1. 引言

本文基于C++语言，描述OpenGL的坐标系统

前置知识可参考：

• 基于C++的OpenGL 04 之变换 - 当时明月在曾照彩云归 - 博客园 (cnblogs.com)

笔者这里不过多描述每个名词、函数和细节，更详细的文档可以参考：

• 坐标系统 - LearnOpenGL CN (learnopengl-cn.github.io)

2. 概述

OpenGL中坐标变换的流程如下图：

有图可知：

• 创建一个物体到屏幕绘制需要三个矩阵变换：模型（Model）、观察（View）、投影（Projection）（即，MVP）

• 裁剪坐标：\(V_{clip} = M_{projrction} \cdot M_{view} \cdot M_{model} \cdot V_{local}\)

投影时主要有两者投影方式：

• 正交投影：平行视角

• 透视投影：近大远小

3. 编码

编码实现只需设置MVP矩阵即可

设置Model矩阵：

glm::mat4 model = glm::mat4(1.0f);

model = glm::rotate(model, glm::radians(-55.0f), glm::vec3(1.0f, 0.0f, 0.0f));

设置View矩阵：

glm::mat4 view = glm::mat4(1.0f);

// 注意，我们将矩阵向我们要进行移动场景的反方向移动。

view = glm::translate(view, glm::vec3(0.0f, 0.0f, -3.0f));

设置投影矩阵：

glm::mat4 projection = glm::mat4(1.0f);

projection = glm::perspective(glm::radians(45.0f), screenWidth / screenHeight, 0.1f, 100.0f);

在顶点着色器中设置MVP变换：

#version 330 core

layout (location = 0) in vec3 aPos;

...

uniform mat4 model;

uniform mat4 view;

uniform mat4 projection;

void main()

{

    // 注意乘法要从右向左读

    gl_Position = projection * view * model * vec4(aPos, 1.0);

    ...

}

将变换矩阵传输到GPU：

// 模型矩阵

int modelLoc = glGetUniformLocation(ourShader.ID, "model"));

glUniformMatrix4fv(modelLoc, 1, GL_FALSE, glm::value_ptr(model));

// 观察矩阵和投影矩阵与之类似

int viewLoc = glGetUniformLocation(ourShader_ID, "view");

glUniformMatrix4fv(viewLoc, 1, GL_FALSE, glm::value_ptr(view));

int projectionLoc = glGetUniformLocation(ourShader_ID, "projection");

glUniformMatrix4fv(projectionLoc, 1, GL_FALSE, glm::value_ptr(projection));

至此就完成了一次简单的MVP变换，结果图如下：

4. 立体化

构建一个立体的箱子：

设置立方体的六个面（12个三角形，36个点）：

float vertices[] = {

    -0.5f, -0.5f, -0.5f,  0.0f, 0.0f,

     0.5f, -0.5f, -0.5f,  1.0f, 0.0f,

     0.5f,  0.5f, -0.5f,  1.0f, 1.0f,

     0.5f,  0.5f, -0.5f,  1.0f, 1.0f,

    -0.5f,  0.5f, -0.5f,  0.0f, 1.0f,

    -0.5f, -0.5f, -0.5f,  0.0f, 0.0f,

    -0.5f, -0.5f,  0.5f,  0.0f, 0.0f,

     0.5f, -0.5f,  0.5f,  1.0f, 0.0f,

     0.5f,  0.5f,  0.5f,  1.0f, 1.0f,

     0.5f,  0.5f,  0.5f,  1.0f, 1.0f,

    -0.5f,  0.5f,  0.5f,  0.0f, 1.0f,

    -0.5f, -0.5f,  0.5f,  0.0f, 0.0f,

    -0.5f,  0.5f,  0.5f,  1.0f, 0.0f,

    -0.5f,  0.5f, -0.5f,  1.0f, 1.0f,

    -0.5f, -0.5f, -0.5f,  0.0f, 1.0f,

    -0.5f, -0.5f, -0.5f,  0.0f, 1.0f,

    -0.5f, -0.5f,  0.5f,  0.0f, 0.0f,

    -0.5f,  0.5f,  0.5f,  1.0f, 0.0f,

     0.5f,  0.5f,  0.5f,  1.0f, 0.0f,

     0.5f,  0.5f, -0.5f,  1.0f, 1.0f,

     0.5f, -0.5f, -0.5f,  0.0f, 1.0f,

     0.5f, -0.5f, -0.5f,  0.0f, 1.0f,

     0.5f, -0.5f,  0.5f,  0.0f, 0.0f,

     0.5f,  0.5f,  0.5f,  1.0f, 0.0f,

    -0.5f, -0.5f, -0.5f,  0.0f, 1.0f,

     0.5f, -0.5f, -0.5f,  1.0f, 1.0f,

     0.5f, -0.5f,  0.5f,  1.0f, 0.0f,

     0.5f, -0.5f,  0.5f,  1.0f, 0.0f,

    -0.5f, -0.5f,  0.5f,  0.0f, 0.0f,

    -0.5f, -0.5f, -0.5f,  0.0f, 1.0f,

    -0.5f,  0.5f, -0.5f,  0.0f, 1.0f,

     0.5f,  0.5f, -0.5f,  1.0f, 1.0f,

     0.5f,  0.5f,  0.5f,  1.0f, 0.0f,

     0.5f,  0.5f,  0.5f,  1.0f, 0.0f,

    -0.5f,  0.5f,  0.5f,  0.0f, 0.0f,

    -0.5f,  0.5f, -0.5f,  0.0f, 1.0f

};

开启深度测试：

glEnable(GL_DEPTH_TEST);

清除深度缓冲：

glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

可选项，让箱子旋转：

model = glm::rotate(model, (float)glfwGetTime() * glm::radians(50.0f), glm::vec3(0.5f, 1.0f, 0.0f));

如果顺利的话，结果如下：

6. 多个立方体

这里的多个立方体实质就是指定（同一个立方体）平移到多个位置

设置多个位置：

glm::vec3 cubePositions[] = {

  glm::vec3( 0.0f,  0.0f,  0.0f),

  glm::vec3( 2.0f,  5.0f, -15.0f),

  glm::vec3(-1.5f, -2.2f, -2.5f),

  glm::vec3(-3.8f, -2.0f, -12.3f),

  glm::vec3( 2.4f, -0.4f, -3.5f),

  glm::vec3(-1.7f,  3.0f, -7.5f),

  glm::vec3( 1.3f, -2.0f, -2.5f),

  glm::vec3( 1.5f,  2.0f, -2.5f),

  glm::vec3( 1.5f,  0.2f, -1.5f),

  glm::vec3(-1.3f,  1.0f, -1.5f)

};

绘制多个Model：

glBindVertexArray(VAO);

for (unsigned int i = 0; i < 10; i++)

{

    glm::mat4 model = glm::mat4(1.0f);

    model = glm::translate(model, cubePositions[i]);

    model = glm::rotate(model, (float)glfwGetTime() * glm::radians(50.0f), glm::vec3(1.0f, 0.3f, 0.5f));

    glUniformMatrix4fv(modelLoc, 1, GL_FALSE, glm::value_ptr(model));

    glDrawArrays(GL_TRIANGLES, 0, 36);

}

实现效果：

7. 完整代码

主要文件test.cpp：

#include <glad/glad.h>

#include <GLFW/glfw3.h>

#include <iostream>

#include <math.h>

#include "Shader.hpp"

#define STB_IMAGE_IMPLEMENTATION

#include "stb_image.h"

#include <glm/glm.hpp>

#include <glm/ext/matrix_transform.hpp>  // glm::translate, glm::rotate, glm::scale

#include <glm/ext/matrix_clip_space.hpp> // glm::perspective

#include <glm/gtc/type_ptr.hpp>

void framebuffer_size_callback(GLFWwindow *window, int width, int height);

void process_input(GLFWwindow *window);

unsigned int *renderInit();

void render(unsigned int shaderProgram, unsigned int VAO, unsigned int texture1, unsigned int texture2);

bool checkCompile(unsigned int shader);

bool checkProgram(unsigned int shaderProgram);

int main()

{

    glfwInit();

    glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);

    glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);

    GLFWwindow *window = glfwCreateWindow(800, 600, "CoordinateSystem", nullptr, nullptr);

    if (window == nullptr)

    {

        std::cout << "Faild to create window" << std::endl;

        glfwTerminate();

    }

    glfwMakeContextCurrent(window);

    if (!gladLoadGLLoader((GLADloadproc)glfwGetProcAddress))

    {

        std::cout << "Faild to initialize glad" << std::endl;

        return -1;

    }

    glad_glViewport(0, 0, 800, 600);

    glfwSetFramebufferSizeCallback(window, framebuffer_size_callback);

    unsigned int *arr = renderInit();

    while (!glfwWindowShouldClose(window))

    {

        process_input(window);

        // render

        std::cout << arr[0] << " " << arr[1] << " " << arr[2] << " " << arr[3] << " " << arr[4] << std::endl;

        render(arr[0], arr[1], arr[3], arr[4]);

        glfwSwapBuffers(window);

        glfwPollEvents();

    }

    glDeleteProgram(arr[0]);

    glDeleteVertexArrays(1, &arr[1]);

    glDeleteBuffers(1, &arr[2]);

    glfwTerminate();

    return 0;

}

void framebuffer_size_callback(GLFWwindow *window, int width, int height)

{

    glViewport(0, 0, width, height);

}

void process_input(GLFWwindow *window)

{

    if (glfwGetKey(window, GLFW_KEY_ESCAPE) == GLFW_PRESS)

    {

        glfwSetWindowShouldClose(window, true);

    }

}

unsigned int *renderInit()

{

    //配置项

    glEnable(GL_DEPTH_TEST);

    unsigned int VAO;

    glGenVertexArrays(1, &VAO);

    glBindVertexArray(VAO);

    unsigned int texture1;

    glGenTextures(1, &texture1);

    glBindTexture(GL_TEXTURE_2D, texture1);

    // 为当前绑定的纹理对象设置环绕、过滤方式

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);

    // 加载并生成纹理

    int width, height, nrChannels;

    unsigned char *data = stbi_load("../container.jpg", &width, &height, &nrChannels, 0);

    if (data)

    {

        glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, data);

        glGenerateMipmap(GL_TEXTURE_2D);

    }

    else

    {

        std::cout << "Failed to load texture" << std::endl;

    }

    stbi_image_free(data);

    unsigned int texture2;

    glGenTextures(1, &texture2);

    glBindTexture(GL_TEXTURE_2D, texture2);

    // 为当前绑定的纹理对象设置环绕、过滤方式

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);

    // // 加载并生成纹理

    int width2, height2, nrChannels2;

    stbi_set_flip_vertically_on_load(true);

    unsigned char *data2 = stbi_load("../awesomeface.png", &width2, &height2, &nrChannels2, 0);

    if (data2)

    {

        glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width2, height2, 0, GL_RGBA, GL_UNSIGNED_BYTE, data2);

        glGenerateMipmap(GL_TEXTURE_2D);

    }

    else

    {

        std::cout << "Failed to load texture" << std::endl;

    }

    stbi_image_free(data2);

    float vertices[] = {

        -0.5f, -0.5f, -0.5f, 0.0f, 0.0f,

        0.5f, -0.5f, -0.5f, 1.0f, 0.0f,

        0.5f, 0.5f, -0.5f, 1.0f, 1.0f,

        0.5f, 0.5f, -0.5f, 1.0f, 1.0f,

        -0.5f, 0.5f, -0.5f, 0.0f, 1.0f,

        -0.5f, -0.5f, -0.5f, 0.0f, 0.0f,

        -0.5f, -0.5f, 0.5f, 0.0f, 0.0f,

        0.5f, -0.5f, 0.5f, 1.0f, 0.0f,

        0.5f, 0.5f, 0.5f, 1.0f, 1.0f,

        0.5f, 0.5f, 0.5f, 1.0f, 1.0f,

        -0.5f, 0.5f, 0.5f, 0.0f, 1.0f,

        -0.5f, -0.5f, 0.5f, 0.0f, 0.0f,

        -0.5f, 0.5f, 0.5f, 1.0f, 0.0f,

        -0.5f, 0.5f, -0.5f, 1.0f, 1.0f,

        -0.5f, -0.5f, -0.5f, 0.0f, 1.0f,

        -0.5f, -0.5f, -0.5f, 0.0f, 1.0f,

        -0.5f, -0.5f, 0.5f, 0.0f, 0.0f,

        -0.5f, 0.5f, 0.5f, 1.0f, 0.0f,

        0.5f, 0.5f, 0.5f, 1.0f, 0.0f,

        0.5f, 0.5f, -0.5f, 1.0f, 1.0f,

        0.5f, -0.5f, -0.5f, 0.0f, 1.0f,

        0.5f, -0.5f, -0.5f, 0.0f, 1.0f,

        0.5f, -0.5f, 0.5f, 0.0f, 0.0f,

        0.5f, 0.5f, 0.5f, 1.0f, 0.0f,

        -0.5f, -0.5f, -0.5f, 0.0f, 1.0f,

        0.5f, -0.5f, -0.5f, 1.0f, 1.0f,

        0.5f, -0.5f, 0.5f, 1.0f, 0.0f,

        0.5f, -0.5f, 0.5f, 1.0f, 0.0f,

        -0.5f, -0.5f, 0.5f, 0.0f, 0.0f,

        -0.5f, -0.5f, -0.5f, 0.0f, 1.0f,

        -0.5f, 0.5f, -0.5f, 0.0f, 1.0f,

        0.5f, 0.5f, -0.5f, 1.0f, 1.0f,

        0.5f, 0.5f, 0.5f, 1.0f, 0.0f,

        0.5f, 0.5f, 0.5f, 1.0f, 0.0f,

        -0.5f, 0.5f, 0.5f, 0.0f, 0.0f,

        -0.5f, 0.5f, -0.5f, 0.0f, 1.0f};

    unsigned int VBO;

    glGenBuffers(1, &VBO);

    glBindBuffer(GL_ARRAY_BUFFER, VBO);

    glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW);

    glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 5 * sizeof(float), (void *)0);

    glEnableVertexAttribArray(0);

    glVertexAttribPointer(1, 2, GL_FLOAT, GL_FALSE, 5 * sizeof(float), (void *)(3 * sizeof(float)));

    glEnableVertexAttribArray(1);

    Shader shaderProgram = Shader("../test.vs.glsl", "../test.fs.glsl");

    shaderProgram.use();

    glUniform1i(glGetUniformLocation(shaderProgram.ID, "texture1"), 0);

    glUniform1i(glGetUniformLocation(shaderProgram.ID, "texture2"), 1);

    return new unsigned int[5]{shaderProgram.ID, VAO, VBO, texture1, texture2};

}

void render(unsigned int shaderProgram, unsigned int VAO, unsigned int texture1, unsigned int texture2)

{

    glClearColor(0.2, 0.3, 0.3, 1.0);

    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    glActiveTexture(GL_TEXTURE0);

    glBindTexture(GL_TEXTURE_2D, texture1);

    glActiveTexture(GL_TEXTURE1);

    glBindTexture(GL_TEXTURE_2D, texture2);

    glUseProgram(shaderProgram);

    glm::vec3 cubePositions[] = {

        glm::vec3(0.0f, 0.0f, 0.0f),

        glm::vec3(2.0f, 5.0f, -15.0f),

        glm::vec3(-1.5f, -2.2f, -2.5f),

        glm::vec3(-3.8f, -2.0f, -12.3f),

        glm::vec3(2.4f, -0.4f, -3.5f),

        glm::vec3(-1.7f, 3.0f, -7.5f),

        glm::vec3(1.3f, -2.0f, -2.5f),

        glm::vec3(1.5f, 2.0f, -2.5f),

        glm::vec3(1.5f, 0.2f, -1.5f),

        glm::vec3(-1.3f, 1.0f, -1.5f)};

    glm::mat4 view = glm::mat4(1.0f);

    // 注意，我们将矩阵向我们要进行移动场景的反方向移动。

    view = glm::translate(view, glm::vec3(0.0f, 0.0f, -3.0f));

    glm::mat4 projection = glm::mat4(1.0f);

    projection = glm::perspective(glm::radians(45.0f), 800.0f / 600.0f, 0.1f, 100.0f);

    // 模型矩阵

    int modelLoc = glGetUniformLocation(shaderProgram, "model");

    // 观察矩阵

    int viewLoc = glGetUniformLocation(shaderProgram, "view");

    glUniformMatrix4fv(viewLoc, 1, GL_FALSE, glm::value_ptr(view));

    // 投影矩阵

    int projectionLoc = glGetUniformLocation(shaderProgram, "projection");

    glUniformMatrix4fv(projectionLoc, 1, GL_FALSE, glm::value_ptr(projection));

    glBindVertexArray(VAO);

    for (unsigned int i = 0; i < 10; i++)

    {

        glm::mat4 model = glm::mat4(1.0f);

        model = glm::translate(model, cubePositions[i]);

        float angle = 20.0f * (i + 1);

        model = glm::rotate(model, (float)glfwGetTime() * glm::radians(50.0f), glm::vec3(1.0f, 0.3f, 0.5f));

        glUniformMatrix4fv(modelLoc, 1, GL_FALSE, glm::value_ptr(model));

        glDrawArrays(GL_TRIANGLES, 0, 36);

    }

}

• Shader.hpp见：基于C++的OpenGL 02 之着色器 - 当时明月在曾照彩云归 - 博客园 (cnblogs.com)

顶点着色器test.vs.glsl：

#version 330 core

layout (location = 0) in vec3 aPos;

layout (location = 1) in vec2 aTexCoord;

out vec2 TexCoord;

uniform mat4 model;

uniform mat4 view;

uniform mat4 projection;

void main()

{

    // 注意乘法要从右向左读

    gl_Position = projection * view * model * vec4(aPos, 1.0);

    TexCoord = aTexCoord;

}

片段着色器test.fs.glsl：

#version 330 core

out vec4 FragColor;

in vec2 TexCoord;

uniform sampler2D texture1;

uniform sampler2D texture2;

void main()

{

    FragColor = mix(texture(texture1, TexCoord), texture(texture2, TexCoord), 0.2);

}

8. 参考资料

[1]坐标系统 - LearnOpenGL CN (learnopengl-cn.github.io)

[2]OpenGL学习笔记（七）坐标系统 - 知乎 (zhihu.com)

[3]g-truc/glm: OpenGL Mathematics (GLM) (github.com)

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