OpenGL 缺陷 - 不需要的插值

我正在尝试使用贝塞尔表面渲染犹他州茶壶，并取得了成功。然而，我有一些完全不受欢迎的缺陷。正如你在这里看到的，茶壶看起来不错，但存在一些不必要的"插值"。你认为这可能是什么原因造成的？ 顺便说一下，当我将对象写入 .ply 文件时，我可以设法使用 meshlab 打开它，没有问题也没有缺陷。最后，我使用 Xcode 作为我的开发环境。

我非常感谢您能提供的任何帮助。

编辑：添加了代码的某些部分。首先，从这张旧纸中检索到控制点和使用的补丁。

struct position3D { GLfloat x, y, z; };
struct position3D teapot_cp_vertices[] = {
// 1
{ 1.4   ,   0.0   ,  2.4 },
{ 1.4   ,  -0.784 ,  2.4 },
{ 0.784 ,  -1.4   ,  2.4 },
{ 0.0   ,  -1.4   ,  2.4 },
.
.
.
}
#define TEAPOT_NB_PATCHES 32
#define ORDER 3
unsigned short teapot_patches[][ORDER + 1][ORDER + 1] =
{
// rim
{ { 1,   2,   3,   4 },{ 5,   6,   7,   8 },{ 9,  10,  11,  12 },{ 13,  14,  15,  16, } },
{ { 4,  17,  18,  19 },{ 8,  20,  21,  22 },{ 12,  23,  24,  25 },{ 16,  26,  27,  28, } },
{ { 19,  29,  30,  31 },{ 22,  32,  33,  34 },{ 25,  35,  36,  37 },{ 28,  38,  39,  40, } },
{ { 31,  41,  42,   1 },{ 34,  43,  44,   5 },{ 37,  45,  46,   9 },{ 40,  47,  48,  13, } },
...
...
...
} }
}

所有点和补丁都可以在上述论文中找到。

用于渲染茶壶的顶点和三角形使用以下公式计算：

int factorial(int n)
{
assert(n >= 0);
return (n == 1 || n == 0) ? 1 : factorial(n - 1) * n;
}
float binomial_coefficient(int i, int n) {
assert(i >= 0); assert(n >= 0);
return 1.0f * factorial(n) / (factorial(i) * factorial(n-i));
}
float bernstein_polynomial(int i, int n, float u) {
return binomial_coefficient(i, n) * powf(u, i) * powf(1-u, n-i);
}
void build_control_points_k(int p, struct position3D control_points_k[][ORDER+1]) {
for (int i = 0; i <= ORDER; i++) {
for (int j = 0; j <= ORDER; j++) {
control_points_k[i][j] = teapot_cp_vertices[teapot_patches[p][i][j] - 1];
}
}
}
Vertex compute_position(struct position3D control_points_k[][ORDER+1], float u, float v) {
Vertex result = *new Vertex();
for (int i = 0; i <= ORDER; i++) {
float poly_i = bernstein_polynomial(i, ORDER, u);
for (int j = 0; j <= ORDER; j++) {
float poly_j = bernstein_polynomial(j, ORDER, v);
result.x += poly_i * poly_j * control_points_k[i][j].x;
result.y += poly_i * poly_j * control_points_k[i][j].y;
result.z += poly_i * poly_j * control_points_k[i][j].z;
result.r = 0; //default colour 
result.g = 0;
result.b = 0;
}
}
return result;
}
#define RESU 10 //resolution in u axis
#define RESV 10 //resolution in v axis
void Object3D::build_teapot() {
vlist = new Vertex[TEAPOT_NB_PATCHES * RESU*RESV]; //vertex list
tlist = new Triangle[TEAPOT_NB_PATCHES * (RESU-1)*(RESV-1) * 2]; //triangle list
//calculate vertices
for (int p = 0; p < TEAPOT_NB_PATCHES; p++) {
struct position3D control_points_k[ORDER+1][ORDER+1];
build_control_points_k(p, control_points_k);
for (int ru = 0; ru <= RESU-1; ru++) {
float u = 1.0 * ru / (RESU-1);
for (int rv = 0; rv <= RESV-1; rv++) {
float v = 1.0 * rv / (RESV-1);
vlist[p*RESU*RESV + ru*RESV + rv] = compute_position(control_points_k, u, v);
vlist[p*RESU*RESV + ru*RESV + rv].r = 1.0 * p / TEAPOT_NB_PATCHES;
vlist[p*RESU*RESV + ru*RESV + rv].g = 1.0 * p / TEAPOT_NB_PATCHES;
vlist[p*RESU*RESV + ru*RESV + rv].b = 0.7;
}
}
}
//calculate triangle vertex orders or namely triangles
int n = 0;
Triangle tmpTrg = *new Triangle();
tmpTrg.nverts = 3;
for (int p = 0; p < TEAPOT_NB_PATCHES; p++) {
for (int ru = 0; ru < RESU-1; ru++)
for (int rv = 0; rv < RESV-1; rv++) {
// ABCD is a square
// triangle in the order ABC is the first one
tmpTrg.verts = new int[tmpTrg.nverts];
tmpTrg.verts[0] = p*RESU*RESV +  ru   *RESV +  rv   ;
tmpTrg.verts[1] = p*RESU*RESV +  ru   *RESV + (rv+1);
tmpTrg.verts[2] = p*RESU*RESV + (ru+1)*RESV + (rv+1);
tlist[n] = tmpTrg;
n++;
// triangle in the order CDA is the second one
tmpTrg.verts = new int[tmpTrg.nverts];
tmpTrg.verts[0] = p*RESU*RESV + (ru+1)*RESV + (rv+1);
tmpTrg.verts[1] = p*RESU*RESV + (ru+1)*RESV +  rv   ;
tmpTrg.verts[2] = p*RESU*RESV +  ru   *RESV +  rv   ;
tlist[n] = tmpTrg;
n++;
}
}
}

这是 GL 初始化函数：

void init(int w, int h)
{
// Init GLFW
glfwInit();
glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);
glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);
// macOSX requirement :
glfwWindowHint(GLFW_OPENGL_FORWARD_COMPAT, GL_TRUE);
glfwWindowHint(GLFW_RESIZABLE, GL_FALSE);
glfwWindowHint(GLFW_SAMPLES, 4);
window = glfwCreateWindow(w, h, "OpenGLTeapot", nullptr, nullptr); // Windowed
glfwMakeContextCurrent(window);
glfwSetKeyCallback(window, key_callback);
// Initialize GLEW to setup the OpenGL Function pointers
glewExperimental = GL_TRUE;
glewInit();
// Define the viewport dimensions
glViewport(0, 0, w, h);
// Enable depth test
glEnable(GL_DEPTH_TEST);
}

编辑2：我尝试使用Visual Studio15在Windows计算机上运行代码，并且没有这样的缺陷。有没有人知道是什么可能导致如此愚蠢的问题？

编辑3：这是对象创建代码：

void Object3D::CreateObject()
{
int attributeCount = 6;
vertexCount        = TEAPOT_NB_PATCHES * RESU*RESV;
triangleCount      = TEAPOT_NB_PATCHES * (RESU-1)*(RESV-1) * 2;
build_teapot();
//Bind the vertex and index buffers
glGenVertexArrays(1, &VAO);
glGenBuffers(1, &VBO);
glGenBuffers(1, &EBO);
// Bind our Vertex Array Object first, then bind and set our buffers and pointers.
glBindVertexArray(VAO);
//Convert our vertex list into a continuous array, copy the vertices into the vertex buffer.
float* vertexData = new float[vertexCount * attributeCount];
for (int i = 0; i < vertexCount; i++)
memcpy(&vertexData[i*attributeCount], 
vlist[i].getAsArray(), sizeof(float)*attributeCount);
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glBufferData(GL_ARRAY_BUFFER, sizeof(float)*attributeCount*vertexCount, vertexData, GL_STATIC_DRAW);
//Copy the index data found in the list of triangles into the element array buffer (index array)
//We are using a triangles, so we need triangleCount * 3 indices.
int* indexData = new int[triangleCount * 3];
for (int i = 0; i < triangleCount; i++)
memcpy(&indexData[i * 3], tlist[i].verts, sizeof(int) * 3);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, EBO);
glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(int)*3*triangleCount, indexData, GL_STATIC_DRAW);
// Position attribute
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, attributeCount * sizeof(GLfloat), (GLvoid*)0);
glEnableVertexAttribArray(0);
// Color attribute
glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, attributeCount * sizeof(GLfloat), (GLvoid*)(3 * sizeof(GLfloat)));
glEnableVertexAttribArray(1);
// Unbind VAO
glBindVertexArray(0);
// Delete temporary buffers
delete[] vertexData;
delete[] indexData;
}

和主要功能：

int main()
{
int screenWidth = 800;
int screenHeight = 600;
init(screenWidth, screenHeight);
std::vector<Object3D*> listOfObjects;

Object3D* pObj = new Object3D();

pObj->CreateObject();
listOfObjects.push_back(pObj);
//Create the shaders. 
Shader shader(VertexShaderPath, FragmentShaderPath);
while (!glfwWindowShouldClose(window))
{
glfwPollEvents();
// Clear the colorbuffer
glClearColor(0.0f, 0.3f, 0.3f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
// Use the shader
shader.Use();
// Transformations
// Create camera transformation
glm::mat4 view;
glm::vec3 cameraPos = glm::vec3(0.0f, 150.0f, 100.0f);
glm::vec3 cameraTarget = glm::vec3(0.0, 80.0f, 20.0f);
glm::vec3 cameraUp = glm::vec3(0.0f, 1.0f, 0.0f);
view = glm::lookAt(cameraPos, cameraTarget, cameraUp);
// Create projection transformation
glm::mat4 projection;
projection = glm::perspective<float>(90.0, (float)screenWidth / (float)screenHeight, 0.1f, 1000.0f);
// Get the uniform locations
GLint modelLoc = glGetUniformLocation(shader.Program, "model");
GLint viewLoc = glGetUniformLocation(shader.Program, "view");
GLint projLoc = glGetUniformLocation(shader.Program, "projection");
// Pass the view and projection matrices to the shaders
glUniformMatrix4fv(viewLoc, 1, GL_FALSE, glm::value_ptr(view));
glUniformMatrix4fv(projLoc, 1, GL_FALSE, glm::value_ptr(projection));
// Put the bottom of the object on XZ plane and scale it up
pObj->modelMatrix = glm::scale(glm::mat4(1.0f), glm::vec3(30.0f));
pObj->modelMatrix = glm::rotate(pObj->modelMatrix, -90.0f, glm::vec3(1.0f, 0.0f,0.0f));
for (auto pObj : listOfObjects)
{
glBindVertexArray(pObj->VAO);
glUniformMatrix4fv(modelLoc, 1, GL_FALSE, glm::value_ptr(pObj->modelMatrix));
glDrawElements(GL_TRIANGLES, (pObj->vertexCount) * 6, GL_UNSIGNED_INT, 0);
//glDrawElements(GL_TRIANGLES, 50, GL_UNSIGNED_INT, 0);
glBindVertexArray(0);
}
// Swap the buffers
glfwSwapBuffers(window);
}
for (auto pObj : listOfObjects)
{
glDeleteVertexArrays(1, &pObj->VAO);
glDeleteBuffers(1, &pObj->VBO);
glDeleteBuffers(1, &pObj->EBO);
delete pObj;
}
glfwTerminate();
return 0;
}