osg实现物体沿着控制点生成的Cardinal样条轨迹曲线运动

本文主要是介绍osg实现物体沿着控制点生成的Cardinal样条轨迹曲线运动，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

目录

1. 前言

2. 预备知识

3. 用osg实现三维Cardinal曲线

 3.1. 工具/ 原料

 3.2. 代码实现

4. 说明

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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Cardinal曲线效果，如何用osg实现三维的Cardinal曲线，且物体（本例指球体）沿着Cardinal曲线运动呢？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，可以更改曲线的圆滑度，使曲线从圆滑变为直线。
6.  单击“运动”按钮，生成一个蓝色的球体，且该球体沿着Cardinal曲线运动。

2. 预备知识

      在阅读本博文之前，请阅读以下博文，否则很难看懂本博文。

• [计算机动画] 路径曲线与运动物体控制（Cardinal样条曲线）。
• 三次参数样条曲线与Cardinal曲线。
• Qt实现三次样条Cardinal曲线。
• osg实现三次样条Cardinal曲线。

3. 用osg实现三维Cardinal曲线

 3.1. 工具/ 原料

开发环境如下：

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

 3.2. 代码实现

main.cpp 

#include "osgCardinal.h"
#include <QtWidgets/QApplication>int main(int argc, char *argv[])
{QApplication a(argc, argv);osgCardinal w;w.show();return a.exec();
}

myEventHandler.cpp

#include "myEventHandler.h"
#include<osgViewer/Viewer>
bool myEventHandler::handle(const osgGA::GUIEventAdapter& ea, osgGA::GUIActionAdapter& aa, osg::Object* obj, osg::NodeVisitor* nv)
{auto pViewer = dynamic_cast<osgViewer::Viewer*>(&aa);auto eventType = ea.getEventType();switch (eventType){case GUIEventAdapter::PUSH:{if(_bPickPoint && (GUIEventAdapter::LEFT_MOUSE_BUTTON == ea.getButton())){osgUtil::LineSegmentIntersector::Intersections intersections;auto bRet = pViewer->computeIntersections(ea, intersections);if (!bRet) // 判断是否相交{return false;}auto iter = intersections.begin();  // 取相交的第1个点auto interPointCoord = iter->getLocalIntersectPoint();_pOsgCardinal->drawEllipse(interPointCoord);}}break;} // end switchreturn false;
}void myEventHandler::setPickPoint(bool bPickPoint)
{_bPickPoint = bPickPoint;
}

myEventHandler.h

#ifndef MYEVENTHANDLER_H
#define MYEVENTHANDLER_H
#include<osgGA/GUIEventHandler>
#include<osgCardinal.h>
using namespace osgGA;class myEventHandler:public GUIEventHandler
{
public:myEventHandler(osgCardinal* p) { _pOsgCardinal = p; }
public:void setPickPoint(bool bPickPoint);private:virtual bool handle(const osgGA::GUIEventAdapter& ea, osgGA::GUIActionAdapter& aa, osg::Object* obj, osg::NodeVisitor* nv) override;private:bool _bPickPoint{false};osgCardinal* _pOsgCardinal{nullptr};
};#endif MYEVENTHANDLER_H

osgCardinal.h 

#pragma once#include <QtWidgets/QWidget>
#include "ui_osgCardinal.h"
using std::list;QT_BEGIN_NAMESPACE
namespace Ui { class osgCardinalClass; };
QT_END_NAMESPACEclass myEventHandler;class osgCardinal : public QWidget
{Q_OBJECTpublic:osgCardinal(QWidget *parent = nullptr);~osgCardinal();public:// 画点。以小圆表示void  drawEllipse(const osg::Vec3d& pt);private:void motion();// 生成一个球osg::Geode* createSphere();void addBaseScene();osg::Geode* createGrid();void valueChanged(double dfValue);void startDraw();void pickPoint();void clear();// 计算MC矩阵void calMcMatrix(double s);// 压入头部和尾部两个点，用于计算void pushHeadAndTailPoint();// 画Cardinal曲线void drawCardinal();void drawLines(osg::Vec3Array* pVertArray);// 创建球动画路径osg::AnimationPath* createSphereAnimationPath();// 插入控制点到动画路径void insertCtrlPoint(const osg::Vec3d&currrentPoint , const osg::Vec3d& nextPoint, osg::AnimationPath* sphereAnimationPath, double time);
private:Ui::osgCardinalClass *ui;myEventHandler*_myEventHandler{nullptr};bool _startPickPoint{false};bool _lastPointHasPoped{ false }; // 最后一个点是否被弹出（删除）bool _hasDrawed{ false }; // 以前是否绘制过Cardinal曲线double _dfMcMatrix[4][4];list<osg::Vec3d> _lstInterPoint;osg::Vec3Array*_pVertArray{ nullptr };          // 用于保存绘制Cardinal曲线的点的容器osg::Geometry* _pCardinalCurveGemo{ nullptr }; // Cardinal曲线float _radius{0.2};osg::Geode* _pSphere{ nullptr };      // 球osg::AnimationPathCallback* _sphereAnimationPathCb{nullptr}; // 球动画路径回调函数double _twoPi{ 2 * 3.1415926 };
};

osgCardinal.cpp

#include "osgCardinal.h"
#include"myEventHandler.h"
#include<osg/MatrixTransform>
#include<osg/PositionAttitudeTransform>
#include<osg/PolygonMode>
#include<osg/LineWidth>
#include<osg/ShapeDrawable>
#include<osg/PolygonOffset>
#include<vector>
using std::vector;osgCardinal::osgCardinal(QWidget *parent): QWidget(parent), ui(new Ui::osgCardinalClass())
{ui->setupUi(this);setWindowState(Qt::WindowMaximized);addBaseScene();ui->doubleSpinBox->setMinimum(0);ui->doubleSpinBox->setMaximum(1);ui->doubleSpinBox->setValue(0.5);ui->doubleSpinBox->setSingleStep(0.1);connect(ui->doubleSpinBox, QOverload<double>::of(&QDoubleSpinBox::valueChanged), this, &osgCardinal::valueChanged);connect(ui->startDrawBtn, &QAbstractButton::clicked, this, &osgCardinal::startDraw);connect(ui->clearBtn, &QAbstractButton::clicked, this, &osgCardinal::clear);connect(ui->pickPointBtn, &QAbstractButton::clicked, this, &osgCardinal::pickPoint);connect(ui->motionBtn, &QAbstractButton::clicked, this, &osgCardinal::motion);calMcMatrix(0.5);
}osgCardinal::~osgCardinal()
{delete ui;
}// 生成一个球
osg::Geode* osgCardinal::createSphere()
{if (_lstInterPoint.size() < 2){return nullptr;}auto it = _lstInterPoint.begin(); ++it; // 越过人为插入的控制点auto center = osg::Vec3(0, 0, 0)/**it*/;center.z() += _radius;auto pSphere = new osg::Sphere(center, _radius);auto pSphereGeode = new osg::Geode();auto pTlh = new osg::TessellationHints();pTlh->setDetailRatio(0.5);auto pSphereDrawable = new osg::ShapeDrawable(pSphere, pTlh);pSphereDrawable->setColor(osg::Vec4(0.0, 0.0, 1.0, 1.0));pSphereGeode->addDrawable(pSphereDrawable);return pSphereGeode;
}// 插入控制点到动画路径
void osgCardinal::insertCtrlPoint(const osg::Vec3d& currrentPoint, const osg::Vec3d&nextPoint , osg::AnimationPath* sphereAnimationPath, double time)
{auto angle = atan2f((nextPoint.y() - currrentPoint.y()), (nextPoint.x() - currrentPoint.x()));if (angle < 0){angle = _twoPi + angle;}osg::Quat quat(angle, osg::Vec3(0, 0, 1));osg::AnimationPath::ControlPoint ctrlPoint(currrentPoint, quat);sphereAnimationPath->insert(time, ctrlPoint);
}// 创建球动画路径
osg::AnimationPath* osgCardinal::createSphereAnimationPath()
{auto sphereAnimationPath = new osg::AnimationPath();sphereAnimationPath->setLoopMode(osg::AnimationPath::NO_LOOPING);double time = 0.0;for (auto iPointIndex = 0; iPointIndex < _pVertArray->size() - 2; ++iPointIndex){auto currrentPoint = (*_pVertArray)[iPointIndex];auto nextPoint = (*_pVertArray)[iPointIndex + 1];     // 下一个点insertCtrlPoint(currrentPoint, nextPoint, sphereAnimationPath, time);time += 0.02;}// 最后一个点auto currrentPoint = (*_pVertArray)[_pVertArray->size() - 1];auto prevPoint = (*_pVertArray)[_pVertArray->size() - 2];insertCtrlPoint(prevPoint, currrentPoint, sphereAnimationPath, time);return sphereAnimationPath;
}void osgCardinal::motion()
{// Cardinal曲线还未生成if (nullptr == _pVertArray){return;}auto pMatrixTransform = ui->osg_widget->getSceneData()->asGroup()->getChild(0)->asTransform()->asMatrixTransform();_pSphere = createSphere();auto sphereAnimationPath = createSphereAnimationPath();osg::ref_ptr<osg::PositionAttitudeTransform> pat = new osg::PositionAttitudeTransform();pat->setPosition((*_pVertArray)[0]); // 鼠标按下的第1个点pat->removeChild(_pSphere); // 删除上次生成的球_sphereAnimationPathCb = new osg::AnimationPathCallback(sphereAnimationPath, 0.0);if (nullptr != _sphereAnimationPathCb){_pSphere->removeUpdateCallback(_sphereAnimationPathCb);}pat->setUpdateCallback(_sphereAnimationPathCb);pat->addChild(_pSphere);pMatrixTransform->addChild(pat);
}void osgCardinal::valueChanged(double dfValue)
{auto s = (1 - dfValue) / 2.0;// 计算MC矩阵calMcMatrix(s);drawCardinal();
}// 画点。以小圆表示
void osgCardinal::drawEllipse(const osg::Vec3d& pt)
{if (!_lastPointHasPoped && _hasDrawed && !_lstInterPoint.empty()){/* 在上次绘制Cardinal曲线时，通过pushHeadAndTailPoint()*  压入的尾部用户控制点去掉，以便在开始绘制函数（参见startDraw）中重新压入尾部用户控制点* ,便于绘制本次曲线*/_lstInterPoint.pop_back();_lastPointHasPoped = true;}_lstInterPoint.emplace_back(pt);auto pGeometry = new osg::Geometry;// 注意：为了防止Z值冲突，为几何体设置多边形偏移属性。具体参见：https://blog.csdn.net/danshiming/article/details/133958200?spm=1001.2014.3001.5502auto pPgo = new osg::PolygonOffset();pPgo->setFactor(-1.0);pPgo->setUnits(-1.0);pGeometry->getOrCreateStateSet()->setAttributeAndModes(pPgo);auto pVertArray = new osg::Vec3Array;_radius = 0.2;auto twoPi = 2 * 3.1415926;for (auto iAngle = 0.0; iAngle < twoPi; iAngle += 0.001){auto x = pt.x() + _radius * std::cosf(iAngle);auto y = pt.y() + _radius * std::sinf(iAngle);// 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auto z = pt.z()/* + 0.001*/; pVertArray->push_back(osg::Vec3d(x, y, z));}pGeometry->setVertexArray(pVertArray);auto pColorArray = new osg::Vec4Array;pColorArray->push_back(osg::Vec4d(1.0, 0.0, 0.0, 1.0));pGeometry->setColorArray(pColorArray/*, osg::Array::BIND_OVERALL*/);pGeometry->setColorBinding(osg::Geometry::BIND_OVERALL);pGeometry->addPrimitiveSet(new osg::DrawArrays(GL_POLYGON, 0, pVertArray->size()));auto pMatrixTransform =  ui->osg_widget->getSceneData()->asGroup()->getChild(0)->asTransform()->asMatrixTransform();pMatrixTransform->addChild(pGeometry);
}void osgCardinal::pickPoint()
{_startPickPoint = !_startPickPoint;_myEventHandler->setPickPoint(_startPickPoint);if (_startPickPoint){ui->pickPointBtn->setText(QString::fromLocal8Bit("关闭拾取点"));}else{ui->pickPointBtn->setText(QString::fromLocal8Bit("拾取点"));}
}void osgCardinal::startDraw()
{if (nullptr != _pCardinalCurveGemo) // 如果以前绘制过Cardinal曲线{/* 在上次绘制Cardinal曲线时，通过pushHeadAndTailPoint()*  压入的头部点去掉，以重新压入头部用户控制的两个点* ,便于绘制本次曲线*/if (_lstInterPoint.size() >= 0 ) {_lstInterPoint.pop_front();}}pushHeadAndTailPoint();drawCardinal();_hasDrawed = true;
}// 压入头部和尾部两个点，用于计算
void osgCardinal::pushHeadAndTailPoint()
{// 随便构造两个点auto ptBegin = _lstInterPoint.begin();auto x = ptBegin->x() + 20;auto y = ptBegin->y() + 20;auto z = ptBegin->z();_lstInterPoint.insert(_lstInterPoint.begin(), osg::Vec3d(x, y, z));auto ptEnd = _lstInterPoint.back();x = ptEnd.x() + 20;y = ptEnd.y() + 20;z = ptBegin->z();_lstInterPoint.insert(_lstInterPoint.end(), osg::Vec3d(x, y, z));
}// 画Cardinal曲线
void osgCardinal::drawCardinal()
{if (_lstInterPoint.size() < 4){return;}if (nullptr == _pVertArray){_pVertArray = new osg::Vec3Array();}else{_pVertArray->clear();}auto iter = _lstInterPoint.begin();++iter; // 第1个点（基于0的索引）_pVertArray->push_back(*iter);--iter;auto endIter = _lstInterPoint.end();int nIndex = 0;while (true){--endIter;++nIndex;if (3 == nIndex){break;}}for (; iter != endIter; ++iter){auto& p0 = *iter;auto& p1 = *(++iter);auto& p2 = *(++iter);auto& p3 = *(++iter);--iter;--iter;--iter;vector<osg::Vec3d>vtTempPoint;vtTempPoint.push_back(p0);vtTempPoint.push_back(p1);vtTempPoint.push_back(p2);vtTempPoint.push_back(p3);for (auto i = 0; i < 4; ++i){vtTempPoint[i] = p0 * _dfMcMatrix[i][0]  + p1 * _dfMcMatrix[i][1] + p2 * _dfMcMatrix[i][2] + p3 * _dfMcMatrix[i][3];}float t3, t2, t1, t0;for (double t = 0.0; t < 1; t += 0.01){t3 = t * t * t; t2 = t * t; t1 = t; t0 = 1;osg::Vec3d newPoint;newPoint =  vtTempPoint[0] * t3 + vtTempPoint[1] * t2 + vtTempPoint[2] * t1 + vtTempPoint[3] * t0;_pVertArray->push_back(newPoint);}}drawLines(_pVertArray);
}void osgCardinal::drawLines(osg::Vec3Array* pVertArray)
{if (nullptr == _pCardinalCurveGemo){_pCardinalCurveGemo = new osg::Geometry;auto pLineWidth = new osg::LineWidth(50);_pCardinalCurveGemo->getOrCreateStateSet()->setAttributeAndModes(pLineWidth);auto pColorArray = new osg::Vec4Array;pColorArray->push_back(osg::Vec4d(0.0, 1.0, 0.0, 1.0));_pCardinalCurveGemo->setColorArray(pColorArray/*, osg::Array::BIND_OVERALL*/);_pCardinalCurveGemo->setColorBinding(osg::Geometry::BIND_OVERALL);auto pMatrixTransform = ui->osg_widget->getSceneData()->asGroup()->getChild(0)->asTransform()->asMatrixTransform();pMatrixTransform->addChild(_pCardinalCurveGemo);}// 曲线可能变了，先删除上次的曲线_pCardinalCurveGemo->removePrimitiveSet(0);_pCardinalCurveGemo->setVertexArray(pVertArray);// 再用新点绘制新曲线_pCardinalCurveGemo->addPrimitiveSet(new osg::DrawArrays(GL_LINE_STRIP, 0, pVertArray->size()));
}// 计算MC矩阵
void osgCardinal::calMcMatrix(double s)
{_dfMcMatrix[0][0] = -s, _dfMcMatrix[0][1] = 2 - s, _dfMcMatrix[0][2] = s - 2, _dfMcMatrix[0][3] = s;_dfMcMatrix[1][0] = 2 * s, _dfMcMatrix[1][1] = s - 3, _dfMcMatrix[1][2] = 3 - 2 * s, _dfMcMatrix[1][3] = -s;_dfMcMatrix[2][0] = -s, _dfMcMatrix[2][1] = 0, _dfMcMatrix[2][2] = s, _dfMcMatrix[2][3] = 0;_dfMcMatrix[3][0] = 0, _dfMcMatrix[3][1] = 1, _dfMcMatrix[3][2] = 0, _dfMcMatrix[3][3] = 0;
}void osgCardinal::clear()
{_lstInterPoint.clear();_hasDrawed = false;_lastPointHasPoped = false;
}osg::Geode* osgCardinal::createGrid()
{auto pGeode = new osg::Geode;auto pVertArray = new osg::Vec3Array;for (auto y = -10; y < 10; ++y){for (auto x = -10; x < 10; ++x){pVertArray->push_back(osg::Vec3d(x, y, 0.0));pVertArray->push_back(osg::Vec3d(x + 1, y, 0.0));pVertArray->push_back(osg::Vec3d(x + 1, y + 1, 0.0));pVertArray->push_back(osg::Vec3d(x, y + 1, 0.0));}}auto iSize = pVertArray->size();osg::DrawElementsUShort* pEle{ nullptr };osg::Geometry* pGeomerty{ nullptr };osg::Vec4Array* pColorArray{ nullptr };auto nQuardIndex = 0;bool bNewLineQuard = true;  // 新的一行四边形for (auto iVertIndex = 0; iVertIndex < iSize; ++iVertIndex){if (0 == (iVertIndex % 4)){pEle = new osg::DrawElementsUShort(GL_QUADS);pGeomerty = new osg::Geometry;pGeomerty->getOrCreateStateSet()->setMode(GL_LIGHTING, osg::StateAttribute::OFF);pGeomerty->addPrimitiveSet(pEle);pGeode->addDrawable(pGeomerty);pGeomerty->setVertexArray(pVertArray);pColorArray = new osg::Vec4Array();if (bNewLineQuard){pColorArray->push_back(osg::Vec4d(1.0, 1.0, 1.0, 1.0));}else{pColorArray->push_back(osg::Vec4d(0.0, 0.0, 0.0, 1.0));}++nQuardIndex;if (0 != (nQuardIndex % 20)){bNewLineQuard = !bNewLineQuard;}pGeomerty->setColorArray(pColorArray, osg::Array::Binding::BIND_PER_PRIMITIVE_SET);}pEle->push_back(iVertIndex);} // end forreturn pGeode;
}void osgCardinal::addBaseScene()
{auto pAxis = osgDB::readRefNodeFile(R"(E:\osg\OpenSceneGraph-Data\axes.osgt)");if (nullptr == pAxis){OSG_WARN << "axes node is nullpr!";return;}auto pRoot = new osg::Group();pRoot->getOrCreateStateSet()->setMode(GL_LIGHTING, osg::StateAttribute::OFF);auto pMatrixRoot = new osg::MatrixTransform;auto pGrid = createGrid();pMatrixRoot->addChild(pGrid);pMatrixRoot->addChild(pAxis);pRoot->addChild(pMatrixRoot);pMatrixRoot->setMatrix(osg::Matrix::rotate(osg::inDegrees(60.0), osg::Vec3(1, 0, 0)));ui->osg_widget->setSceneData(pRoot);ui->osg_widget->setCameraManipulator(new osgGA::TrackballManipulator);ui->osg_widget->addEventHandler(new osgViewer::WindowSizeHandler);ui->osg_widget->addEventHandler(new osgViewer::StatsHandler);_myEventHandler = new myEventHandler(this);ui->osg_widget->addEventHandler(_myEventHandler);// 模拟鼠标滚轮朝向人滚动三次，以便场景离人显得更近些for (auto iLoop = 0; iLoop < 3; ++iLoop){ui->osg_widget->getEventQueue()->mouseScroll(osgGA::GUIEventAdapter::SCROLL_DOWN);}  
}

4. 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

        三维球的运动用到了osg中的动画路径和动画路径控制点，通过控制点来控制小球运动的轨迹，以保持小球始终沿着cardinal曲线运动。

        注意：要想使物体通过动画路径来进行动画，必须将物体作为子节点加入到osg::PositionAttitudeTransform或osg::MatrixTransform，然后调用它们的setUpdateCallback设置动画路径回调函数。直接在物体上调用是不会开启动画的，即如果在本例中像下面代码那样直接对球设置动画回调，则球不会运动：

_pSphere->setUpdateCallback(_sphereAnimationPathCb);

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