为什么旋转矩阵不在文本中心旋转？
Why doesn't the rotation matrix rotate in the center of the text?
我正在尝试在 OpenGL 中旋转文本，但是，问题是文本按应有的方式旋转但在错误的点，即它没有在文本的中心旋转（而且我想知道我是怎么做到的！）。
我之所以感到困惑，是因为我对文本的不同字母使用了多个纹理，这让我感到困惑。
如果您想知道我使用的是哪个库，那就是 CGLM
但是当我编译这段代码时，rotate 函数以错误的旋转点旋转对象。
根据 Rabbid76。我做了以下得到整个文本的大小：-
for (int i = 0; i < (signed)strlen(text); i++)
{
tw += iterator[(int)text[i]].Character_Array.Size[0];
th += iterator[(int)text[i]].Character_Array.Size[1];
}
我仍然没有得到正确的结果，文本仍然错位。
在任何轮换之前（这是它应该轮换的地方）：-
旋转 45 度后（从其位置错位）：-
编辑：源文件的全部代码：-
// Std. Includes
#include <stdio.h>
#include <stdlib.h>
// GLEW
#define GLEW_STATIC
#include <GL/glew.h>
// GLFW
#include <GLFW/glfw3.h>
// GLM
#include <cglm/cglm.h>
// FreeType
#include <ft2build.h>
#include FT_FREETYPE_H
// Properties
const GLuint WIDTH = 800, HEIGHT = 600;
const GLchar * vertexShaderSource =
"#version 330 core\n"
"layout(location = 0) in vec4 vertex;\n"
"out vec2 TexCoords;\n"
"uniform mat4 projection;\n"
"uniform mat4 model;\n"
"void main()\n"
"{\n"
"gl_Position = projection * model * vec4(vertex.xy, 0.0, 1.0);\n"
"TexCoords = vertex.zw;\n"
"}\n[=11=]";
const GLchar * fragmentShaderSource =
"#version 330 core\n"
"in vec2 TexCoords;\n"
"out vec4 color;\n"
"uniform sampler2D text;\n"
"uniform vec4 textColor;\n"
"void main()\n"
"{\n"
"vec4 sampled = vec4(1.0, 1.0, 1.0, texture(text, TexCoords).r);\n"
"color = textColor * sampled;\n"
"}\n[=11=]";
/// Holds all state information relevant to a character as loaded using FreeType
typedef struct {
GLuint TextureID; // ID handle of the glyph texture
int Size[2]; // Size of glyph
int Bearing[2]; // Offset from baseline to left/top of glyph
GLuint Advance; // Horizontal offset to advance to next glyph
} Character;
typedef struct
{
GLchar char_Array;
Character Character_Array;
} Iterator;
Iterator * iterator;
GLuint VAO, VBO;
// RenderText function.. to render our text...
void RenderText(GLuint program, const char * text, GLfloat originx, GLfloat originy, GLfloat x, GLfloat y, GLfloat scalex, GLfloat scaley, float rotation, float r, float g, float b, float a);
// The MAIN function, from here we start our application and run the Game loop
int main()
{
iterator = NULL;
// Init GLFW
glfwInit();
glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);
glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);
glfwWindowHint(GLFW_RESIZABLE, GL_FALSE);
GLFWwindow* window = glfwCreateWindow(WIDTH, HEIGHT, "LearnOpenGL", NULL, NULL); // Windowed
glfwMakeContextCurrent(window);
// Initialize GLEW to setup the OpenGL Function pointers
glewExperimental = GL_TRUE;
glewInit();
// Define the viewport dimensions
glViewport(0, 0, WIDTH, HEIGHT);
// Set OpenGL options
glEnable(GL_CULL_FACE);
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
// Compile and setup the shader
GLuint vertex_shader = glCreateShader(GL_VERTEX_SHADER);
glShaderSource(vertex_shader, 1, &vertexShaderSource, NULL);
glCompileShader(vertex_shader);
GLuint fragment_shader = glCreateShader(GL_FRAGMENT_SHADER);
glShaderSource(fragment_shader, 1, &fragmentShaderSource, NULL);
glCompileShader(fragment_shader);
GLuint program = glCreateProgram();
glAttachShader(program, vertex_shader);
glAttachShader(program, fragment_shader);
glLinkProgram(program);
glDeleteShader(vertex_shader);
glDeleteShader(fragment_shader);
mat4 projection;
glm_ortho(0.0f, (GLfloat)WIDTH, (GLfloat)HEIGHT, 0.0f, -1, 1, projection);
glUseProgram(program);
glUniformMatrix4fv(glGetUniformLocation(program, "projection"), 1, GL_FALSE, (GLfloat *)projection);
// FreeType
FT_Library ft;
// All functions return a value different than 0 whenever an error occurred
if (FT_Init_FreeType(&ft))
printf("ERROR::FREETYPE: Could not init FreeType Library\n");
// Load font as face
FT_Face face;
if (FT_New_Face(ft, "playfair.ttf", 0, &face))
printf("ERROR::FREETYPE: Failed to load font\n");
// Set size to load glyphs as
FT_Set_Pixel_Sizes(face, 0, 72);
// Disable byte-alignment restriction
glPixelStorei(GL_UNPACK_ALIGNMENT, 1);
int i = 0;
// Load first 128 characters of ASCII set
for (GLubyte c = 0; c < 255; c++)
{
// Load character glyph
if (FT_Load_Char(face, c, FT_LOAD_RENDER))
{
printf("ERROR::FREETYTPE: Failed to load Glyph\n");
continue;
}
// Generate texture
GLuint texture;
glGenTextures(1, &texture);
glBindTexture(GL_TEXTURE_2D, texture);
glTexImage2D(
GL_TEXTURE_2D,
0,
GL_RED,
face->glyph->bitmap.width,
face->glyph->bitmap.rows,
0,
GL_RED,
GL_UNSIGNED_BYTE,
face->glyph->bitmap.buffer
);
// Set texture options
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
// Now store character for later use
Character character = {
texture,
{(signed)face->glyph->bitmap.width, (signed)face->glyph->bitmap.rows},
{face->glyph->bitmap_left, face->glyph->bitmap_top},
(GLuint)face->glyph->advance.x
};
iterator = (Iterator*)realloc(iterator, sizeof(Iterator) * (i + 1));
iterator[i].Character_Array = character;
iterator[i].char_Array = c;
i++;
}
glBindTexture(GL_TEXTURE_2D, 0);
// Destroy FreeType once we're finished
FT_Done_Face(face);
FT_Done_FreeType(ft);
// Configure VAO/VBO for texture quads
glGenVertexArrays(1, &VAO);
glGenBuffers(1, &VBO);
glBindVertexArray(VAO);
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glBufferData(GL_ARRAY_BUFFER, sizeof(GLfloat) * 6 * 4, NULL, GL_DYNAMIC_DRAW);
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 4, GL_FLOAT, GL_FALSE, 4 * sizeof(GLfloat), 0);
glBindBuffer(GL_ARRAY_BUFFER, 0);
glBindVertexArray(0);
glfwVulkanSupported();
// Game loop
float k = 0;
while (!glfwWindowShouldClose(window))
{
// Check and call events
glfwPollEvents();
// Clear the colorbuffer
glClearColor(0.2f, 0.3f, 0.3f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT);
if (k > 360)
{
k = 0;
}
k += 0.1f;
RenderText(program, "Rotation", 0, 0, 10.0f, 10.0f, 1.0f, 1.0f, k, 0.5f, 0.8f, 0.2f, 1.0f);
// Swap the buffers
glfwSwapBuffers(window);
}
glfwTerminate();
return 0;
}
void RenderText(GLuint program, const char * text, GLfloat originx, GLfloat originy, GLfloat x, GLfloat y, GLfloat scalex, GLfloat scaley, float rotation, float r, float g, float b, float a)
{
// Activate corresponding render state
glUseProgram(program);
glUniform4f(glGetUniformLocation(program, "textColor"), r, g, b, a);
glActiveTexture(GL_TEXTURE0);
glBindVertexArray(VAO);
GLfloat tw = iterator[(int)text[i]].Character_Array.Bearing[0],
th = 0.0f;
for (int i = 0; i < (signed)strlen(text); i++)
{
Character ch = iterator[(int)text[i]].Character_Array;
tw += (ch.Advance >> 6);
th += ch.Size[1];
}
GLfloat rx = tw / 2.0f;
GLfloat ry = th / 2.0f;
mat4 model;
glm_mat4_identity(model);
glm_translate(model, (vec3) { originx, originy, 0.0f });
glm_translate(model, (vec3) { scalex * rx, scaley * ry, 0.0f });
glm_rotate(model, glm_rad(rotation), (vec3) { 0.0f, 0.0f, 1.0f });
glm_translate(model, (vec3) { -scalex * rx, -scaley * ry, 0.0f });
glm_scale(model, (vec3) { scalex, scaley, 1.0f });
GLfloat xpos = 0.0;
GLfloat ypos = 0.0;
for (int i = 0; i < (signed)strlen(text); i++)
{
Character ch = iterator[(int)text[i]].Character_Array;
mat4 ch_model;
memcpy(ch_model, model, 16 * sizeof(float));
glm_translate(ch_model, (vec3) { x, 0.0f, 0.0f });
// Now advance cursors for next glyph (note that advance is number of 1/64 pixels)
x += (ch.Advance >> 6); // Bitshift by 6 to get value in pixels (2^6 = 64 (divide amount of 1/64th pixels by 64 to get amount of pixels))
glUniformMatrix4fv(glGetUniformLocation(program, "model"), 1, GL_FALSE, (GLfloat *)ch_model);
// Render glyph texture over quad
glBindTexture(GL_TEXTURE_2D, ch.TextureID);
GLfloat w = ch.Size[0] * scalex;
GLfloat h = ch.Size[1] * scaley;
GLfloat vertices[6][4] = {
{ 0.0f, h, 0.0, 1.0 },
{ w, 0.0f, 1.0, 0.0 },
{ 0.0f, 0.0f, 0.0, 0.0 },
{ 0.0f, h, 0.0, 1.0 },
{ w, h, 1.0, 01.0 },
{ w, 0.0f, 01.0, 0.0 },
};
// Update content of VBO memory
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glBufferSubData(GL_ARRAY_BUFFER, 0, sizeof(vertices), vertices); // Be sure to use glBufferSubData and not glBufferData
glBindBuffer(GL_ARRAY_BUFFER, 0);
// Render quad
glDrawArrays(GL_TRIANGLES, 0, 6);
}
glBindVertexArray(0);
glBindTexture(GL_TEXTURE_2D, 0);
}
glm_rotate 在原点应用旋转。因此，如果您的 几何体的中心 不在原点，则不会围绕 object/geometry 的中心进行旋转。
解决方案：X = T(p)Rz(φ)T(−p) 其中 X 是最终变换，p 是枢轴
- 将枢轴（或对象中心，不是对象的位置，它不相同）平移到原点
- 应用旋转或缩放
- 将枢轴平移回其原始位置
如果您想围绕对象的中心旋转（如果对象的中心不在原点），那么您必须计算该对象的中心 object/geometry。在应用任何旋转之前。您可以计算边界框然后获取该框的中心。
cglm 也为此提供了函数：glm_vec_center(min, max, pivot); /* pivot = center of object */。现在我们有了中心点。让我们围绕那个点旋转：
/* ... */
glm_vec_center(min, max, pivot); /* center of object */
glm_vec_inv_to(pivot, pivotInv); /* -pivot */
/* ... */
glm_translate(model, pivot);
glm_rotate(model, angle, axis);
glm_translate(model, pivotInv);
上面的代码与 X = T(p)Rz(φ)T(−p)（平移（-pivot），旋转，平移（pivot） ).代码中的顺序似乎是相反的，因为 glm_translate = Transform * Translate。如果 glm_translate = Translate * Transform 则不会倒序。 cglm 将来可能也会提供这种替代翻译乘法
编辑： 通过启动 v0.4.2 版本 cglm 为此目的提供函数：检查 glm_rotate_at() 和 glm_quat_rotate_at()、glm_rotate_atm 和 glm_quat_rotate_atm 自 glm_rotate_at 和 glm_quat_rotate_at 以来为枢轴点创建新的旋转旋转现有的变换。要使用这些功能，请确保您拥有最新版本。
我正在尝试在 OpenGL 中旋转文本，但是，问题是文本按应有的方式旋转但在错误的点，即它没有在文本的中心旋转（而且我想知道我是怎么做到的！）。
我之所以感到困惑，是因为我对文本的不同字母使用了多个纹理，这让我感到困惑。
如果您想知道我使用的是哪个库，那就是 CGLM
但是当我编译这段代码时，rotate 函数以错误的旋转点旋转对象。
根据 Rabbid76。我做了以下得到整个文本的大小：-
for (int i = 0; i < (signed)strlen(text); i++)
{
tw += iterator[(int)text[i]].Character_Array.Size[0];
th += iterator[(int)text[i]].Character_Array.Size[1];
}
我仍然没有得到正确的结果，文本仍然错位。
在任何轮换之前（这是它应该轮换的地方）：-
编辑：源文件的全部代码：-
// Std. Includes
#include <stdio.h>
#include <stdlib.h>
// GLEW
#define GLEW_STATIC
#include <GL/glew.h>
// GLFW
#include <GLFW/glfw3.h>
// GLM
#include <cglm/cglm.h>
// FreeType
#include <ft2build.h>
#include FT_FREETYPE_H
// Properties
const GLuint WIDTH = 800, HEIGHT = 600;
const GLchar * vertexShaderSource =
"#version 330 core\n"
"layout(location = 0) in vec4 vertex;\n"
"out vec2 TexCoords;\n"
"uniform mat4 projection;\n"
"uniform mat4 model;\n"
"void main()\n"
"{\n"
"gl_Position = projection * model * vec4(vertex.xy, 0.0, 1.0);\n"
"TexCoords = vertex.zw;\n"
"}\n[=11=]";
const GLchar * fragmentShaderSource =
"#version 330 core\n"
"in vec2 TexCoords;\n"
"out vec4 color;\n"
"uniform sampler2D text;\n"
"uniform vec4 textColor;\n"
"void main()\n"
"{\n"
"vec4 sampled = vec4(1.0, 1.0, 1.0, texture(text, TexCoords).r);\n"
"color = textColor * sampled;\n"
"}\n[=11=]";
/// Holds all state information relevant to a character as loaded using FreeType
typedef struct {
GLuint TextureID; // ID handle of the glyph texture
int Size[2]; // Size of glyph
int Bearing[2]; // Offset from baseline to left/top of glyph
GLuint Advance; // Horizontal offset to advance to next glyph
} Character;
typedef struct
{
GLchar char_Array;
Character Character_Array;
} Iterator;
Iterator * iterator;
GLuint VAO, VBO;
// RenderText function.. to render our text...
void RenderText(GLuint program, const char * text, GLfloat originx, GLfloat originy, GLfloat x, GLfloat y, GLfloat scalex, GLfloat scaley, float rotation, float r, float g, float b, float a);
// The MAIN function, from here we start our application and run the Game loop
int main()
{
iterator = NULL;
// Init GLFW
glfwInit();
glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3);
glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);
glfwWindowHint(GLFW_RESIZABLE, GL_FALSE);
GLFWwindow* window = glfwCreateWindow(WIDTH, HEIGHT, "LearnOpenGL", NULL, NULL); // Windowed
glfwMakeContextCurrent(window);
// Initialize GLEW to setup the OpenGL Function pointers
glewExperimental = GL_TRUE;
glewInit();
// Define the viewport dimensions
glViewport(0, 0, WIDTH, HEIGHT);
// Set OpenGL options
glEnable(GL_CULL_FACE);
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
// Compile and setup the shader
GLuint vertex_shader = glCreateShader(GL_VERTEX_SHADER);
glShaderSource(vertex_shader, 1, &vertexShaderSource, NULL);
glCompileShader(vertex_shader);
GLuint fragment_shader = glCreateShader(GL_FRAGMENT_SHADER);
glShaderSource(fragment_shader, 1, &fragmentShaderSource, NULL);
glCompileShader(fragment_shader);
GLuint program = glCreateProgram();
glAttachShader(program, vertex_shader);
glAttachShader(program, fragment_shader);
glLinkProgram(program);
glDeleteShader(vertex_shader);
glDeleteShader(fragment_shader);
mat4 projection;
glm_ortho(0.0f, (GLfloat)WIDTH, (GLfloat)HEIGHT, 0.0f, -1, 1, projection);
glUseProgram(program);
glUniformMatrix4fv(glGetUniformLocation(program, "projection"), 1, GL_FALSE, (GLfloat *)projection);
// FreeType
FT_Library ft;
// All functions return a value different than 0 whenever an error occurred
if (FT_Init_FreeType(&ft))
printf("ERROR::FREETYPE: Could not init FreeType Library\n");
// Load font as face
FT_Face face;
if (FT_New_Face(ft, "playfair.ttf", 0, &face))
printf("ERROR::FREETYPE: Failed to load font\n");
// Set size to load glyphs as
FT_Set_Pixel_Sizes(face, 0, 72);
// Disable byte-alignment restriction
glPixelStorei(GL_UNPACK_ALIGNMENT, 1);
int i = 0;
// Load first 128 characters of ASCII set
for (GLubyte c = 0; c < 255; c++)
{
// Load character glyph
if (FT_Load_Char(face, c, FT_LOAD_RENDER))
{
printf("ERROR::FREETYTPE: Failed to load Glyph\n");
continue;
}
// Generate texture
GLuint texture;
glGenTextures(1, &texture);
glBindTexture(GL_TEXTURE_2D, texture);
glTexImage2D(
GL_TEXTURE_2D,
0,
GL_RED,
face->glyph->bitmap.width,
face->glyph->bitmap.rows,
0,
GL_RED,
GL_UNSIGNED_BYTE,
face->glyph->bitmap.buffer
);
// Set texture options
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
// Now store character for later use
Character character = {
texture,
{(signed)face->glyph->bitmap.width, (signed)face->glyph->bitmap.rows},
{face->glyph->bitmap_left, face->glyph->bitmap_top},
(GLuint)face->glyph->advance.x
};
iterator = (Iterator*)realloc(iterator, sizeof(Iterator) * (i + 1));
iterator[i].Character_Array = character;
iterator[i].char_Array = c;
i++;
}
glBindTexture(GL_TEXTURE_2D, 0);
// Destroy FreeType once we're finished
FT_Done_Face(face);
FT_Done_FreeType(ft);
// Configure VAO/VBO for texture quads
glGenVertexArrays(1, &VAO);
glGenBuffers(1, &VBO);
glBindVertexArray(VAO);
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glBufferData(GL_ARRAY_BUFFER, sizeof(GLfloat) * 6 * 4, NULL, GL_DYNAMIC_DRAW);
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 4, GL_FLOAT, GL_FALSE, 4 * sizeof(GLfloat), 0);
glBindBuffer(GL_ARRAY_BUFFER, 0);
glBindVertexArray(0);
glfwVulkanSupported();
// Game loop
float k = 0;
while (!glfwWindowShouldClose(window))
{
// Check and call events
glfwPollEvents();
// Clear the colorbuffer
glClearColor(0.2f, 0.3f, 0.3f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT);
if (k > 360)
{
k = 0;
}
k += 0.1f;
RenderText(program, "Rotation", 0, 0, 10.0f, 10.0f, 1.0f, 1.0f, k, 0.5f, 0.8f, 0.2f, 1.0f);
// Swap the buffers
glfwSwapBuffers(window);
}
glfwTerminate();
return 0;
}
void RenderText(GLuint program, const char * text, GLfloat originx, GLfloat originy, GLfloat x, GLfloat y, GLfloat scalex, GLfloat scaley, float rotation, float r, float g, float b, float a)
{
// Activate corresponding render state
glUseProgram(program);
glUniform4f(glGetUniformLocation(program, "textColor"), r, g, b, a);
glActiveTexture(GL_TEXTURE0);
glBindVertexArray(VAO);
GLfloat tw = iterator[(int)text[i]].Character_Array.Bearing[0],
th = 0.0f;
for (int i = 0; i < (signed)strlen(text); i++)
{
Character ch = iterator[(int)text[i]].Character_Array;
tw += (ch.Advance >> 6);
th += ch.Size[1];
}
GLfloat rx = tw / 2.0f;
GLfloat ry = th / 2.0f;
mat4 model;
glm_mat4_identity(model);
glm_translate(model, (vec3) { originx, originy, 0.0f });
glm_translate(model, (vec3) { scalex * rx, scaley * ry, 0.0f });
glm_rotate(model, glm_rad(rotation), (vec3) { 0.0f, 0.0f, 1.0f });
glm_translate(model, (vec3) { -scalex * rx, -scaley * ry, 0.0f });
glm_scale(model, (vec3) { scalex, scaley, 1.0f });
GLfloat xpos = 0.0;
GLfloat ypos = 0.0;
for (int i = 0; i < (signed)strlen(text); i++)
{
Character ch = iterator[(int)text[i]].Character_Array;
mat4 ch_model;
memcpy(ch_model, model, 16 * sizeof(float));
glm_translate(ch_model, (vec3) { x, 0.0f, 0.0f });
// Now advance cursors for next glyph (note that advance is number of 1/64 pixels)
x += (ch.Advance >> 6); // Bitshift by 6 to get value in pixels (2^6 = 64 (divide amount of 1/64th pixels by 64 to get amount of pixels))
glUniformMatrix4fv(glGetUniformLocation(program, "model"), 1, GL_FALSE, (GLfloat *)ch_model);
// Render glyph texture over quad
glBindTexture(GL_TEXTURE_2D, ch.TextureID);
GLfloat w = ch.Size[0] * scalex;
GLfloat h = ch.Size[1] * scaley;
GLfloat vertices[6][4] = {
{ 0.0f, h, 0.0, 1.0 },
{ w, 0.0f, 1.0, 0.0 },
{ 0.0f, 0.0f, 0.0, 0.0 },
{ 0.0f, h, 0.0, 1.0 },
{ w, h, 1.0, 01.0 },
{ w, 0.0f, 01.0, 0.0 },
};
// Update content of VBO memory
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glBufferSubData(GL_ARRAY_BUFFER, 0, sizeof(vertices), vertices); // Be sure to use glBufferSubData and not glBufferData
glBindBuffer(GL_ARRAY_BUFFER, 0);
// Render quad
glDrawArrays(GL_TRIANGLES, 0, 6);
}
glBindVertexArray(0);
glBindTexture(GL_TEXTURE_2D, 0);
}
glm_rotate 在原点应用旋转。因此，如果您的 几何体的中心 不在原点，则不会围绕 object/geometry 的中心进行旋转。
解决方案：X = T(p)Rz(φ)T(−p) 其中 X 是最终变换，p 是枢轴
- 将枢轴（或对象中心，不是对象的位置，它不相同）平移到原点
- 应用旋转或缩放
- 将枢轴平移回其原始位置
如果您想围绕对象的中心旋转（如果对象的中心不在原点），那么您必须计算该对象的中心 object/geometry。在应用任何旋转之前。您可以计算边界框然后获取该框的中心。
cglm 也为此提供了函数：glm_vec_center(min, max, pivot); /* pivot = center of object */。现在我们有了中心点。让我们围绕那个点旋转：
/* ... */
glm_vec_center(min, max, pivot); /* center of object */
glm_vec_inv_to(pivot, pivotInv); /* -pivot */
/* ... */
glm_translate(model, pivot);
glm_rotate(model, angle, axis);
glm_translate(model, pivotInv);
上面的代码与 X = T(p)Rz(φ)T(−p)（平移（-pivot），旋转，平移（pivot） ).代码中的顺序似乎是相反的，因为 glm_translate = Transform * Translate。如果 glm_translate = Translate * Transform 则不会倒序。 cglm 将来可能也会提供这种替代翻译乘法
编辑： 通过启动 v0.4.2 版本 cglm 为此目的提供函数：检查 glm_rotate_at() 和 glm_quat_rotate_at()、glm_rotate_atm 和 glm_quat_rotate_atm 自 glm_rotate_at 和 glm_quat_rotate_at 以来为枢轴点创建新的旋转旋转现有的变换。要使用这些功能，请确保您拥有最新版本。