
        {
            destPath.clear();
        }
 
        destPath.setUsingNonZeroWinding (true);
 
        const float maxMiterExtensionSquared = 9.0f * thickness * thickness;
        const float width = 0.5f * thickness;
 
        // Iterate the path, creating a list of the
        // left/right-hand lines along either side of it...
        PathFlatteningIterator it (*sourcePath, transform, Path::defaultToleranceForMeasurement / extraAccuracy);
 
        Array<LineSection> subPath;
        subPath.ensureStorageAllocated (512);
        LineSection l;
        l.x1 = 0;
        l.y1 = 0;
 
        const float minSegmentLength = 0.0001f;
 
        while (it.next())
        {
            if (it.subPathIndex == 0)
            {
                if (subPath.size() > 0)
                {
                    addSubPath (destPath, subPath, false, width, maxMiterExtensionSquared, jointStyle, endStyle, arrowhead);
                    subPath.clearQuick();
                }
 
                l.x1 = it.x1;
                l.y1 = it.y1;
            }
 
            l.x2 = it.x2;
            l.y2 = it.y2;
 
            float dx = l.x2 - l.x1;
            float dy = l.y2 - l.y1;
 
            auto hypotSquared = dx * dx + dy * dy;
 
            if (it.closesSubPath || hypotSquared > minSegmentLength || it.isLastInSubpath())
            {
                auto len = std::sqrt (hypotSquared);
 
                if (approximatelyEqual (len, 0.0f))
                {
                    l.rx1 = l.rx2 = l.lx1 = l.lx2 = l.x1;
                    l.ry1 = l.ry2 = l.ly1 = l.ly2 = l.y1;
                }
                else
                {
                    auto offset = width / len;
                    dx *= offset;
                    dy *= offset;
 
                    l.rx2 = l.x1 - dy;
                    l.ry2 = l.y1 + dx;
                    l.lx1 = l.x1 + dy;
                    l.ly1 = l.y1 - dx;
 
                    l.lx2 = l.x2 + dy;
                    l.ly2 = l.y2 - dx;
                    l.rx1 = l.x2 - dy;
                    l.ry1 = l.y2 + dx;
                }
 
                subPath.add (l);
 
                if (it.closesSubPath)
                {
                    addSubPath (destPath, subPath, true, width, maxMiterExtensionSquared, jointStyle, endStyle, arrowhead);
                    subPath.clearQuick();
                }
                else
                {
                    l.x1 = it.x2;
                    l.y1 = it.y2;
                }
            }
        }
 
        if (subPath.size() > 0)
            addSubPath (destPath, subPath, false, width, maxMiterExtensionSquared, jointStyle, endStyle, arrowhead);
    }
}
 
void PathStrokeType::createStrokedPath (Path& destPath, const Path& sourcePath,
                                        const AffineTransform& transform, float extraAccuracy) const
{
    PathStrokeHelpers::createStroke (thickness, jointStyle, endStyle, destPath, sourcePath,
                                     transform, extraAccuracy, nullptr);
}
 
void PathStrokeType::createDashedStroke (Path& destPath,
                                         const Path& sourcePath,
                                         const float* dashLengths,
                                         int numDashLengths,
                                         const AffineTransform& transform,
                                         float extraAccuracy) const
{
    jassert (extraAccuracy > 0);
 
    if (thickness <= 0)
        return;
 
    Path newDestPath;
    PathFlatteningIterator it (sourcePath, transform, Path::defaultToleranceForMeasurement / extraAccuracy);
 
    bool first = true;
    int dashNum = 0;
    float pos = 0.0f, lineLen = 0.0f, lineEndPos = 0.0f;
    float dx = 0.0f, dy = 0.0f;
 
    for (;;)
    {
        const bool isSolid = ((dashNum & 1) == 0);
        const float dashLen = dashLengths [dashNum++ % numDashLengths];
 
        jassert (dashLen >= 0); // must be a positive increment!
        if (dashLen <= 0)
            continue;
 
        pos += dashLen;
 
        while (pos > lineEndPos)
        {
            if (! it.next())
            {
                if (isSolid && ! first)
                    newDestPath.lineTo (it.x2, it.y2);
 
                createStrokedPath (destPath, newDestPath, AffineTransform(), extraAccuracy);
                return;
            }
 
            if (isSolid && ! first)
                newDestPath.lineTo (it.x1, it.y1);
            else
                newDestPath.startNewSubPath (it.x1, it.y1);
 
            dx = it.x2 - it.x1;
            dy = it.y2 - it.y1;
            lineLen = juce_hypot (dx, dy);
            lineEndPos += lineLen;
            first = it.closesSubPath;
        }
 
        const float alpha = (pos - (lineEndPos - lineLen)) / lineLen;
 
        if (isSolid)
            newDestPath.lineTo (it.x1 + dx * alpha,
                                it.y1 + dy * alpha);
        else
            newDestPath.startNewSubPath (it.x1 + dx * alpha,
                                         it.y1 + dy * alpha);
    }
}
 
void PathStrokeType::createStrokeWithArrowheads (Path& destPath,
                                                 const Path& sourcePath,
                                                 const float arrowheadStartWidth, const float arrowheadStartLength,
                                                 const float arrowheadEndWidth, const float arrowheadEndLength,
                                                 const AffineTransform& transform,
                                                 const float extraAccuracy) const
{
    PathStrokeHelpers::Arrowhead head;
    head.startWidth = arrowheadStartWidth;
    head.startLength = arrowheadStartLength;
    head.endWidth = arrowheadEndWidth;
    head.endLength = arrowheadEndLength;
 
    PathStrokeHelpers::createStroke (thickness, jointStyle, endStyle,
                                     destPath, sourcePath, transform, extraAccuracy, &head);
}
 
} // namespace juce