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建设网站模板免费,网络销售培训,免费免费网站模板下载,河南网站优化公司哪家好引言这是一个闪耀的时刻，因为我们即将能生产出令人惊叹的3D效果！ 变换向量和矩阵变换包括太多内容，但由于学过线性代数和GAMES101，因此不在此做过多阐述。仅阐述包括代码的GLM内容。 GLM的使用 （1）GLM…

引言

这是一个闪耀的时刻，因为我们即将能生产出令人惊叹的3D效果！

变换

向量和矩阵变换包括太多内容，但由于学过线性代数和GAMES101，因此不在此做过多阐述。仅阐述包括代码的GLM内容。

GLM的使用

（1）GLM的配置

GLM是OpenGL Mathematics的缩写，它是一个只有头文件的库，也就是说我们只需包含对应的头文件就行了，不用链接和编译。GLM可以在它们的网站上下载。把头文件的根目录复制到你的includes文件夹，然后你就可以使用这个库了。
我们需要的GLM的大多数功能都可以从下面这3个头文件中找到：

#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/type_ptr.hpp>

（2）GLM中类型的使用

例子1：定义向量（1，0，0），并使其位移（1，1，0）。注意需要把他定义为一个glm::vec4类型的值，并且其次坐标设定为1.0。

    // 使用glm::vec4定义一个四维向量（齐次坐标为1.0）glm::vec4 vec(1.0f, 0.0f, 0.0f, 1.0f);// 使用glm::mat4定义一个4x4的矩阵// glm::mat4如果不初始化则数据会是未知的，所以用以下方式初始化为单位矩阵glm::mat4 trans = glm::mat4(1.0f);// 使用glm::translate(变换矩阵,位移向量)// glm::translate返回变换矩阵添加位移效果后得到的矩阵trans = glm::translate(trans, glm::vec3(1.0f, 1.0f, 0.0f));// 使用 变换矩阵✖四维向量= 变换后的向量vec = trans * vec;std::cout << vec.x << vec.y << vec.z << std::endl;

例子2：我们来旋转和缩放之前教程中的那个箱子。首先我们把箱子逆时针旋转90度。然后缩放0.5倍，使它变成原来的一半大。我们来创建变换矩阵：

	glm::mat4 trans;trans = glm::rotate(trans, 90.0f, glm::vec3(0.0, 0, 1.0));trans = glm::scale(trans, glm::vec3(0.5, 0.5, 0.5));

针对变换顺序的讨论：
绝大多数情况下，我们约定的变换顺序是先缩放，再旋转，最后平移。这样变换顺序的依据是，比如我们Blender里面建模了一个可乐罐，我们要将它从自己的局部坐标转换到世界坐标，比如我们希望它：位移到桌子上、倾斜45°、x和y轴均匀缩放至0.5倍。我们可以试想，如果先将可乐瓶倾斜45°再缩放的话，原本针对x轴和y轴的缩放应将可乐瓶的半径和高进行缩放至一半，但是现在可乐瓶倾斜了，导致缩放不是针对可乐瓶的半径和高了（即可乐瓶的半径不在x轴上，高不在y轴上），由此我们得出结论：缩放要在旋转之前进行，因为我们潜意识里的缩放就是针对模型未旋转时体态的缩放。还有一个很重要的事情是，我们推导旋转矩阵是基于旋转中心在原点时，因此我们使用旋转矩阵务必要保证旋转中心在原点，试想我们从Blender中建模的对象，其所在局部坐标一定旋转中心是在原点的，但是当我们对他进行平移之后，它的几何中心就不在原点了。因此我们的旋转应该是针对物体最初的位置进行的，所以我们得到结论：旋转需要在位移之前。综上所述，我们就明白了，需要先缩放、再旋转、最后位移。
设变换矩阵初始为M0单位矩阵,设我们需要变换的坐标为 ve4,设我们需要对ve4做的一系列顺序变换为(S1,S2,S3)，设这一系列变换对应的变换矩阵为(M1,M2,M3)。则我们应该做的是：M3✖M2✖M1✖ve4，这样我们则对ve4按顺序执行了变换。那么如果我们要使用一个变换矩阵M包含所有的变换怎么办呢？
由于矩阵乘法满足结合律，即A✖B✖C=(A✖B)✖C=A✖(B✖C)。因此M3✖M2✖M1✖ve4=(M3✖M2✖M1)✖ve4，M=(M3✖M2✖M1)。我们要先计M3再乘M2再乘M1，即可得到M变换矩阵。而对于平移旋转缩放而言，优先级为平移<旋转<缩放，所以应算平移矩阵、再旋转、再计算缩放。如此就可以解释上文中对图形先缩放再旋转的变化顺序，也可以解释代码中先对变化矩阵进行了旋转，再对变换矩阵进行了缩放。
在这里插入图片描述
如果在后续程序中你的笑脸旋转了，但是不是正确你预料之中的角度，那么可能是下图的问题。如果你不对你程序中的glm::mat4对象初始化，可能你就看不到你的笑脸了。顶点着色器：

// 声明OpenGL版本
#version 330 core
// 定义包含位置值的输入变量
layout  (location = 0) in vec3 position;	// 顶点位置
layout (location = 1) in vec3 color;	// 顶点颜色
layout (location = 2) in vec3 textCoord;	// 顶点的纹理坐标
// 定义输出变量（到片段着色器）
out vec3 ourColor;	//	顶点颜色
out vec2 TexCoord;	//	顶点的纹理坐标uniform mat4 transform;	// 	变换矩阵void main()
{// 使用变换矩阵左乘顶点位置得到变换后位置并赋值gl_Position = transform * vec4(position, 1.0f);// 将顶点颜色输出给片段着色器ourColor = color;// 顶点的纹理坐标（由于图片是反的，所以纹理坐标的y值“取反”）TexCoord = vec2(texCoord.x , 1.0 - texCoord.y);
}

在这里插入图片描述
我们现在需要把变换矩阵传递给着色器：

#version 330 core
in vec3 ourColor;
in vec2 TexCoord;out vec4 color;uniform float mixValue;// Texture samplers
uniform sampler2D ourTexture1;
uniform sampler2D ourTexture2;void main()
{// Linearly interpolate between both textures (second texture is only slightly combined)color = mix(texture(ourTexture1, TexCoord), texture(ourTexture2, TexCoord), mixValue);
}

GLuint transformLoc = glGetUniformLocation(ourShader.Program,"transform");
glUniformMatrix4v(transformLoc, 1, GL_FALSE, glm::value_ptr(trans));

最终效果：
完整代码：

#include <iostream>// GLEW
#define GLEW_STATIC
#include <GL/glew.h>// GLFW
#include <GLFW/glfw3.h>// Other Libs
#include <SOIL.H>// Other includes
#include "Shader.h"#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/type_ptr.hpp>// Function prototypes
void key_callback(GLFWwindow* window, int key, int scancode, int action, int mode);// Window dimensions
const GLuint WIDTH = 800, HEIGHT = 600;GLfloat mixValue = 0.2f;// The MAIN function, from here we start the application and run the game loop
int main()
{glm::mat4 trans = glm::mat4(1.0f);trans = glm::rotate(trans,glm::radians(90.0f), glm::vec3(0.0, 0, 1.0));trans = glm::scale(trans, glm::vec3(0.5, 0.5, 0.5));// Init GLFWglfwInit();// Set all the required options for GLFWglfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);glfwWindowHint(GLFW_RESIZABLE, GL_FALSE);// Create a GLFWwindow object that we can use for GLFW's functionsGLFWwindow* window = glfwCreateWindow(WIDTH, HEIGHT, "LearnOpenGL", nullptr, nullptr);glfwMakeContextCurrent(window);// Set the required callback functionsglfwSetKeyCallback(window, key_callback);// Set this to true so GLEW knows to use a modern approach to retrieving function pointers and extensionsglewExperimental = GL_TRUE;// Initialize GLEW to setup the OpenGL Function pointersglewInit();// Define the viewport dimensionsglViewport(0, 0, WIDTH, HEIGHT);// Build and compile our shader programShader ourShader("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Shader\\vertexShader.txt", "C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Shader\\fragmentShader.txt");// Set up vertex data (and buffer(s)) and attribute pointersGLfloat vertices[] = {// Positions          // Colors           // Texture Coords0.5f,  0.5f, 0.0f,   1.0f, 0.0f, 0.0f,   1.0f, 1.0f, // Top Right0.5f, -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[] = {  // Note that we start from 0!0, 1, 3, // First Triangle1, 2, 3  // Second Triangle};GLuint VBO, VAO, EBO;glGenVertexArrays(1, &VAO);glGenBuffers(1, &VBO);glGenBuffers(1, &EBO);glBindVertexArray(VAO);glBindBuffer(GL_ARRAY_BUFFER, VBO);glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW);glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, EBO);glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(indices), indices, GL_STATIC_DRAW);// Position attributeglVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)0);glEnableVertexAttribArray(0);// Color attributeglVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)(3 * sizeof(GLfloat)));glEnableVertexAttribArray(1);// TexCoord attributeglVertexAttribPointer(2, 2, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)(6 * sizeof(GLfloat)));glEnableVertexAttribArray(2);glBindVertexArray(0); // Unbind VAO// Load and create a texture GLuint texture1;GLuint texture2;// ====================// Texture 1// ====================glGenTextures(1, &texture1);glBindTexture(GL_TEXTURE_2D, texture1); // All upcoming GL_TEXTURE_2D operations now have effect on our texture object// Set our texture parametersglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);	// Set texture wrapping to GL_REPEATglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);// Set texture filteringglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);// Load, create texture and generate mipmapsint width, height;unsigned char* image = SOIL_load_image("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Resource\\container.jpg", &width, &height, 0, SOIL_LOAD_RGB);glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, image);glGenerateMipmap(GL_TEXTURE_2D);SOIL_free_image_data(image);glBindTexture(GL_TEXTURE_2D, 0); // Unbind texture when done, so we won't accidentily mess up our texture.// ===================// Texture 2// ===================glGenTextures(1, &texture2);glBindTexture(GL_TEXTURE_2D, texture2);// Set our texture parametersglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_BORDER);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_BORDER);float borderColor[] = { 1.0f, 1.0f , 0.0f, 1.0f };glTexParameterfv(GL_TEXTURE_2D, GL_TEXTURE_BORDER_COLOR, borderColor);// Set texture filteringglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);// Load, create texture and generate mipmapsimage = SOIL_load_image("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Resource\\awesomeface.png", &width, &height, 0, SOIL_LOAD_RGB);glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, image);glGenerateMipmap(GL_TEXTURE_2D);SOIL_free_image_data(image);glBindTexture(GL_TEXTURE_2D, 0);// Game loopwhile (!glfwWindowShouldClose(window)){// Check if any events have been activiated (key pressed, mouse moved etc.) and call corresponding response functionsglfwPollEvents();// Render// Clear the colorbufferglClearColor(0.2f, 0.3f, 0.3f, 1.0f);glClear(GL_COLOR_BUFFER_BIT);// Activate shaderourShader.Use();// Bind Textures using texture unitsglActiveTexture(GL_TEXTURE0);glBindTexture(GL_TEXTURE_2D, texture1);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture1"), 0);glActiveTexture(GL_TEXTURE1);glBindTexture(GL_TEXTURE_2D, texture2);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture2"), 1);GLuint transformLoc = glGetUniformLocation(ourShader.Program, "transform");glUniformMatrix4fv(transformLoc, 1, GL_FALSE, glm::value_ptr(trans));// 设置混合参数glUniform1f(glGetUniformLocation(ourShader.Program,"mixValue"),mixValue);// Draw containerglBindVertexArray(VAO);glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);glBindVertexArray(0);// Swap the screen buffersglfwSwapBuffers(window);}// Properly de-allocate all resources once they've outlived their purposeglDeleteVertexArrays(1, &VAO);glDeleteBuffers(1, &VBO);glDeleteBuffers(1, &EBO);// Terminate GLFW, clearing any resources allocated by GLFW.glfwTerminate();return 0;
}// Is called whenever a key is pressed/released via GLFW
void key_callback(GLFWwindow* window, int key, int scancode, int action, int mode)
{if (key == GLFW_KEY_ESCAPE && action == GLFW_PRESS)glfwSetWindowShouldClose(window, GL_TRUE);if (key == GLFW_KEY_UP && action == GLFW_PRESS){mixValue += 0.1f;if (mixValue >= 1.0f)mixValue = 1.0f;}if (key == GLFW_KEY_DOWN && action == GLFW_PRESS){mixValue -= 0.1f;if (mixValue <= 0.0f)mixValue = 0.0f;}
}

（3）随时间旋转的笑脸

我们可以定义一个无限数量的变换，把它们组合为仅仅一个矩阵，如果愿意的话我们还可以重复使用它。在着色器中使用矩阵可以省去重新定义顶点数据的功夫，它也能够节省处理时间，因为我们没有一直重新发送我们的数据（这是个非常慢的过程）。
上文中的旋转还是很呆，因为是一个不会动的旋转后笑脸。所以我们现在打算让他动起来，即旋转角度会根据时间变换生成变换矩阵即可。
效果：
在这里插入图片描述

代码如下：

glm::mat4 trans;
trans = glm::translate(trans, glm::vec3(0.5f, -0.5f, 0.0f));
trans = glm::rotate(trans,(GLfloat)glfwGetTime() * 50.0f, glm::vec3(0.0f, 0.0f, 1.0f));

完整代码：

#include <iostream>// GLEW
#define GLEW_STATIC
#include <GL/glew.h>// GLFW
#include <GLFW/glfw3.h>// Other Libs
#include <SOIL.H>// Other includes
#include "Shader.h"#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/type_ptr.hpp>// Function prototypes
void key_callback(GLFWwindow* window, int key, int scancode, int action, int mode);// Window dimensions
const GLuint WIDTH = 800, HEIGHT = 600;GLfloat mixValue = 0.2f;// The MAIN function, from here we start the application and run the game loop
int main()
{// Init GLFWglfwInit();// Set all the required options for GLFWglfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);glfwWindowHint(GLFW_RESIZABLE, GL_FALSE);// Create a GLFWwindow object that we can use for GLFW's functionsGLFWwindow* window = glfwCreateWindow(WIDTH, HEIGHT, "LearnOpenGL", nullptr, nullptr);glfwMakeContextCurrent(window);// Set the required callback functionsglfwSetKeyCallback(window, key_callback);// Set this to true so GLEW knows to use a modern approach to retrieving function pointers and extensionsglewExperimental = GL_TRUE;// Initialize GLEW to setup the OpenGL Function pointersglewInit();// Define the viewport dimensionsglViewport(0, 0, WIDTH, HEIGHT);// Build and compile our shader programShader ourShader("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Shader\\vertexShader.txt", "C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Shader\\fragmentShader.txt");// Set up vertex data (and buffer(s)) and attribute pointersGLfloat vertices[] = {// Positions          // Colors           // Texture Coords0.5f,  0.5f, 0.0f,   1.0f, 0.0f, 0.0f,   1.0f, 1.0f, // Top Right0.5f, -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[] = {  // Note that we start from 0!0, 1, 3, // First Triangle1, 2, 3  // Second Triangle};GLuint VBO, VAO, EBO;glGenVertexArrays(1, &VAO);glGenBuffers(1, &VBO);glGenBuffers(1, &EBO);glBindVertexArray(VAO);glBindBuffer(GL_ARRAY_BUFFER, VBO);glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW);glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, EBO);glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(indices), indices, GL_STATIC_DRAW);// Position attributeglVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)0);glEnableVertexAttribArray(0);// Color attributeglVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)(3 * sizeof(GLfloat)));glEnableVertexAttribArray(1);// TexCoord attributeglVertexAttribPointer(2, 2, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)(6 * sizeof(GLfloat)));glEnableVertexAttribArray(2);glBindVertexArray(0); // Unbind VAO// Load and create a texture GLuint texture1;GLuint texture2;// ====================// Texture 1// ====================glGenTextures(1, &texture1);glBindTexture(GL_TEXTURE_2D, texture1); // All upcoming GL_TEXTURE_2D operations now have effect on our texture object// Set our texture parametersglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);	// Set texture wrapping to GL_REPEATglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);// Set texture filteringglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);// Load, create texture and generate mipmapsint width, height;unsigned char* image = SOIL_load_image("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Resource\\container.jpg", &width, &height, 0, SOIL_LOAD_RGB);glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, image);glGenerateMipmap(GL_TEXTURE_2D);SOIL_free_image_data(image);glBindTexture(GL_TEXTURE_2D, 0); // Unbind texture when done, so we won't accidentily mess up our texture.// ===================// Texture 2// ===================glGenTextures(1, &texture2);glBindTexture(GL_TEXTURE_2D, texture2);// Set our texture parametersglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_BORDER);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_BORDER);float borderColor[] = { 1.0f, 1.0f , 0.0f, 1.0f };glTexParameterfv(GL_TEXTURE_2D, GL_TEXTURE_BORDER_COLOR, borderColor);// Set texture filteringglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);// Load, create texture and generate mipmapsimage = SOIL_load_image("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Resource\\awesomeface.png", &width, &height, 0, SOIL_LOAD_RGB);glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, image);glGenerateMipmap(GL_TEXTURE_2D);SOIL_free_image_data(image);glBindTexture(GL_TEXTURE_2D, 0);// Game loopwhile (!glfwWindowShouldClose(window)){// Check if any events have been activiated (key pressed, mouse moved etc.) and call corresponding response functionsglfwPollEvents();// Render// Clear the colorbufferglClearColor(0.2f, 0.3f, 0.3f, 1.0f);glClear(GL_COLOR_BUFFER_BIT);// Activate shaderourShader.Use();glm::mat4 trans = glm::mat4(1.0f);trans = glm::rotate(trans, glm::radians((GLfloat)glfwGetTime()*50.0f), glm::vec3(0.0, 0, 1.0));trans = glm::scale(trans, glm::vec3(0.5, 0.5, 0.5));// Bind Textures using texture unitsglActiveTexture(GL_TEXTURE0);glBindTexture(GL_TEXTURE_2D, texture1);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture1"), 0);glActiveTexture(GL_TEXTURE1);glBindTexture(GL_TEXTURE_2D, texture2);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture2"), 1);GLuint transformLoc = glGetUniformLocation(ourShader.Program, "transform");glUniformMatrix4fv(transformLoc, 1, GL_FALSE, glm::value_ptr(trans));// 设置混合参数glUniform1f(glGetUniformLocation(ourShader.Program,"mixValue"),mixValue);// Draw containerglBindVertexArray(VAO);glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);glBindVertexArray(0);// Swap the screen buffersglfwSwapBuffers(window);}// Properly de-allocate all resources once they've outlived their purposeglDeleteVertexArrays(1, &VAO);glDeleteBuffers(1, &VBO);glDeleteBuffers(1, &EBO);// Terminate GLFW, clearing any resources allocated by GLFW.glfwTerminate();return 0;
}// Is called whenever a key is pressed/released via GLFW
void key_callback(GLFWwindow* window, int key, int scancode, int action, int mode)
{if (key == GLFW_KEY_ESCAPE && action == GLFW_PRESS)glfwSetWindowShouldClose(window, GL_TRUE);if (key == GLFW_KEY_UP && action == GLFW_PRESS){mixValue += 0.1f;if (mixValue >= 1.0f)mixValue = 1.0f;}if (key == GLFW_KEY_DOWN && action == GLFW_PRESS){mixValue -= 0.1f;if (mixValue <= 0.0f)mixValue = 0.0f;}
}

变换的练习

练习一

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。
诸如我们上文所说，旋转矩阵的运算是针对旋转中心在原点的，代码中先将矩阵旋转再位移，相当于对矩阵先位移再旋转。这时会发现笑脸绕着窗口中心原点不停的逆时针旋转。这是由于旋转中心的不同导致的差距。当先进行移动后，笑脸的几何中心就不在原点了，原本打算让它绕着几何中心旋转变成了绕着原点（非几何中心）旋转。
结果：
在这里插入图片描述

源代码：

#include <iostream>// GLEW
#define GLEW_STATIC
#include <GL/glew.h>// GLFW
#include <GLFW/glfw3.h>// Other Libs
#include <SOIL.H>// Other includes
#include "Shader.h"#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/type_ptr.hpp>// Function prototypes
void key_callback(GLFWwindow* window, int key, int scancode, int action, int mode);// Window dimensions
const GLuint WIDTH = 800, HEIGHT = 600;GLfloat mixValue = 0.2f;// The MAIN function, from here we start the application and run the game loop
int main()
{// Init GLFWglfwInit();// Set all the required options for GLFWglfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);glfwWindowHint(GLFW_RESIZABLE, GL_FALSE);// Create a GLFWwindow object that we can use for GLFW's functionsGLFWwindow* window = glfwCreateWindow(WIDTH, HEIGHT, "LearnOpenGL", nullptr, nullptr);glfwMakeContextCurrent(window);// Set the required callback functionsglfwSetKeyCallback(window, key_callback);// Set this to true so GLEW knows to use a modern approach to retrieving function pointers and extensionsglewExperimental = GL_TRUE;// Initialize GLEW to setup the OpenGL Function pointersglewInit();// Define the viewport dimensionsglViewport(0, 0, WIDTH, HEIGHT);// Build and compile our shader programShader ourShader("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Shader\\vertexShader.txt", "C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Shader\\fragmentShader.txt");// Set up vertex data (and buffer(s)) and attribute pointersGLfloat vertices[] = {// Positions          // Colors           // Texture Coords0.5f,  0.5f, 0.0f,   1.0f, 0.0f, 0.0f,   1.0f, 1.0f, // Top Right0.5f, -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[] = {  // Note that we start from 0!0, 1, 3, // First Triangle1, 2, 3  // Second Triangle};GLuint VBO, VAO, EBO;glGenVertexArrays(1, &VAO);glGenBuffers(1, &VBO);glGenBuffers(1, &EBO);glBindVertexArray(VAO);glBindBuffer(GL_ARRAY_BUFFER, VBO);glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW);glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, EBO);glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(indices), indices, GL_STATIC_DRAW);// Position attributeglVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)0);glEnableVertexAttribArray(0);// Color attributeglVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)(3 * sizeof(GLfloat)));glEnableVertexAttribArray(1);// TexCoord attributeglVertexAttribPointer(2, 2, GL_FLOAT, GL_FALSE, 8 * sizeof(GLfloat), (GLvoid*)(6 * sizeof(GLfloat)));glEnableVertexAttribArray(2);glBindVertexArray(0); // Unbind VAO// Load and create a texture GLuint texture1;GLuint texture2;// ====================// Texture 1// ====================glGenTextures(1, &texture1);glBindTexture(GL_TEXTURE_2D, texture1); // All upcoming GL_TEXTURE_2D operations now have effect on our texture object// Set our texture parametersglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);	// Set texture wrapping to GL_REPEATglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);// Set texture filteringglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);// Load, create texture and generate mipmapsint width, height;unsigned char* image = SOIL_load_image("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Resource\\container.jpg", &width, &height, 0, SOIL_LOAD_RGB);glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, image);glGenerateMipmap(GL_TEXTURE_2D);SOIL_free_image_data(image);glBindTexture(GL_TEXTURE_2D, 0); // Unbind texture when done, so we won't accidentily mess up our texture.// ===================// Texture 2// ===================glGenTextures(1, &texture2);glBindTexture(GL_TEXTURE_2D, texture2);// Set our texture parametersglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_BORDER);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_BORDER);float borderColor[] = { 1.0f, 1.0f , 0.0f, 1.0f };glTexParameterfv(GL_TEXTURE_2D, GL_TEXTURE_BORDER_COLOR, borderColor);// Set texture filteringglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);// Load, create texture and generate mipmapsimage = SOIL_load_image("C:\\Users\\32156\\source\\repos\\LearnOpenGL\\Resource\\awesomeface.png", &width, &height, 0, SOIL_LOAD_RGB);glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, image);glGenerateMipmap(GL_TEXTURE_2D);SOIL_free_image_data(image);glBindTexture(GL_TEXTURE_2D, 0);// Game loopwhile (!glfwWindowShouldClose(window)){// Check if any events have been activiated (key pressed, mouse moved etc.) and call corresponding response functionsglfwPollEvents();// Render// Clear the colorbufferglClearColor(0.2f, 0.3f, 0.3f, 1.0f);glClear(GL_COLOR_BUFFER_BIT);// Activate shaderourShader.Use();glm::mat4 trans = glm::mat4(1.0f);trans = glm::rotate(trans, (GLfloat)glfwGetTime() * 2.0f, glm::vec3(0.0f, 0.0f, 1.0f));trans = glm::translate(trans, glm::vec3(0.5f, -0.5f, 0.0f));// Bind Textures using texture unitsglActiveTexture(GL_TEXTURE0);glBindTexture(GL_TEXTURE_2D, texture1);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture1"), 0);glActiveTexture(GL_TEXTURE1);glBindTexture(GL_TEXTURE_2D, texture2);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture2"), 1);GLuint transformLoc = glGetUniformLocation(ourShader.Program, "transform");glUniformMatrix4fv(transformLoc, 1, GL_FALSE, glm::value_ptr(trans));// 设置混合参数glUniform1f(glGetUniformLocation(ourShader.Program,"mixValue"),mixValue);// Draw containerglBindVertexArray(VAO);glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);glBindVertexArray(0);// Swap the screen buffersglfwSwapBuffers(window);}// Properly de-allocate all resources once they've outlived their purposeglDeleteVertexArrays(1, &VAO);glDeleteBuffers(1, &VBO);glDeleteBuffers(1, &EBO);// Terminate GLFW, clearing any resources allocated by GLFW.glfwTerminate();return 0;
}// Is called whenever a key is pressed/released via GLFW
void key_callback(GLFWwindow* window, int key, int scancode, int action, int mode)
{if (key == GLFW_KEY_ESCAPE && action == GLFW_PRESS)glfwSetWindowShouldClose(window, GL_TRUE);if (key == GLFW_KEY_UP && action == GLFW_PRESS){mixValue += 0.1f;if (mixValue >= 1.0f)mixValue = 1.0f;}if (key == GLFW_KEY_DOWN && action == GLFW_PRESS){mixValue -= 0.1f;if (mixValue <= 0.0f)mixValue = 0.0f;}
}

练习二

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。
最终效果：
在这里插入图片描述

其实还是很简单的，直接上核心代码：

while (!glfwWindowShouldClose(window)){// Check if any events have been activiated (key pressed, mouse moved etc.) and call corresponding response functionsglfwPollEvents();// Render// Clear the colorbufferglClearColor(0.2f, 0.3f, 0.3f, 1.0f);glClear(GL_COLOR_BUFFER_BIT);// Activate shaderourShader.Use();// 计算右下角笑脸的变换矩阵glm::mat4 trans = glm::mat4(1.0f);trans = glm::translate(trans, glm::vec3(0.5f, -0.5f, 0.0f));trans = glm::rotate(trans, (GLfloat)glfwGetTime() * 2.0f, glm::vec3(0.0f, 0.0f, 1.0f));GLuint transformLoc = glGetUniformLocation(ourShader.Program, "transform");glUniformMatrix4fv(transformLoc, 1, GL_FALSE, glm::value_ptr(trans));// Bind Textures using texture unitsglActiveTexture(GL_TEXTURE0);glBindTexture(GL_TEXTURE_2D, texture1);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture1"), 0);glActiveTexture(GL_TEXTURE1);glBindTexture(GL_TEXTURE_2D, texture2);glUniform1i(glGetUniformLocation(ourShader.Program, "ourTexture2"), 1);// 设置混合参数glUniform1f(glGetUniformLocation(ourShader.Program,"mixValue"),mixValue);// Draw containerglBindVertexArray(VAO);glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);// 计算左上角笑脸的变换矩阵trans = glm::mat4(1.0f);trans = glm::translate(trans, glm::vec3(-0.5f, 0.5f, 0.0f));// 利用sin/2+0.5，将时间 0到正无穷 转换为 0到1GLfloat scaleValue = sin((GLfloat)glfwGetTime()) / 2 + 0.5;trans = glm::scale(trans, glm::vec3(scaleValue,scaleValue,scaleValue));glUniformMatrix4fv(transformLoc, 1, GL_FALSE, glm::value_ptr(trans));glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);glBindVertexArray(0);// Swap the screen buffersglfwSwapBuffers(window);}