C++ OPENGL 贝塞尔曲线绘制

代码 

#include <glad/glad.h>
#include <GLFW/glfw3.h>

#include <iostream>
#include <vector>

struct Point {
    float x;
    float y;
};

// 二次贝塞尔
Point bezier(float t, Point a, Point c, Point z)
{
    return {
        (1 - t) * (1 - t) * a.x + 2 * t * (1 - t) * c.x + t * t * z.x,
        (1 - t) * (1 - t) * a.y + 2 * t * (1 - t) * c.y + t * t * z.y,
    };
}

// 定义三次贝塞尔曲线的函数
void bezierCurve2(float t, std::vector<GLfloat> &controlPoints, GLfloat &x, GLfloat &y)
{
    // 假设我们有4个控制点，绘制一个三次贝塞尔曲线
    GLfloat p0x = controlPoints[0], p0y = controlPoints[1];
    GLfloat p1x = controlPoints[2], p1y = controlPoints[3];
    GLfloat p2x = controlPoints[4], p2y = controlPoints[5];
    GLfloat p3x = controlPoints[6], p3y = controlPoints[7];

    x = pow(1 - t, 3) * p0x + 3 * t * pow(1 - t, 2) * p1x + 3 * pow(t, 2) * (1 - t) * p2x + pow(t, 3) * p3x;
    y = pow(1 - t, 3) * p0y + 3 * t * pow(1 - t, 2) * p1y + 3 * pow(t, 2) * (1 - t) * p2y + pow(t, 3) * p3y;
}

// 绘制贝塞尔曲线
void drawBezierCurve()
{
    std::vector<GLfloat> controlPoints = {0.0, 0.0, 0.2, 0.5, 0.8, 0.5, 1.0, 1.0};  // 控制点

    glBegin(GL_LINE_STRIP);
    for (float t = 0.0; t <= 1.0; t += 0.01) {
        GLfloat x, y;
        bezierCurve2(t, controlPoints, x, y);
        glVertex2f(x, y);
    }
    glEnd();

    glBegin(GL_LINE_STRIP);
    for (float t = 0.0; t <= 1.0; t += 0.01) {
        auto pt = bezier(t,
                         {controlPoints[0], controlPoints[1]},
                         {controlPoints[2], controlPoints[3]},
                         {controlPoints[4], controlPoints[5]});
        glVertex2f(pt.x, pt.y);
    }
    glEnd();
}

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

// settings
const unsigned int SCR_WIDTH  = 800;
const unsigned int SCR_HEIGHT = 600;

const char *vertexShaderSource   = "#version 330 core\n"
                                   "layout (location = 0) in vec3 aPos;\n"
                                   "void main()\n"
                                   "{\n"
                                   "   gl_Position = vec4(aPos.x, aPos.y, aPos.z, 1.0);\n"
                                   "}\0";
const char *fragmentShaderSource = "#version 330 core\n"
                                   "out vec4 FragColor;\n"
                                   "void main()\n"
                                   "{\n"
                                   "   FragColor = vec4(1.0f, 0.5f, 0.2f, 1.0f);\n"
                                   "}\n\0";

int main()
{
    // glfw: initialize and configure
    // ------------------------------
    glfwInit();
    glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);
    glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
    glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);

#ifdef __APPLE__
    glfwWindowHint(GLFW_OPENGL_FORWARD_COMPAT, GL_TRUE);
#endif

    // glfw window creation
    // --------------------
    GLFWwindow *window = glfwCreateWindow(SCR_WIDTH, SCR_HEIGHT, "LearnOpenGL", NULL, NULL);
    if (window == NULL) {
        std::cout << "Failed to create GLFW window" << std::endl;
        glfwTerminate();
        return -1;
    }
    glfwMakeContextCurrent(window);
    glfwSetFramebufferSizeCallback(window, framebuffer_size_callback);

    // glad: load all OpenGL function pointers
    // ---------------------------------------
    if (!gladLoadGLLoader((GLADloadproc)glfwGetProcAddress)) {
        std::cout << "Failed to initialize GLAD" << std::endl;
        return -1;
    }

    // build and compile our shader program
    // ------------------------------------
    // vertex shader
    unsigned int vertexShader = glCreateShader(GL_VERTEX_SHADER);
    glShaderSource(vertexShader, 1, &vertexShaderSource, NULL);
    glCompileShader(vertexShader);
    // check for shader compile errors
    int  success;
    char infoLog[512];
    glGetShaderiv(vertexShader, GL_COMPILE_STATUS, &success);
    if (!success) {
        glGetShaderInfoLog(vertexShader, 512, NULL, infoLog);
        std::cout << "ERROR::SHADER::VERTEX::COMPILATION_FAILED\n" << infoLog << std::endl;
    }
    // fragment shader
    unsigned int fragmentShader = glCreateShader(GL_FRAGMENT_SHADER);
    glShaderSource(fragmentShader, 1, &fragmentShaderSource, NULL);
    glCompileShader(fragmentShader);
    // check for shader compile errors
    glGetShaderiv(fragmentShader, GL_COMPILE_STATUS, &success);
    if (!success) {
        glGetShaderInfoLog(fragmentShader, 512, NULL, infoLog);
        std::cout << "ERROR::SHADER::FRAGMENT::COMPILATION_FAILED\n" << infoLog << std::endl;
    }
    // link shaders
    unsigned int shaderProgram = glCreateProgram();
    glAttachShader(shaderProgram, vertexShader);
    glAttachShader(shaderProgram, fragmentShader);
    glLinkProgram(shaderProgram);
    // check for linking errors
    glGetProgramiv(shaderProgram, GL_LINK_STATUS, &success);
    if (!success) {
        glGetProgramInfoLog(shaderProgram, 512, NULL, infoLog);
        std::cout << "ERROR::SHADER::PROGRAM::LINKING_FAILED\n" << infoLog << std::endl;
    }
    glDeleteShader(vertexShader);
    glDeleteShader(fragmentShader);

    // set up vertex data (and buffer(s)) and configure vertex attributes
    // ------------------------------------------------------------------
    float vertices[] = {
        0.5f,
        0.5f,
        0.0f,  // top right
        0.5f,
        -0.5f,
        0.0f,  // bottom right
        -0.5f,
        -0.5f,
        0.0f,  // bottom left
        -0.5f,
        0.5f,
        0.0f  // top left
    };
    unsigned int indices[] = {
        // note that we start from 0!
        0,
        1,
        3,  // first Triangle
        1,
        2,
        3  // second Triangle
    };
    unsigned int VBO, VAO, EBO;
    glGenVertexArrays(1, &VAO);
    glGenBuffers(1, &VBO);
    glGenBuffers(1, &EBO);
    // bind the Vertex Array Object first, then bind and set vertex buffer(s), and then configure vertex attributes(s).
    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);

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

    // note that this is allowed, the call to glVertexAttribPointer registered VBO as the vertex attribute's bound vertex
    // buffer object so afterwards we can safely unbind
    glBindBuffer(GL_ARRAY_BUFFER, 0);

    // remember: do NOT unbind the EBO while a VAO is active as the bound element buffer object IS stored in the VAO; keep
    // the EBO bound.
    // glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, 0);

    // You can unbind the VAO afterwards so other VAO calls won't accidentally modify this VAO, but this rarely happens.
    // Modifying other VAOs requires a call to glBindVertexArray anyways so we generally don't unbind VAOs (nor VBOs) when
    // it's not directly necessary.
    glBindVertexArray(0);

    // uncomment this call to draw in wireframe polygons.
    // glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);

    // render loop
    // -----------
    while (!glfwWindowShouldClose(window)) {
        // input
        // -----
        processInput(window);

        // render
        // ------
        glClearColor(0.2f, 0.3f, 0.3f, 1.0f);
        glClear(GL_COLOR_BUFFER_BIT);

        // draw our first triangle
        glUseProgram(shaderProgram);
        glBindVertexArray(VAO);  // seeing as we only have a single VAO there's no need to bind it every time, but we'll do
                                 // so to keep things a bit more organized
                                 // glDrawArrays(GL_TRIANGLES, 0, 6);
                                 //        glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);
                                 // glBindVertexArray(0); // no need to unbind it every time
        drawBezierCurve();       // 绘制曲线
        // glfw: swap buffers and poll IO events (keys pressed/released, mouse moved etc.)
        // -------------------------------------------------------------------------------
        glfwSwapBuffers(window);
        glfwPollEvents();
    }

    // optional: de-allocate all resources once they've outlived their purpose:
    // ------------------------------------------------------------------------
    glDeleteVertexArrays(1, &VAO);
    glDeleteBuffers(1, &VBO);
    glDeleteBuffers(1, &EBO);
    glDeleteProgram(shaderProgram);

    // glfw: terminate, clearing all previously allocated GLFW resources.
    // ------------------------------------------------------------------
    glfwTerminate();
    return 0;
}

// process all input: query GLFW whether relevant keys are pressed/released this frame and react accordingly
// ---------------------------------------------------------------------------------------------------------
void processInput(GLFWwindow *window)
{
    if (glfwGetKey(window, GLFW_KEY_ESCAPE) == GLFW_PRESS)
        glfwSetWindowShouldClose(window, true);
}

// glfw: whenever the window size changed (by OS or user resize) this callback function executes
// ---------------------------------------------------------------------------------------------
void framebuffer_size_callback(GLFWwindow *window, int width, int height)
{
    // make sure the viewport matches the new window dimensions; note that width and
    // height will be significantly larger than specified on retina displays.
    glViewport(0, 0, width, height);
}

效果

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