# OpenGL rotate around arbitrary point

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Hi, all I'd like to do something like Gooogle earth e.g., if I click on an arbitrary location on the map and drag the mouse, the whole map should rotate about the location where mouse is clicked at. I did it like this: (following are MATLAB code, realvec is the absolute coordinate in OpenGL world, lastvec and currvec are cross products of M.v)
lastmat = rotm(-90, 0, 0, 0, 0, -15);
lastvec = [2.5601 -0.0001 1.7256 1]
realvec = (inv(lastmat)*lastvec')'

currmat = rotm(-90, -5, 0, 0, 0, -15);
currvec = (currmat*realvec')'
currmat(1:4,4) = currmat(1:4,4)-(currvec-lastvec)';

thisvec = (currmat*origvec')'


I had it tested in MatLab, it seemed perfectly alright, but when implemented in OpenGL, it did not. I've been stuck here for a while, does anyone know how on this?
function X = rotm(xAngle, yAngle, zAngle, xOffset, yOffset, zOffset);

txMatrix = [1 0 0 xOffset; 0 1 0 0; 0 0 1 0; 0 0 0 1];
tyMatrix = [1 0 0 0; 0 1 0 yOffset; 0 0 1 0; 0 0 0 1];
tzMatrix = [1 0 0 0; 0 1 0 0; 0 0 1 zOffset; 0 0 0 1];

X = txMatrix * tyMatrix * tzMatrix * xMatrix * yMatrix * zMatrix;


Thanks! [Edited by - thinhare on January 3, 2010 3:44:45 PM]

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I've tried to put together some c code to show the problem.

Up to now, what I achieved is when I click on a point on the white line, the sheet rotate around that point, but if I click not on the white line, the sheet will rotate around a point on the white line, and that point is aligned vertically with the point I click.

Not sure if I have made myself clear, maybe the code explains better.

(You can press ESC to reset the scene)

#include <GL/gl.h>#include <GL/glu.h>#include <glut.h>#include <math.h>int mWidth, mHeight;float mZTrans;float mYAngle;int mMouseX, mMouseY;double mPosX, mPosY, mPosZ;int mMouseMove;void getClickCoord(int x, int y, double *posX, double *posY, double *posZ){  int viewport[4];  double modelview[16];  double projection[16];  float winX, winY, winZ;    glGetDoublev(GL_MODELVIEW_MATRIX, modelview);  glGetDoublev(GL_PROJECTION_MATRIX, projection);  glGetIntegerv(GL_VIEWPORT, viewport);  winX = (float)x;  winY = (float)(viewport[3] - y - 1);  glReadPixels((int)winX, (int)winY, 1, 1,      GL_DEPTH_COMPONENT, GL_FLOAT, &winZ );  gluUnProject(winX, winY, winZ, modelview, projection, viewport,      posX, posY, posZ);}float normalizeAngle(float angle){  angle -= (360*(int)(angle/360));  if (angle < 0) angle += 360;  return angle;}void glOrthoBegin(){  glMatrixMode(GL_PROJECTION);  glPushMatrix();  glLoadIdentity();  glOrtho(0, mWidth, 0, mHeight, -1, 1);  glMatrixMode(GL_MODELVIEW);  glPushMatrix();  glLoadIdentity();}void glOrthoEnd(){  glMatrixMode(GL_PROJECTION);  glPopMatrix();  glMatrixMode(GL_MODELVIEW);  glPopMatrix();}void paintCircle(float radius, GLint xoffset, GLint yoffset){  float delta = 0.05;  glPushAttrib(GL_CURRENT_BIT);  glColor3f(0.0, 1.0, 0.0);  glBegin(GL_LINE_LOOP);  float theta;  for (theta = 0; theta < 2*M_PI; theta += delta) {    glVertex2i((int)(radius*cos(theta))+xoffset,        (int)(radius*sin(theta))+yoffset);  }  glEnd();  glPopAttrib();}void paintQuads(){  int row, col;  float xoffset, zoffset;  glPushAttrib(GL_CURRENT_BIT);  glBegin(GL_QUADS);  for (row = 0; row < 10; row++) {    zoffset = 1*row+0.5 - 5;    for (col = 0; col < 10; col++) {      xoffset = 1*col+0.5 - 5;      glColor3f(row*0.1, col*0.1, 0.0);      glVertex3f(-0.5+xoffset, 0, -0.5+zoffset);      glVertex3f(-0.5+xoffset, 0,  0.5+zoffset);      glVertex3f( 0.5+xoffset, 0,  0.5+zoffset);      glVertex3f( 0.5+xoffset, 0, -0.5+zoffset);    }  }  glEnd();  glPopAttrib();}void reset(){  mZTrans = -15.0;  mYAngle = 0.0;  mMouseX = mMouseY = 0;  mMouseMove = 0;}void init() {  glClearColor(0.0, 0.0, 0.0, 1.0);  glClearDepth(1.0);  glShadeModel(GL_SMOOTH);  glDepthFunc(GL_LEQUAL);  glEnable(GL_DEPTH_TEST);  glEnable(GL_CULL_FACE);  float ambient[] = {0.5, 0.5, 0.5, 1.0};  float diffuse[] = {0.8, 0.8, 0.8, 1.0};  float specular[] = {1.0, 1.0, 1.0, 1.0};  float position[] = {0.0, 0.0, 0.0, 1.0};  glLightfv(GL_LIGHT0, GL_AMBIENT, ambient);  glLightfv(GL_LIGHT0, GL_DIFFUSE, diffuse);  glLightfv(GL_LIGHT0, GL_SPECULAR, specular);  glLightfv(GL_LIGHT0, GL_POSITION, position);  glEnable(GL_LIGHTING);  glEnable(GL_LIGHT0);  glEnable(GL_COLOR_MATERIAL);}void display(){  glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);  glLoadIdentity();  glTranslatef(0, 0, mZTrans);  if (mMouseMove) glTranslatef(mPosX, mPosY, mPosZ);  glRotatef(45.0, 1, 0, 0);  glRotatef(mYAngle, 0, 1, 0);  if (mMouseMove) glTranslatef(-mPosX, -mPosY, -mPosZ);  paintQuads();  if (mMouseMove) {    glOrthoBegin();    paintCircle(20.0, mMouseX, (mHeight-mMouseY-1));    glOrthoEnd();  }  mMouseMove = 0;  glutSwapBuffers();}void reshape(int width, int height) {  glViewport(0, 0, width, height);  glMatrixMode(GL_PROJECTION);  glLoadIdentity();  mWidth = width; mHeight = height;  float aspect = (float)width/(float)height;  float top, bottom, left, right;  top = 0.1*tan(20.0/180.0*M_PI);  if (aspect < 1.0) top *= (1.0/aspect);  bottom = -top;  right = top*aspect;  left = -right;  glFrustum(left, right, bottom, top, 0.1, 100);  glMatrixMode(GL_MODELVIEW);  glLoadIdentity();}void mouse(int button, int state, int x, int y){  if (state == GLUT_DOWN) {    mMouseX = x; mMouseY = y;    getClickCoord(x, y, &mPosX, &mPosY, &mPosZ);  }  else if (state == GLUT_UP) {    glutPostRedisplay();  }}void motion(int x, int y){  mYAngle = normalizeAngle(mYAngle + 5);  mMouseMove = 1;  glutPostRedisplay();}void keyboard(unsigned char key, int x, int y){  switch (key) {    case 27:      reset();      glutPostRedisplay();      break;    case '=':    case '+':      mZTrans /= 1.2;      glutPostRedisplay();      break;    case '-':    case '_':      mZTrans *= 1.2;      glutPostRedisplay();      break;    case 'Q':    case 'q':      exit(0);      break;    default:      break;  }}int main(int argc, char** argv){  glutInit(&argc, argv);  glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);  glutInitWindowSize(640, 480);   glutInitWindowPosition(100, 60);  glutCreateWindow(argv[0]);  reset();  init();  glutDisplayFunc(display);   glutReshapeFunc(reshape);  glutMouseFunc(mouse);  glutMotionFunc(motion);  glutKeyboardFunc(keyboard);  glutMainLoop();  return 0;}

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Video:

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Take a look at my code:
Sprite Class
(You mostly need to see the Constructor, the Render Method and the Move Method)
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Renderer Class
#include "Renderer.h" #include "Error.h" Renderer::Renderer() { } Renderer::~Renderer() { } void Renderer::Draw(VertexArray * vao, IndexBuffer * ibo, Texture *texture, Shader * program) { vao->Bind(); ibo->Bind(); program->Bind(); if (texture != NULL) texture->Bind(); GLCall(glDrawElements(GL_TRIANGLES, ibo->GetCount(), GL_UNSIGNED_INT, NULL)); } void Renderer::Clear(float r, float g, float b) { GLCall(glClearColor(r, g, b, 1.0)); GLCall(glClear(GL_COLOR_BUFFER_BIT)); } void Renderer::Update(GLFWwindow *window) { /* Swap front and back buffers */ glfwSwapBuffers(window); /* Poll for and process events */ glfwPollEvents(); }
#shader vertex #version 330 core layout(location = 0) in vec4 aPos; layout(location = 1) in vec2 aTexCoord; out vec2 t_TexCoord; uniform mat4 u_MVP; void main() { gl_Position = u_MVP * aPos; t_TexCoord = aTexCoord; } #shader fragment #version 330 core out vec4 aColor; in vec2 t_TexCoord; uniform sampler2D u_Texture; void main() { aColor = texture(u_Texture, t_TexCoord); } Also i'm pretty sure that every time i'm hitting the up, down, left and right arrows on the keyboard, i'm changing the model Matrix of the Player and not the others.

Window Class:
#include "Window.h" #include <GL/glew.h> #include <GLFW/glfw3.h> #include "Error.h" #include "Renderer.h" #include "Scene.h" #include "Input.h" //Global Variables. int screen_width, screen_height; //On Window Resize. void OnWindowResize(GLFWwindow *window, int width, int height); //Implementation Structure. struct Window::Implementation { //GLFW Window. GLFWwindow *GLFW_window; //Renderer. Renderer *renderer; //Delta Time. double delta_time; //Frames Per Second. int fps; //Scene. Scene *scnene; //Input. Input *input; //Deconstructor. ~Implementation(); }; //Window Constructor. Window::Window(std::string title, int width, int height) { //Initializing width and height. screen_width = width; screen_height = height; //Create Pointer To Implementation. m_Impl = new Implementation(); //Try initializing GLFW. if (!glfwInit()) { std::cout << "GLFW could not be initialized!" << std::endl; std::cout << "Press ENTER to exit..." << std::endl; std::cin.get(); exit(-1); } //Setting up OpenGL Version 3.3 Core Profile. glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 3); glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3); glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE); /* Create a windowed mode window and its OpenGL context */ m_Impl->GLFW_window = glfwCreateWindow(width, height, title.c_str(), NULL, NULL); if (!m_Impl->GLFW_window) { std::cout << "GLFW could not create a window!" << std::endl; std::cout << "Press ENTER to exit..." << std::endl; std::cin.get(); glfwTerminate(); exit(-1); } /* Make the window's context current */ glfwMakeContextCurrent(m_Impl->GLFW_window); //Initialize GLEW. if(glewInit() != GLEW_OK) { std::cout << "GLEW could not be initialized!" << std::endl; std::cout << "Press ENTER to exit..." << std::endl; std::cin.get(); glfwTerminate(); exit(-1); } //Enabling Blending. GLCall(glEnable(GL_BLEND)); GLCall(glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)); //Setting the ViewPort. GLCall(glViewport(0, 0, width, height)); //**********Initializing Implementation**********// m_Impl->renderer = new Renderer(); m_Impl->delta_time = 0.0; m_Impl->fps = 0; m_Impl->input = new Input(this); //**********Initializing Implementation**********// //Set Frame Buffer Size Callback. glfwSetFramebufferSizeCallback(m_Impl->GLFW_window, OnWindowResize); } //Window Deconstructor. Window::~Window() { delete m_Impl; } //Window Main Loop. void Window::MainLoop() { //Time Variables. double start_time = 0, end_time = 0, old_time = 0, total_time = 0; //Frames Counter. int frames = 0; /* Loop until the user closes the window */ while (!glfwWindowShouldClose(m_Impl->GLFW_window)) { old_time = start_time; //Total time of previous frame. start_time = glfwGetTime(); //Current frame start time. //Calculate the Delta Time. m_Impl->delta_time = start_time - old_time; //Get Frames Per Second. if (total_time >= 1) { m_Impl->fps = frames; total_time = 0; frames = 0; } //Clearing The Screen. m_Impl->renderer->Clear(0, 0, 0); //Render The Scene. if (m_Impl->scnene != NULL) m_Impl->scnene->Render(this); //Updating the Screen. m_Impl->renderer->Update(m_Impl->GLFW_window); //Increasing frames counter. frames++; //End Time. end_time = glfwGetTime(); //Total time after the frame completed. total_time += end_time - start_time; } //Terminate GLFW. glfwTerminate(); } //Load Scene. void Window::LoadScene(Scene * scene) { //Set the scene. m_Impl->scnene = scene; } //Get Delta Time. double Window::GetDeltaTime() { return m_Impl->delta_time; } //Get FPS. int Window::GetFPS() { return m_Impl->fps; } //Get Width. int Window::GetWidth() { return screen_width; } //Get Height. int Window::GetHeight() { return screen_height; } //Get Input. Input * Window::GetInput() { return m_Impl->input; } Renderer * Window::GetRenderer() { return m_Impl->renderer; } GLFWwindow * Window::GetGLFWindow() { return m_Impl->GLFW_window; } //Implementation Deconstructor. Window::Implementation::~Implementation() { delete renderer; delete input; } //OnWindowResize void OnWindowResize(GLFWwindow *window, int width, int height) { screen_width = width; screen_height = height; //Updating the ViewPort. GLCall(glViewport(0, 0, width, height)); }
Brain Class
#include "Brain.h" #include "Sprite.h" #include "Window.h" struct Brain::Implementation { //Just A Flag. bool started; //Window Pointer. Window *window; //Sprite Pointer. Sprite *sprite; }; Brain::Brain(Window *window, Sprite *sprite) { //Create Pointer To Implementation. m_Impl = new Implementation(); //Initialize Implementation. m_Impl->started = true; m_Impl->window = window; m_Impl->sprite = sprite; } Brain::~Brain() { //Delete Pointer To Implementation. delete m_Impl; } void Brain::Start() { } void Brain::Update() { } Window * Brain::GetWindow() { return m_Impl->window; } Sprite * Brain::GetSprite() { return m_Impl->sprite; } bool Brain::GetStart() { return m_Impl->started; } void Brain::SetStart(bool value) { m_Impl->started = value; } Script Class (Its a Brain Subclass!!!)
#include "Script.h" Script::Script(Window *window, Sprite *sprite) : Brain(window, sprite) { } Script::~Script() { } void Script::Start() { std::cout << "Game Started!" << std::endl; } void Script::Update() { Input *input = this->GetWindow()->GetInput(); Sprite *sp = this->GetSprite(); //Move this sprite. this->GetSprite()->Move(200 * this->GetWindow()->GetDeltaTime(), input->GetKeyDown("left"), input->GetKeyDown("right"), input->GetKeyDown("up"), input->GetKeyDown("down")); std::cout << sp->GetTag().c_str() << ".x = " << sp->GetPos()->x << ", " << sp->GetTag().c_str() << ".y = " << sp->GetPos()->y << std::endl; }
Main:
#include "SpaceShooterEngine.h" #include "Script.h" int main() { Window w("title", 600,600); Scene *scene = new Scene(); Sprite *player = new Sprite("Resources/Images/player.png", "Player", 100,100); Sprite *other = new Sprite("Resources/Images/cherno.png", "Other", 400, 100); Sprite *other2 = new Sprite("Resources/Images/cherno.png", "Other", 300, 400); Brain *brain = new Script(&w, player); player->AddBrain(brain); scene->AddSprite(player); scene->AddSprite(other); scene->AddSprite(other2); w.LoadScene(scene); w.MainLoop(); return 0; }

I literally can't find what is wrong. If you need more code, ask me to post it. I will also attach all the source files.
Brain.cpp
Error.cpp
IndexBuffer.cpp
Input.cpp
Renderer.cpp
Scene.cpp
Sprite.cpp
Texture.cpp
VertexArray.cpp
VertexBuffer.cpp
VertexBufferLayout.cpp
Window.cpp
Brain.h
Error.h
IndexBuffer.h
Input.h
Renderer.h
Scene.h
SpaceShooterEngine.h
Sprite.h
Texture.h
VertexArray.h
VertexBuffer.h
VertexBufferLayout.h
Window.h

• Hello fellow programmers,
For a couple of days now i've decided to build my own planet renderer just to see how floating point precision issues
can be tackled. As you probably imagine, i've quickly faced FPP issues when trying to render absurdly large planets.

I have used the classical quadtree LOD approach;
I've generated my grids with 33 vertices, (x: -1 to 1, y: -1 to 1, z = 0).
Each grid is managed by a TerrainNode class that, depending on the side it represents (top, bottom, left right, front, back),
creates a special rotation-translation matrix that moves and rotates the grid away from the origin so that when i finally
normalize all the vertices on my vertex shader i can get a perfect sphere.
T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, 1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(180.0), glm::dvec3(1.0, 0.0, 0.0)); sides[0] = new TerrainNode(1.0, radius, T * R, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_FRONT)); T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, -1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(0.0), glm::dvec3(1.0, 0.0, 0.0)); sides[1] = new TerrainNode(1.0, radius, R * T, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_BACK)); // So on and so forth for the rest of the sides As you can see, for the front side grid, i rotate it 180 degrees to make it face the camera and push it towards the eye;
the back side is handled almost the same way only that i don't need to rotate it but simply push it away from the eye.
The same technique is applied for the rest of the faces (obviously, with the proper rotations / translations).
The matrix that result from the multiplication of R and T (in that particular order) is send to my vertex shader as r_Grid'.
// spherify vec3 V = normalize((r_Grid * vec4(r_Vertex, 1.0)).xyz); gl_Position = r_ModelViewProjection * vec4(V, 1.0); The r_ModelViewProjection' matrix is generated on the CPU in this manner.
// No the most efficient way, but it works. glm::dmat4 Camera::getMatrix() { // Create the view matrix // Roll, Yaw and Pitch are all quaternions. glm::dmat4 View = glm::toMat4(Roll) * glm::toMat4(Pitch) * glm::toMat4(Yaw); // The model matrix is generated by translating in the oposite direction of the camera. glm::dmat4 Model = glm::translate(glm::dmat4(1.0), -Position); // Projection = glm::perspective(fovY, aspect, zNear, zFar); // zNear = 0.1, zFar = 1.0995116e12 return Projection * View * Model; } I managed to get rid of z-fighting by using a technique called Logarithmic Depth Buffer described in this article; it works amazingly well, no z-fighting at all, at least not visible.
Each frame i'm rendering each node by sending the generated matrices this way.
// set the r_ModelViewProjection uniform // Sneak in the mRadiusMatrix which is a matrix that contains the radius of my planet. Shader::setUniform(0, Camera::getInstance()->getMatrix() * mRadiusMatrix); // set the r_Grid matrix uniform i created earlier. Shader::setUniform(1, r_Grid); grid->render(); My planet's radius is around 6400000.0 units, absurdly large, but that's what i really want to achieve;
Everything works well, the node's split and merge as you'd expect, however whenever i get close to the surface
of the planet the rounding errors start to kick in giving me that lovely stairs effect.
I've read that if i could render each grid relative to the camera i could get better precision on the surface, effectively
getting rid of those rounding errors.

My question is how can i achieve this relative to camera rendering in my scenario here?
I know that i have to do most of the work on the CPU with double, and that's exactly what i'm doing.
I only use double on the CPU side where i also do most of the matrix multiplications.
As you can see from my vertex shader i only do the usual r_ModelViewProjection * (some vertex coords).