本文主要介绍如何使用 C++ 生成圆柱几何体以及如何在 OpenGL 中绘制它。

1.绘制方法

由于我们无法绘制一个完美的圆形底面和圆柱体的弯曲侧面，我们只能通过将底面除以扇区（切片）来采样有限数量的点。因此，它在技术上是通过将这些采样点连接在一起来构建棱柱体。随着样本数量的增加，几何形状更接近于圆柱体。

假设一个圆柱体以原点为中心，半径为r，高度为h。圆柱体上的任意点 ( x, y, z ) 可以从具有相应扇形角θ的圆方程计算出来：

扇形角的范围是从 0 到 360 度。每个步骤的扇形角可以通过以下方式计算：

2.创建存放顶点向量和法向量的结构体：

struct TVertex {
	// position
	glm::vec3 Position;
	// normal
	glm::vec3 Normal;
};

​3.计算圆周上的点

const int sectorCount = 36; 
const float pierRadius = 2.0f;
const float pierHeight = 5.0f;
// 圆周顶点
std::vector<TVertex> getUnitCircleVertices()
{
    const float PI = 3.1415926f;
    float sectorStep = 2 * PI / sectorCount;
    float sectorAngle = 0.0f;
​
    glm::vec3 position;
    glm::vec3 normal;
    TVertex tVertex;
​
    std::vector<TVertex> unitCircleVertices;
    for (int i = 0; i <= sectorCount; ++i)
    {
        sectorAngle = i * sectorStep;
        position.x = pierRadius * cos(sectorAngle);
        position.y = 0.0f;
        position.z = pierRadius * sin(sectorAngle);
​
        normal.x = cos(sectorAngle);
        normal.y = 0.0f;
        normal.z = sin(sectorAngle);
​
        tVertex.Position = position;
        tVertex.Normal = normal;
​
        unitCircleVertices.push_back(tVertex);
    }
​
    return unitCircleVertices;
}

4.获取圆柱体侧面、顶面、底面的顶点和法向量

// generate vertices for a cylinder
void buildCylinderVertices(std::vector<TVertex>& vertices)
{
    std::vector<TVertex> unitVertices = getUnitCircleVertices();
​
    // 获取上、下圆周点数组
    std::vector<TVertex> vctTop;
    std::vector<TVertex> vctBot;
​
    TVertex tVertex;
    for(int i = 0; i < unitVertices.size(); ++i)
    {
        tVertex.Position = unitVertices[i].Position;
        tVertex.Position.y = pierHeight;
        tVertex.Normal = unitVertices[i].Normal;
        vctTop.push_back(tVertex);  
​
        tVertex.Position.y = 0.0f;
        vctBot.push_back(tVertex);     
    }
​
    assert(vctTop.size() >= 2);
    assert(vctBot.size() >= 2);
​
    // 圆柱侧面
    for(int i = 0; i < vctTop.size() - 1; ++i)
    {
        // 左三角形
        vertices.push_back(vctTop[i]);
        vertices.push_back(vctBot[i]);
        vertices.push_back(vctBot[i+1]);
        
        // 右三角形
        vertices.push_back(vctTop[i]);
        vertices.push_back(vctTop[i+1]);
        vertices.push_back(vctBot[i+1]);
    }
    
    // 顶部圆形
    glm::vec3 position;
    for (int i = 0; i < vctTop.size() - 1; ++i)
    {
        glm::vec3 position(0.0f, pierHeight, 0.0f);
        glm::vec3 normal(0.0f, 1.0f, 0.0f);
        tVertex.Position = position;
        tVertex.Normal = normal;
        vertices.push_back(tVertex);
​
        tVertex.Position = vctTop[i].Position;
        vertices.push_back(tVertex);
​
        tVertex.Position = vctTop[i+1].Position;
        vertices.push_back(tVertex);
    }
​
    // 底部圆形
    for (int i = 0; i < vctBot.size() - 1; ++i)
    {
        glm::vec3 position(0.0f, 0.0f, 0.0f);
        glm::vec3 normal(0.0f, -1.0f, 0.0f);
        tVertex.Position = position;
        tVertex.Normal = normal;
        vertices.push_back(tVertex);
​
        tVertex.Position = vctBot[i].Position;
        vertices.push_back(tVertex);
​
        tVertex.Position = vctBot[i+1].Position;
        vertices.push_back(tVertex);
    }
}

5.将顶点和法向量存入缓冲区

  std::vector<TVertex> pierVertices;
  buildCylinderVertices(pierVertices);
  
  unsigned int pierVBO, pierVAO;
  glGenVertexArrays(1, &pierVAO);
  glGenBuffers(1, &pierVBO);
​
  glBindVertexArray(pierVAO);
  glBindBuffer(GL_ARRAY_BUFFER, pierVBO);
​
  glBufferData(GL_ARRAY_BUFFER, pierVertices.size() * sizeof(TVertex), &pierVertices[0], GL_STATIC_DRAW);
  
  // position attribute
  glEnableVertexAttribArray(0);
  glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, sizeof(TVertex), (void*)0);
  // normal attribute
  glEnableVertexAttribArray(1);
  glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, sizeof(TVertex), (void*)offsetof(TVertex, Normal));
​
  glBindVertexArray(0);

6.绘制圆柱体

        glClearColor(0.9f, 0.9f, 0.9f, 1.0f);
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); 
​
        // be sure to activate shader when setting uniforms/drawing objects
        lightingShader.use();
        lightingShader.setVec3("lightDirection", -direction); // 平行光方向
        //lightingShader.setVec3("lightPos", lightPos);
        lightingShader.setVec3("lightColor", 1.0f, 1.0f, 1.0f);
        lightingShader.setVec3("viewPos", camera.Position); 
​
        // 正交平行的视景体
        float fRatio = (float)SCR_WIDTH / (float)SCR_HEIGHT;
        float fHeight = 10.0f;
        float fWidth = fHeight*fRatio;
        //glm::mat4 projection = glm::ortho(-fWidth, fWidth, -fHeight, fHeight, -10.f, 100.f);
        glm::mat4 projection = glm::perspective(glm::radians(camera.Zoom), (float)SCR_WIDTH / (float)SCR_HEIGHT, 0.1f, 100.0f); // 透视投影     
        lightingShader.setMat4("projection", projection);
​
        glm::mat4 viewOrigin = camera.GetViewMatrix();
        lightingShader.setMat4("view", viewOrigin);
​
        // 绘制圆柱体
        viewOrigin = glm::rotate(viewOrigin, glm::radians(30.0f), glm::vec3(1.0f, 0.0f, 0.0f));
        viewOrigin = glm::rotate(viewOrigin, glm::radians(15.0f), glm::vec3(0.0f, 0.0f, -1.0f));
        lightingShader.setMat4("view", viewOrigin);
        glm::mat4 modelPier = glm::mat4(1.0f);
        lightingShader.setMat4("model", modelPier);
        lightingShader.setVec3("objectColor", glm::vec3(0.5f, 0.1f,0.3f));
​
        glBindVertexArray(pierVAO);
        glDrawArrays(GL_TRIANGLES, 0, pierVertices.size());

7.删除缓冲区

    glDeleteVertexArrays(1, &pierVAO);
    glDeleteBuffers(1, &pierVBO);

8.效果

9.完整的项目源代码

https://pan.baidu.com/s/1cEUuAmY3JNUbt7sTNvTuyA

提取码：lf5q