• osg实现三次样条Cardinal曲线

    目录

    1. 前言

    2. 预备知识

    3. Qt实现的二维Cardinal曲线

    4. 用osg实现三维Cardinal曲线

     4.1. 工具/ 原料

     4.2. 代码实现

    1. 前言

           在设计矢量图案的时候，我们常常需要用到曲线来表达物体造型，单纯用鼠标轨迹绘制显然是不足的。于是我们希望能够实现这样的方法：通过设计师手工选择控制点，再通过插值得到过控制点（或在附近）的一条平滑曲线。在这样的需求下，样条曲线诞生了。简而言之，样条曲线是由多个多项式按比例系数组成的多项式函数，而比例系数是由控制点决定的。Hermite曲线、Cardinal曲线在平时的开发中，经常用于模拟运动物体的轨迹，如下：

    以上是二维下的Cardinal曲线效果，如何用osg实现 三维的Cardinal曲线呢？即像下面那样：

    即：

    1. 单击“拾取点”按钮，该按钮文字变为“关闭拾取点”，此时可以用鼠标在棋盘格上单击，点击的点用红色圆圈表示。
    2. 当所有的点都拾取完，单击“绘制”，可以绘制三维Cardinal曲线。
    3. 当绘制完三维Cardinal曲线后，再次用鼠标在棋盘格上单击，单击“绘制”，可以绘制新的三维Cardinal曲线。
    4. 单击“关闭拾取点”按钮，鼠标在棋盘格上单击时，无法拾取点。
    5. 调整阈值，可以更改曲线的圆弧度，使曲线从圆滑变为直线。

    2. 预备知识

           关于Hermite曲线、Cardinal曲线的数学理论，参见如下博文：

    3. Qt实现的二维Cardinal曲线

           如下博文为Qt实现的二维Cardinal曲线：

    Qt实现三次样条Cardinal曲线

    4. 用osg实现三维Cardinal曲线

     4.1. 工具/ 原料

    开发环境如下：

    • Qt 5.14.1。
    • Visual Studio 2022。
    • OpenSceneGraph 3.6.2。

     4.2. 代码实现

    main.cpp

    1. #include "osgCardinal.h"
    2. #include 
    3.  
    4. int main(int argc, char *argv[])
    5. {
    6.     QApplication a(argc, argv);
    7.     osgCardinal w;
    8.     w.show();
    9.     return a.exec();
    10. }

    myEventHandler.cpp

    1. #include "myEventHandler.h"
    2. #include
    3. bool myEventHandler::handle(const osgGA::GUIEventAdapter& ea, 
    4.                             osgGA::GUIActionAdapter& aa, 
    5.                             osg::Object* obj, osg::NodeVisitor* nv)
    6. {
    7.     auto pViewer = dynamic_cast(&aa);
    8.     auto eventType = ea.getEventType();
    9.     switch (eventType)
    10.     {
    11.         case GUIEventAdapter::PUSH:
    12.         {
    13.             if(_bPickPoint && (GUIEventAdapter::LEFT_MOUSE_BUTTON == ea.getButton()))
    14.             {
    15.                 osgUtil::LineSegmentIntersector::Intersections intersections;
    16.                 auto bRet = pViewer->computeIntersections(ea, intersections);
    17.                 if (!bRet) // 判断是否相交
    18.                 {
    19.                     return false;
    20.                 }
    21.  
    22.                 auto iter = intersections.begin();  // 取相交的第1个点
    23.                 auto interPointCoord = iter->getLocalIntersectPoint();
    24.                 _pOsgCardinal->drawEllipse(interPointCoord);
    25.                 
    26.             }
    27.         }
    28.         break;
    29.     } // end switch
    30.  
    31.     return false;
    32. }
    33.  
    34.  
    35. void myEventHandler::setPickPoint(bool bPickPoint)
    36. {
    37.     _bPickPoint = bPickPoint;
    38. }

    myEventHandler.h

    1. #ifndef MYEVENTHANDLER_H
    2. #define MYEVENTHANDLER_H
    3. #include
    4. #include
    5. using namespace osgGA;
    6.  
    7. class myEventHandler:public GUIEventHandler
    8. {
    9. public:
    10.     myEventHandler(osgCardinal* p) { _pOsgCardinal = p; }
    11. public:
    12.  
    13.     void setPickPoint(bool bPickPoint);
    14.  
    15. private:
    16.     virtual bool handle(const osgGA::GUIEventAdapter& ea, 
    17.                         osgGA::GUIActionAdapter& aa, 
    18.                         osg::Object* obj, osg::NodeVisitor* nv) override;
    19.  
    20.  
    21. private:
    22.     bool _bPickPoint{false};
    23.     osgCardinal* _pOsgCardinal{nullptr};
    24. };
    25.  
    26. #endif MYEVENTHANDLER_H
    27.

    osgCardinal.h 

    1. #pragma once
    2.  
    3. #include 
    4. #include "ui_osgCardinal.h"
    5. using std::list;
    6.  
    7. QT_BEGIN_NAMESPACE
    8. namespace Ui { class osgCardinalClass; };
    9. QT_END_NAMESPACE
    10.  
    11. class myEventHandler;
    12.  
    13. class osgCardinal : public QWidget
    14. {
    15.     Q_OBJECT
    16.  
    17. public:
    18.     osgCardinal(QWidget *parent = nullptr);
    19.     ~osgCardinal();
    20.  
    21. public:
    22.  
    23.     // 画点。以小圆表示
    24.     void  drawEllipse(const osg::Vec3d& pt);
    25.  
    26. private:
    27.  
    28.     void addBaseScene();
    29.  
    30.     osg::Geode* createGrid();
    31.  
    32.     void valueChanged(double dfValue);
    33.  
    34.     void startDraw();
    35.  
    36.     void pickPoint();
    37.  
    38.     void clear();
    39.  
    40.     // 计算MC矩阵
    41.     void calMcMatrix(double s);
    42.  
    43.     // 压入头部和尾部两个点，用于计算
    44.     void pushHeadAndTailPoint();
    45.  
    46.     // 画Cardinal曲线
    47.     void drawCardinal();
    48.  
    49.     void drawLines(osg::Vec3Array* pVertArray);
    50. private:
    51.     Ui::osgCardinalClass *ui;
    52.     myEventHandler*_myEventHandler{nullptr};
    53.     bool _startPickPoint{false};
    54.     bool _lastPointHasPoped{ false }; // 最后一个点是否被弹出（删除）
    55.     bool _hasDrawed{ false }; // 以前是否绘制过Cardinal曲线
    56.     double _dfMcMatrix[4][4];
    57.     list _lstInterPoint;
    58.     osg::Vec3Array*_pVertArray{ nullptr };
    59.     osg::Geometry* _pCardinalCurveGemo{ nullptr };
    60. };

    osgCardinal.cpp

    1. #include "osgCardinal.h"
    2. #include"myEventHandler.h"
    3. #include
    4. #include
    5. #include
    6. #include
    7. #include
    8. #include
    9. using std::vector;
    10.  
    11. osgCardinal::osgCardinal(QWidget *parent)
    12.     : QWidget(parent)
    13.     , ui(new Ui::osgCardinalClass())
    14. {
    15.     ui->setupUi(this);
    16.  
    17. 	setWindowState(Qt::WindowMaximized);
    18.  
    19. 	addBaseScene();
    20.  
    21.     ui->doubleSpinBox->setMinimum(0);
    22.     ui->doubleSpinBox->setMaximum(1);
    23.     ui->doubleSpinBox->setValue(0.5);
    24.     ui->doubleSpinBox->setSingleStep(0.1);
    25.  
    26.     connect(ui->doubleSpinBox, QOverload<double>::of(&QDoubleSpinBox::valueChanged), this, &osgCardinal::valueChanged);
    27.     connect(ui->startDrawBtn, &QAbstractButton::clicked, this, &osgCardinal::startDraw);
    28.     connect(ui->clearBtn, &QAbstractButton::clicked, this, &osgCardinal::clear);
    29.     connect(ui->pickPointBtn, &QAbstractButton::clicked, this, &osgCardinal::pickPoint);
    30.     calMcMatrix(0.5);
    31. }
    32.  
    33. osgCardinal::~osgCardinal()
    34. {
    35.     delete ui;
    36. }
    37.  
    38. void osgCardinal::valueChanged(double dfValue)
    39. {
    40.     auto s = (1 - dfValue) / 2.0;
    41.  
    42.     // 计算MC矩阵
    43.     calMcMatrix(s);
    44.  
    45.     drawCardinal();
    46. }
    47.  
    48. // 画点。以小圆表示
    49. void osgCardinal::drawEllipse(const osg::Vec3d& pt)
    50. {
    51.     if (!_lastPointHasPoped && _hasDrawed && !_lstInterPoint.empty())
    52.     {
    53.         _lstInterPoint.pop_back();
    54.         _lastPointHasPoped = true;
    55.     }
    56.  
    57.     _lstInterPoint.emplace_back(pt);
    58.  
    59.     auto pGeometry = new osg::Geometry;
    60.     auto pPgo = new osg::PolygonOffset();
    61.     pPgo->setFactor(-1.0);
    62.     pPgo->setUnits(-1.0);
    63.     pGeometry->getOrCreateStateSet()->setAttributeAndModes(pPgo);
    64.     auto pVertArray = new osg::Vec3Array;
    65.     auto radius = 0.2;
    66.     auto twoPi = 2 * 3.1415926;
    67.     for (auto iAngle = 0.0; iAngle < twoPi; iAngle += 0.001)
    68.     {
    69.         auto x = pt.x() + radius * std::cosf(iAngle);
    70.         auto y = pt.y() + radius * std::sinf(iAngle);
    71.         auto z = pt.z()/* + 0.001*/; // 注意：适当增加点，否则和网格重合了，会导致圆形绘制不正常
    72.         pVertArray->push_back(osg::Vec3d(x, y, z));
    73.     }
    74.  
    75.     pGeometry->setVertexArray(pVertArray);
    76.  
    77.     auto pColorArray = new osg::Vec4Array;
    78.     pColorArray->push_back(osg::Vec4d(1.0, 0.0, 0.0, 1.0));
    79.     pGeometry->setColorArray(pColorArray/*, osg::Array::BIND_OVERALL*/);
    80.     pGeometry->setColorBinding(osg::Geometry::BIND_OVERALL);
    81.  
    82.     pGeometry->addPrimitiveSet(new osg::DrawArrays(GL_POLYGON, 0, pVertArray->size()));
    83.     auto pMatrixTransform =  ui->osg_widget->getSceneData()->asGroup()->getChild(0)->asTransform()->asMatrixTransform();
    84.     pMatrixTransform->addChild(pGeometry);
    85. }
    86.  
    87. void osgCardinal::pickPoint()
    88. {
    89.     _startPickPoint = !_startPickPoint;
    90.     _myEventHandler->setPickPoint(_startPickPoint);
    91.     if (_startPickPoint)
    92.     {
    93.         ui->pickPointBtn->setText(QString::fromLocal8Bit("关闭拾取点"));
    94.     }
    95.     else
    96.     {
    97.         ui->pickPointBtn->setText(QString::fromLocal8Bit("拾取点"));
    98.     }
    99. }
    100.  
    101. void osgCardinal::startDraw()
    102. {
    103.     if (nullptr != _pCardinalCurveGemo) // 如果以前绘制过Cardinal曲线
    104.     {
    105.         /* 在上次绘制Cardinal曲线时，通过pushHeadAndTailPoint()
    106.         *  压入的头部、尾部用户控制的两个点去掉，以重新压入头部、尾部用户控制的两个点
    107.         * ,便于绘制本次曲线
    108.         */
    109.         if (_lstInterPoint.size() >= 0 ) 
    110.         {
    111.             _lstInterPoint.pop_front();
    112.         }
    113.     }
    114.  
    115.     pushHeadAndTailPoint();
    116.  
    117.     drawCardinal();
    118.  
    119.     _hasDrawed = true;
    120. }
    121.  
    122. // 压入头部和尾部两个点，用于计算
    123. void osgCardinal::pushHeadAndTailPoint()
    124. {
    125.     // 随便构造两个点
    126.     auto ptBegin = _lstInterPoint.begin();
    127.     auto x = ptBegin->x() + 20;
    128.     auto y = ptBegin->y() + 20;
    129.     auto z = ptBegin->z();
    130.     _lstInterPoint.insert(_lstInterPoint.begin(), osg::Vec3d(x, y, z));
    131.  
    132.     auto ptEnd = _lstInterPoint.back();
    133.     x = ptEnd.x() + 20;
    134.     y = ptEnd.y() + 20;
    135.     z = ptBegin->z();
    136.     _lstInterPoint.insert(_lstInterPoint.end(), osg::Vec3d(x, y, z));
    137. }
    138.  
    139.  
    140. // 画Cardinal曲线
    141. void osgCardinal::drawCardinal()
    142. {
    143.     if (_lstInterPoint.size() < 4)
    144.     {
    145.         return;
    146.     }
    147.     
    148.     if (nullptr == _pVertArray)
    149.     {
    150.         _pVertArray = new osg::Vec3Array();
    151.     }
    152.     else
    153.     {
    154.         _pVertArray->clear();
    155.     }
    156.  
    157.     auto iter = _lstInterPoint.begin();
    158.     ++iter; // 第1个点（基于0的索引）
    159.     _pVertArray->push_back(*iter);
    160.     --iter;
    161.  
    162.     auto endIter = _lstInterPoint.end();
    163.     int nIndex = 0;
    164.     while (true)
    165.     {
    166.         --endIter;
    167.         ++nIndex;
    168.         if (3 == nIndex)
    169.         {
    170.             break;
    171.         }
    172.     }
    173.  
    174.     for (; iter != endIter; ++iter)
    175.     {
    176.         auto& p0 = *iter;
    177.         auto& p1 = *(++iter);
    178.         auto& p2 = *(++iter);
    179.         auto& p3 = *(++iter);
    180.  
    181.         --iter;
    182.         --iter;
    183.         --iter;
    184.  
    185.         vectorvtTempPoint;
    186.         vtTempPoint.push_back(p0);
    187.         vtTempPoint.push_back(p1);
    188.         vtTempPoint.push_back(p2);
    189.         vtTempPoint.push_back(p3);
    190.  
    191.         for (auto i = 0; i < 4; ++i)
    192.         {
    193.            vtTempPoint[i] = p0 * _dfMcMatrix[i][0]  + p1 * _dfMcMatrix[i][1] + p2 * _dfMcMatrix[i][2] + p3 * _dfMcMatrix[i][3];
    194.         }
    195.  
    196.         float t3, t2, t1, t0;
    197.         for (double t = 0.0; t < 1; t += 0.01)
    198.         {
    199.             t3 = t * t * t; t2 = t * t; t1 = t; t0 = 1;
    200.             osg::Vec3d newPoint;
    201.             newPoint =  vtTempPoint[0] * t3 + vtTempPoint[1] * t2 + vtTempPoint[2] * t1 + vtTempPoint[3] * t0;
    202.             _pVertArray->push_back(newPoint);
    203.         }
    204.     }
    205.  
    206.     drawLines(_pVertArray);
    207. }
    208.  
    209. void osgCardinal::drawLines(osg::Vec3Array* pVertArray)
    210. {
    211.     if (nullptr == _pCardinalCurveGemo)
    212.     {
    213.         _pCardinalCurveGemo = new osg::Geometry;
    214.  
    215.         auto pLineWidth = new osg::LineWidth(50);
    216.         _pCardinalCurveGemo->getOrCreateStateSet()->setAttributeAndModes(pLineWidth);
    217.  
    218.         auto pColorArray = new osg::Vec4Array;
    219.         pColorArray->push_back(osg::Vec4d(0.0, 1.0, 0.0, 1.0));
    220.         _pCardinalCurveGemo->setColorArray(pColorArray/*, osg::Array::BIND_OVERALL*/);
    221.         _pCardinalCurveGemo->setColorBinding(osg::Geometry::BIND_OVERALL);
    222.  
    223.         auto pMatrixTransform = ui->osg_widget->getSceneData()->asGroup()->getChild(0)->asTransform()->asMatrixTransform();
    224.         pMatrixTransform->addChild(_pCardinalCurveGemo);
    225.     }
    226.  
    227.      // 曲线可能变了，先删除上次的曲线
    228.     _pCardinalCurveGemo->removePrimitiveSet(0);
    229.     _pCardinalCurveGemo->setVertexArray(pVertArray);
    230.  
    231.     // 再用新点绘制新曲线
    232.     _pCardinalCurveGemo->addPrimitiveSet(new osg::DrawArrays(GL_LINE_STRIP, 0, pVertArray->size()));
    233. }
    234.  
    235. // 计算MC矩阵
    236. void osgCardinal::calMcMatrix(double s)
    237. {
    238.     _dfMcMatrix[0][0] = -s, _dfMcMatrix[0][1] = 2 - s, _dfMcMatrix[0][2] = s - 2, _dfMcMatrix[0][3] = s;
    239.     _dfMcMatrix[1][0] = 2 * s, _dfMcMatrix[1][1] = s - 3, _dfMcMatrix[1][2] = 3 - 2 * s, _dfMcMatrix[1][3] = -s;
    240.     _dfMcMatrix[2][0] = -s, _dfMcMatrix[2][1] = 0, _dfMcMatrix[2][2] = s, _dfMcMatrix[2][3] = 0;
    241.     _dfMcMatrix[3][0] = 0, _dfMcMatrix[3][1] = 1, _dfMcMatrix[3][2] = 0, _dfMcMatrix[3][3] = 0;
    242. }
    243.  
    244. void osgCardinal::clear()
    245. {
    246.     _lstInterPoint.clear();
    247.     _hasDrawed = false;
    248.     _lastPointHasPoped = false;
    249. }
    250.  
    251. osg::Geode* osgCardinal::createGrid()
    252. {
    253.     auto pGeode = new osg::Geode;
    254.  
    255.     auto pVertArray = new osg::Vec3Array;
    256.     for (auto y = -10; y < 10; ++y)
    257.     {
    258.         for (auto x = -10; x < 10; ++x)
    259.         {
    260.             pVertArray->push_back(osg::Vec3d(x, y, 0.0));
    261.             pVertArray->push_back(osg::Vec3d(x + 1, y, 0.0));
    262.             pVertArray->push_back(osg::Vec3d(x + 1, y + 1, 0.0));
    263.             pVertArray->push_back(osg::Vec3d(x, y + 1, 0.0));
    264.         }
    265.     }
    266.  
    267.     auto iSize = pVertArray->size();
    268.     osg::DrawElementsUShort* pEle{ nullptr };
    269.     osg::Geometry* pGeomerty{ nullptr };
    270.     osg::Vec4Array* pColorArray{ nullptr };
    271.  
    272.     auto nQuardIndex = 0;
    273.     bool bNewLineQuard = true;  // 新的一行四边形
    274.     for (auto iVertIndex = 0; iVertIndex < iSize; ++iVertIndex)
    275.     {
    276.         if (0 == (iVertIndex % 4))
    277.         {
    278.             pEle = new osg::DrawElementsUShort(GL_QUADS);
    279.  
    280.             pGeomerty = new osg::Geometry;
    281.             pGeomerty->getOrCreateStateSet()->setMode(GL_LIGHTING, osg::StateAttribute::OFF);
    282.             pGeomerty->addPrimitiveSet(pEle);
    283.             pGeode->addDrawable(pGeomerty);
    284.  
    285.             pGeomerty->setVertexArray(pVertArray);
    286.             pColorArray = new osg::Vec4Array();
    287.             if (bNewLineQuard)
    288.             {
    289.                 pColorArray->push_back(osg::Vec4d(1.0, 1.0, 1.0, 1.0));
    290.             }
    291.             else
    292.             {
    293.                 pColorArray->push_back(osg::Vec4d(0.0, 0.0, 0.0, 1.0));
    294.             }
    295.  
    296.             ++nQuardIndex;
    297.  
    298.             if (0 != (nQuardIndex % 20))
    299.             {
    300.                 bNewLineQuard = !bNewLineQuard;
    301.             }
    302.  
    303.             pGeomerty->setColorArray(pColorArray, osg::Array::Binding::BIND_PER_PRIMITIVE_SET);
    304.         }
    305.  
    306.         pEle->push_back(iVertIndex);
    307.     } // end for
    308.  
    309.     return pGeode;
    310. }
    311.  
    312. void osgCardinal::addBaseScene()
    313. {
    314.     auto pAxis = osgDB::readRefNodeFile(R"(E:\osg\OpenSceneGraph-Data\axes.osgt)");
    315.     if (nullptr == pAxis)
    316.     {
    317.         OSG_WARN << "axes node is nullpr!";
    318.         return;
    319.     }
    320.  
    321.     auto pRoot = new osg::Group();
    322.     pRoot->getOrCreateStateSet()->setMode(GL_LIGHTING, osg::StateAttribute::OFF);
    323.     auto pMatrixRoot = new osg::MatrixTransform;
    324.     auto pGrid = createGrid();
    325.     pMatrixRoot->addChild(pGrid);
    326.     pMatrixRoot->addChild(pAxis);
    327.     pRoot->addChild(pMatrixRoot);
    328.  
    329.     pMatrixRoot->setMatrix(osg::Matrix::rotate(osg::inDegrees(60.0), osg::Vec3(1, 0, 0)));
    330.  
    331.     ui->osg_widget->setSceneData(pRoot);
    332.     
    333.     // 操控器一定要加上，否则场景不会显示
    334.     ui->osg_widget->setCameraManipulator(new osgGA::TrackballManipulator);
    335.     ui->osg_widget->addEventHandler(new osgViewer::WindowSizeHandler);
    336.     ui->osg_widget->addEventHandler(new osgViewer::StatsHandler);
    337.     _myEventHandler = new myEventHandler(this);
    338.     ui->osg_widget->addEventHandler(_myEventHandler);
    339.  
    340.     // 模拟鼠标滚轮朝向人滚动三次，以便场景离人显得更近些
    341.     for (auto iLoop = 0; iLoop < 3; ++iLoop)
    342.     {
    343.         ui->osg_widget->getEventQueue()->mouseScroll(osgGA::GUIEventAdapter::SCROLL_DOWN);
    344.     }    
    345. }

    说明：

           上述代码drawEllipse的函数中，通过构造osg::PolygonOffset对象，加入了多边形漂移，从而解决了Z冲突问题 ，否则绘制圆形不正常，具体参见：

    如何避免osg绘制场景时因Z冲突导致绘制重影或不正常

          ui->osg_widget是QtOsgView类型指针，QtOsgView.h、QtOsgView.cpp文件参见：osg嵌入到Qt窗体，实现Qt和osg混合编程 博文。

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  • 原文地址：https://blog.csdn.net/danshiming/article/details/133925477