基于C++的OpenGL 05 之坐标系统
本文基于C++语言，描述OpenGL的坐标系统
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：
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：
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);
}
}
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)
