变换
1、矩阵具有坐标变换的作用,例如:左乘一个旋转矩阵,实现点的坐标旋转,左乘一个平移矩阵实现,点的平移
2、一个点可以同时串联相乘几个变换矩阵,实现坐标连续变换,根据左乘规则,右边矩阵先作用于点,作用顺序从右往左,例如:C*B*A*point(注:C,B,A分别为变换矩阵,point为一个vector3的位置向量,即点的x,y,z坐标)运算式子,矩阵A先作用于point,其次是B,C
3、QMatrix4x4矩阵类本身就支持translate,rotate,projection等连续变换函数,那么问题来了,这些变换的作用顺序是怎么样的,实际上和上面说的矩阵作用规则是一样的。
顺序是按照后变换,先作用的,具体如下,
matrix.perspective(45,w/h,0.1,100); // 透视矩阵变换
matrix.translate(0.8,0,-5); // 平移变换
matrix.rotate(30,0,1,0) // 绕着y轴旋转30度
matrix*point; // 注:此时这给点是先执行了旋转,再平移,最后透视处理。
// 而不是从上往下顺序,先透视,再平移和旋转
上面代码作用等同于如下代码:
matrix1.perspective(45,w/h,0.1,100); // 用一个单独矩阵,透视矩阵变换
matrix2.translate(0.8,0,-5); // 用另一个单独矩阵,平移变换
matrix3.rotate(30,0,1,0) // 再用一个单独矩阵,绕着y轴旋转30度
matrix1*matrix2*matrix3*point; // 先执行了旋转,再平移,最后透视处理
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版权声明:本文为CSDN博主「biao2488890051」的原创文章,遵循 CC 4.0 BY-SA 版权协议,转载请附上原文出处链接及本声明。
原文链接:https://blog.csdn.net/kangkanglhb88008/article/details/80537544
变换测试代码:
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#ifndef TRIANGLE_H #define TRIANGLE_H #include <QWidget> #include <QGLWidget> #include <QOpenGLShader> #include <QOpenGLShaderProgram> #include <QDebug> #include <QOpenGLFunctions> #include <QOpenGLFunctions_3_3_Core> #include <QTime> #include <QtMath> #include <QTimer> #include <QOpenGLTexture> #include "shader.h" namespace Ui { class Triangle; } class Triangle : public QGLWidget, protected QOpenGLFunctions { Q_OBJECT public: explicit Triangle(); ~Triangle(); public slots: void slotUpdateTimer(); protected: virtual void initializeGL(); virtual void paintGL(); virtual void resizeGL(int w, int h); private: QOpenGLFunctions_3_3_Core *core; QOpenGLTexture *texture1, *texture2; Shader *ourShader; QTime time; QTimer updateTimer; }; #endif // TRIANGLE_H
triangle.cpp:
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#include "triangle.h" #include "ui_triangle.h" GLuint VBO, VAO, EBO; Triangle::Triangle() { } Triangle::~Triangle() { delete ourShader; core->glDeleteVertexArrays(1, &VAO); core->glDeleteBuffers(1, &VBO); core->glDeleteBuffers(1, &EBO); texture1->destroy(); texture2->destroy(); } void Triangle::slotUpdateTimer() { update(); } void Triangle::initializeGL() { //着色器部分 core = QOpenGLContext::currentContext()->versionFunctions<QOpenGLFunctions_3_3_Core>(); if (!core) { qWarning() << "Could not obtain required OpenGL context version"; exit(1); } ourShader = new Shader(":/vertexshader.vert", ":/fragmentshader.frag"); connect(&updateTimer, &QTimer::timeout, this, &Triangle::slotUpdateTimer); //VAO,VBO数据部分 GLfloat vertices[] = { 0.5f, 0.5f, 0.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, // top right //注意新的数据,有纹理单元 0.5f, -0.5f, 0.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, // bottom right -0.5f, -0.5f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, // bottom left -0.5f, 0.5f, 0.0f, 1.0f, 1.0f, 0.0f, 0.0f, 1.0f // top left }; GLuint indices[] = { 0, 1, 3, // first triangle 1, 2, 3 // second triangle }; core->glGenVertexArrays(1, &VAO); core->glGenBuffers(1, &VBO); core->glGenBuffers(1, &EBO); core->glBindVertexArray(VAO); core->glBindBuffer(GL_ARRAY_BUFFER, VBO); core->glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW); core->glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, EBO); core->glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(indices), indices, GL_STATIC_DRAW); //position attribute core->glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 8*sizeof(GLfloat), nullptr); core->glEnableVertexAttribArray(0); //color attribute core->glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 8*sizeof(GLfloat), (void*)(3 * sizeof(float))); core->glEnableVertexAttribArray(1); core->glVertexAttribPointer(2, 2, GL_FLOAT, GL_FALSE, 8*sizeof(GLfloat), (void *)(6*sizeof(float))); core->glEnableVertexAttribArray(2); //纹理1 texture1 = new QOpenGLTexture(QImage(":/box.jpg").mirrored(), QOpenGLTexture::GenerateMipMaps); //直接生成绑定一个2d纹理, 并生成多级纹理MipMaps if(!texture1->isCreated()) { qDebug()<<"Failed to load texture" << endl; } texture1->setWrapMode(QOpenGLTexture::DirectionS, QOpenGLTexture::Repeat); texture1->setWrapMode(QOpenGLTexture::DirectionT, QOpenGLTexture::Repeat); texture1->setMinificationFilter(QOpenGLTexture::Linear); texture1->setMagnificationFilter(QOpenGLTexture::Linear); texture1->setFormat(QOpenGLTexture::RGBFormat); texture2 = new QOpenGLTexture(QImage(":/awesomeface.png").mirrored(), QOpenGLTexture::GenerateMipMaps); //直接生成绑定一个2d纹理, 并生成多级纹理MipMaps if(!texture2->isCreated()) { qDebug()<<"Failed to load texture" << endl; } texture2->setWrapMode(QOpenGLTexture::DirectionS, QOpenGLTexture::Repeat); texture2->setWrapMode(QOpenGLTexture::DirectionT, QOpenGLTexture::Repeat); texture2->setMinificationFilter(QOpenGLTexture::Linear); texture2->setMagnificationFilter(QOpenGLTexture::Linear); texture2->setFormat(QOpenGLTexture::RGBFormat); ourShader->use(); ourShader->shaderProgram.setUniformValue("texture1", 0); ourShader->shaderProgram.setUniformValue("texture2", 1); time.start(); // updateTimer.start(20); } void Triangle::paintGL() { core->glClearColor(0.2f, 0.3f, 0.3f, 1.0f); core->glClear(GL_COLOR_BUFFER_BIT); ourShader->use(); core->glActiveTexture(GL_TEXTURE1); texture2->bind(); core->glActiveTexture(GL_TEXTURE0); texture1->bind(); QMatrix4x4 transform; transform.translate(QVector3D(0.5f, -0.5f, 0.0f)); transform.rotate((float)time.elapsed()/10, QVector3D(0.0f, 0.0f, 1.0f)); ourShader->use(); ourShader->shaderProgram.setUniformValue(ourShader->shaderProgram.uniformLocation("transform"), transform); core->glBindVertexArray(VAO); core->glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, nullptr); update(); } void Triangle::resizeGL(int w, int h) { core->glViewport(0, 0, w, h); }
shader.h
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#ifndef SHADER_H #define SHADER_H #include <QObject> #include <QDebug> #include <QOpenGLShader> #include <QOpenGLShaderProgram> #include <QString> class Shader : public QObject { Q_OBJECT public: explicit Shader(const QString& vertexSourcePath, const QString &fragmentSourcePath); ~Shader(); QOpenGLShaderProgram shaderProgram; void use() { shaderProgram.bind(); } signals: public slots: }; #endif // SHADER_H
shader.cpp
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#include "shader.h" Shader::Shader(const QString &vertexSourcePath, const QString &fragmentSourcePath) { QOpenGLShader vertexShader(QOpenGLShader::Vertex); bool success = vertexShader.compileSourceFile(vertexSourcePath); if(!success){ qDebug() << "ERROR::SHADER::VERTEX::COMPILATION_FAILED" << endl; qDebug() << vertexShader.log() << endl; } QOpenGLShader fragmentShader(QOpenGLShader::Fragment); success =fragmentShader.compileSourceFile(fragmentSourcePath); if(!success){ qDebug() << "ERROR::SHADER::FRAGMENT::COMPILATION_FAILED" << endl; qDebug() << fragmentShader.log() << endl; } shaderProgram.addShader(&vertexShader); shaderProgram.addShader(&fragmentShader); success = shaderProgram.link(); if(!success){ qDebug() << "ERROR::SHADER::PROGRAM::LINKING_FAILED" << endl; qDebug() << shaderProgram.log() << endl; } } Shader::~Shader() { }
main.cpp
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#include "triangle.h" #include <QApplication> int main(int argc, char *argv[]) { QApplication a(argc, argv); Triangle w; w.show(); return a.exec(); }
fragmentshader.frag
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#version 330 core out vec4 FragColor; in vec3 ourColor; in vec2 TexCoord; uniform sampler2D texture1; uniform sampler2D texture2; void main() { FragColor = mix(texture2D(texture1, TexCoord), texture2D(texture2, TexCoord), 0.2f); }
vertexshader.vert
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#version 330 core layout (location = 0) in vec3 aPos; layout (location = 1) in vec3 aColor; layout (location = 2) in vec2 aTexCoord; out vec3 ourColor; out vec2 TexCoord; uniform mat4 transform; void main(){ gl_Position = transform * vec4(aPos, 1.0f); ourColor = aColor; TexCoord = aTexCoord; }
- 使用应用在箱子上的最后一个变换,尝试将其改变为先旋转,后位移。看看发生了什么,试着想想为什么会发生这样的事情:
void Triangle::paintGL() { core->glClearColor(0.2f, 0.3f, 0.3f, 1.0f); core->glClear(GL_COLOR_BUFFER_BIT); ourShader->use(); core->glActiveTexture(GL_TEXTURE1); texture2->bind(); core->glActiveTexture(GL_TEXTURE0); texture1->bind(); QMatrix4x4 transform; transform.rotate((float)time.elapsed()/10, QVector3D(0.0f, 0.0f, 1.0f)); transform.translate(QVector3D(0.5f, -0.5f, 0.0f)); ourShader->use(); ourShader->shaderProgram.setUniformValue(ourShader->shaderProgram.uniformLocation("transform"), transform); core->glBindVertexArray(VAO); core->glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, nullptr); update(); }
- 尝试再次调用glDrawElements画出第二个箱子,只使用变换将其摆放在不同的位置。让这个箱子被摆放在窗口的左上角,并且会不断的缩放(而不是旋转)。(
sin
函数在这里会很有用,不过注意使用sin
函数时应用负值会导致物体被翻转):void Triangle::paintGL() { core->glClearColor(0.2f, 0.3f, 0.3f, 1.0f); core->glClear(GL_COLOR_BUFFER_BIT); ourShader->use(); core->glActiveTexture(GL_TEXTURE1); texture2->bind(); core->glActiveTexture(GL_TEXTURE0); texture1->bind(); QMatrix4x4 transform1, transform2; transform1.translate(QVector3D(0.5f, -0.5f, 0.0f)); transform1.rotate((float)time.elapsed()/10, QVector3D(0.0f, 0.0f, 1.0f)); ourShader->use(); ourShader->shaderProgram.setUniformValue(ourShader->shaderProgram.uniformLocation("transform"), transform1); core->glBindVertexArray(VAO); core->glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, nullptr); transform2.translate(QVector3D(-0.5f, 0.5f, 0.0f)); float percent = qSin(time.elapsed()); qDebug()<<"percent:"<<percent; transform2.scale(QVector3D(percent, percent, percent)); ourShader->use(); ourShader->shaderProgram.setUniformValue(ourShader->shaderProgram.uniformLocation("transform"), transform2); core->glBindVertexArray(VAO); core->glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, nullptr); update(); }