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OpenGL Rotating Camera

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Hello, I'm playing around with the concepts of having a camera that will orbit a target (i.e. the gaze direction will always be towards the target, and the camera is rotated by having the eye coordinates confined to a sphere around the target). To implement this I'm using OpenGL; to be more specific, I'm trying to use the gluLookAt function and modifying the eye, 'up', and gaze coordinates to achieve this orbiting effect. There's been a lot of problems so far and I was hoping to get some help here :) What I do is, when there is a mouse movement I attempt to translate this to how many degrees it should rotate around the x, y, and z axis. Then I try to rotate the camera; I translate the target and eye of the camera so that the target is at the origin and then I transform the Cartesian coordinates of the camera 'eye' to spherical coordinates. I then add the desired angle of rotation to theta and phi and translate back to Cartesian coordinates. The relevant code is below: Function to rotate camera:
void rotateCamera(GLfloat x, GLfloat y, GLfloat z)
  // Translate eye so that target is at origin
  cam.eye[ 0 ] -= cam.gaze[ 0 ];
  cam.eye[ 1 ] -= cam.gaze[ 1 ];
  cam.eye[ 2 ] -= cam.gaze[ 2 ];
  // Spherical Coordinates
  double theta = 0;
  if(cam.eye[ 0 ] != 0)
    theta = atan(cam.eye[ 1 ] / cam.eye[ 0 ]);
  // x-coordinate is zero... we have a problem
  else if(cam.eye[ 1 ] > 0)
    theta = DEG_TO_RAD(90.0);
  else if(cam.eye[ 1 ] < 0)
    theta = DEG_TO_RAD(270.0);

  double phi = acos(cam.eye[ 2 ] / cam.radius);
  // Rotate around y-axis
  theta += DEG_TO_RAD(y);
  // Rotate around x-axis
  phi += DEG_TO_RAD(x);

  cam.eye[ 0 ] = cam.radius * cos(theta) * sin(phi);
  cam.eye[ 1 ] = cam.radius * sin(theta) * sin(phi);
  cam.eye[ 2 ] = cam.radius * cos(phi);
  // Re-calculate 'up' vector for camera
  GLfloat tmpVec[] = {cam.eye[ 0 ], cam.eye[ 1 ], cam.eye[ 2 ]};
  GLfloat yVec[] = { 0.0f, 1.0f, 0.0f};
  GLfloat tmpLen = sqrt(tmpVec[ 0 ] * tmpVec[ 0 ] + tmpVec[ 1 ] * tmpVec[ 1 ] + tmpVec[ 2 ] * tmpVec[ 2 ]);
  tmpVec[ 0 ] /= tmpLen;
  tmpVec[ 1 ] /= tmpLen;
  tmpVec[ 2 ] /= tmpLen;
  GLfloat xprod1[] = {tmpVec[ 1 ] * yVec[ 2 ] - tmpVec[ 2 ] * yVec[ 1 ],
					  tmpVec[ 2 ] * yVec[ 0 ] - tmpVec[ 0 ] * yVec[ 2 ],
					  tmpVec[ 0 ] * yVec[ 1 ] - tmpVec[ 1 ] * yVec[ 0 ]};

  cam.up[ 0 ] = tmpVec[ 1 ] * xprod1[ 2 ] - tmpVec[ 2 ] * xprod1[ 1 ] * -1.0f;
  cam.up[ 1 ] = tmpVec[ 2 ] * xprod1[ 0 ] - tmpVec[ 0 ] * xprod1[ 2 ] * -1.0f;
  cam.up[ 2 ] = tmpVec[ 0 ] * xprod1[ 1 ] - tmpVec[ 1 ] * xprod1[ 0 ] * -1.0f;
  tmpLen = sqrt(cam.up[ 0 ] * cam.up[ 0 ] + cam.up[ 1 ] * cam.up[ 1 ] + cam.up[ 2 ] * cam.up[ 2 ]);
  cam.up[ 0 ] /= tmpLen;
  cam.up[ 1 ] /= tmpLen;
  cam.up[ 2 ] /= tmpLen;

  // Translate eye back
  cam.eye[ 0 ] += cam.gaze[ 0 ];
  cam.eye[ 1 ] += cam.gaze[ 1 ];
  cam.eye[ 2 ] += cam.gaze[ 2 ];

and translating mouse movements to rotations:
void mouseMove(int x, int y)
	GLfloat degX = mouse.xPos - (float) x;  // How much we rotate around the y-axis
	GLfloat degY = mouse.yPos - (float) y;  // How much we rotate around the x-axis

    rotateCamera(-1.0f * degX, degY, 0.0f);
	mouse.xPos = (x > 0 ? x : 0.0);
	mouse.yPos = (y > 0 ? y : 0.0);

At first for the 'up' vector I was always using (0.0f, 1.0f, 0.0f) as I always wanted the camera's up direction to be parallel with the positive y-axis, but I suspected that that might be the source of my problem, so I added in all the code after the comment 'Re-calculate 'up' vector for camera' to try and fix this. Now I'm suspecting that it might be my mouseMove function and how it translates mouse movements to rotation.

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I'm familiar with what you're trying to do, however I dont usually implement it the way you do.

First I take the difference in the mouse coordinates (cur-prev) and determine the angle the camera has changed along the x and y axis. This is just based on screen size and some magic numbers that I use until moving the mouse from the left to the right side of the screen rotates the camera somewhere between 360 and 720 degrees (use whatever looks best to you).

Movement along the y-axis is considered pitch (up/down movement) and movement along the x-axis is considered yaw (side/side movement.) Then I perform the following calculations to orbit the camera around its target

void Camera::Orbit( float32 yaw, float32 pitch )
// Create a rotation matrix that rotates about the y-axis
Matrix4 rotationY;
rotationY.BuildRotationY( yaw );

// Get the direction vector
Vector3 dir = m_Target - m_Eye;

// Normalize the direction vector and cross it with the UP vector in
// order to get the "right" vector, which is just a vector pointing
// out of my right side. This will be used as our arbitrary axis for
// which to pitch on. If we dont do this, then when we rotate around our
// object and then try and pitch, our pitch direction will be reversed
Vector3 right = dir.Normalize().Cross( m_Up );

// Create a rotation matrix about the arbitary axis created above, by the
// angle passed in from the calling function
Matrix4 rotationX;
rotationX.BuildAxisAngle( right, pitch );

// Create a composite transformation matrix
Matrix4 transform = rotationY * rotationX;

// Transform the direction vector into a new direction
dir = transform.Transform3( dir );

// Subtract the new direction from the target to get the new eye position
m_Eye = m_Target - dir;

// Re-build the camera matrix from the new eye, target, and up vectors
// which represents the view transform

I hope this code helps you out. Please let me know if you have any specific questions on the implementation of anything above.


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Thanks for your help! After some contemplation, I realized that spherical coordinates is actually more complicated than it first sounds. I went with the rotation matrices as you did and it is working much more smoothly now. Thanks!

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I'm still having a couple of problems (although there are fewer problems than I had with spherical coordinates). It seems that if the camera eye is near or on the plane defined by (1, 0, -1), (-1, 0, 1), (0, 1, 0) it has trouble rotating for some reason. Also, using the same plane mentioned above, on one side of the plane, moving the mouse up points the camera down, while on the other side, moving the mouse up points the camera up.

Any ideas? I've used the same method jwalsh has mentioned and have used this as a guide to rotating around and arbitrary axis.

I hope that made sense :p Let me know if I need to clarify anything. Thanks!

The function below rotates the point 'point' around the axis 'axis' specified by 'angle' in degrees:

void rotateMatrixArbitrary(GLfloat angle, GLfloat* axis, GLfloat* point)
GLfloat yzProj[ 3 ] = { 0.0f, axis[ 1 ], axis[ 2 ] };
GLfloat xzProj[ 3 ] = { axis[ 0 ], 0.0f, axis[ 2 ] };
GLfloat d = sqrt(yzProj[ 1 ] * yzProj[ 1 ] + yzProj[ 2 ] * yzProj[ 2 ]);

MATRIX4 m1, m2, m3, mi1, mi2, tmp;

initMatrix(&m1); initMatrix(&m2); initMatrix(&m3);
initMatrix(&mi1); initMatrix(&mi2);

if(d != 0.0)
m1.matrix[ 1 ][ 1 ] = fabs(yzProj[ 2 ]) / d;
m1.matrix[ 1 ][ 2 ] = -1.0f * fabs(yzProj[ 1 ]) / d;
m1.matrix[ 2 ][ 1 ] = fabs(yzProj[ 1 ]) / d;
m1.matrix[ 2 ][ 2 ] = fabs(yzProj[ 2 ]) / d;

mi1.matrix[ 1 ][ 1 ] = fabs(yzProj[ 2 ]) / d;
mi1.matrix[ 1 ][ 2 ] = fabs(yzProj[ 1 ]) / d;
mi1.matrix[ 2 ][ 1 ] = -1.0f * fabs(yzProj[ 1 ]) / d;
mi1.matrix[ 2 ][ 2 ] = fabs(yzProj[ 2 ]) / d;

d = sqrt(xzProj[ 0 ] * xzProj[ 0 ] + xzProj[ 2 ] * xzProj[ 2 ]);

if(d != 0.0)
m2.matrix[ 0 ][ 0 ] = fabs(xzProj[ 2 ]) / d;
m2.matrix[ 0 ][ 2 ] = fabs(xzProj[ 0 ]) / d;
m2.matrix[ 2 ][ 0 ] = -1.0f * fabs(xzProj[ 0 ]) / d;
m2.matrix[ 2 ][ 2 ] = fabs(xzProj[ 2 ]) / d;

mi2.matrix[ 0 ][ 0 ] = fabs(xzProj[ 2 ]) / d;
mi2.matrix[ 0 ][ 2 ] = -1.0f * fabs(xzProj[ 0 ]) / d;
mi2.matrix[ 2 ][ 0 ] = fabs(xzProj[ 0 ]) / d;
mi2.matrix[ 2 ][ 2 ] = fabs(xzProj[ 2 ]) / d;

rotateMatrixZ(angle, &m3);

// Apply rotations
matrixMult(m1, point);
matrixMult(m2, point);
matrixMult(m3, point);
matrixMult(mi2, point);
matrixMult(mi1, point);

This is the function which will rotate the camera eye based on mouse movements. It rotates around the point specified by cam.gaze:

void rotateCamera(GLfloat x, GLfloat y)
// Translate eye so that target is at origin
cam.eye[ 0 ] -= cam.gaze[ 0 ];
cam.eye[ 1 ] -= cam.gaze[ 1 ];
cam.eye[ 2 ] -= cam.gaze[ 2 ];

MATRIX4 rotateY;

rotateMatrixY(y, &rotateY);

GLfloat dir[ 3 ] = { cam.eye[ 0 ], cam.eye[ 1 ], cam.eye[ 2 ] };

GLfloat rightVec[ 3 ];
xprod(dir, cam.up, rightVec);

rotateMatrixArbitrary(x, rightVec, cam.eye);
matrixMult(rotateY, cam.eye);

// Translate eye back
cam.eye[ 0 ] += cam.gaze[ 0 ];
cam.eye[ 1 ] += cam.gaze[ 1 ];
cam.eye[ 2 ] += cam.gaze[ 2 ];

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      // [the following code includes all used gl* functions, other parts are due to readability partialy excluded] // glfw: initialize and configure // ------------------------------ glfwInit(); glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 4); glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 4); glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE); // glfw window creation // -------------------- GLFWwindow* window = glfwCreateWindow(SCR_WIDTH, SCR_HEIGHT, "LearnOpenGL", NULL, NULL); if (window == NULL) { cout << "Failed to create GLFW window" << endl; glfwTerminate(); return -1; } glfwMakeContextCurrent(window); glfwSetFramebufferSizeCallback(window, framebuffer_size_callback); glfwSetCursorPosCallback(window, mouse_callback); glfwSetScrollCallback(window, scroll_callback); // tell GLFW to capture our mouse glfwSetInputMode(window, GLFW_CURSOR, GLFW_CURSOR_DISABLED); // glad: load all OpenGL function pointers // --------------------------------------- if (!gladLoadGLLoader((GLADloadproc)glfwGetProcAddress)) { cout << "Failed to initialize GLAD" << endl; return -1; } // ==================================================================================================== // window and functions are set up // ==================================================================================================== // configure global opengl state // ----------------------------- glEnable(GL_DEPTH_TEST); glEnable(GL_CULL_FACE); // build and compile our shader program [...] // set up vertex data (and buffer(s)) and configure vertex attributes [...] // shader configuration [...] // render loop // =========== while (!glfwWindowShouldClose(window)) { // input processing and fps calculation[...] // render // ------ glClearColor(0.1f, 0.1f, 0.1f, 1.0f); glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glDepthMask(GL_TRUE); //enable depth writing glDepthFunc(GL_LEQUAL); //avoid z-fighting //draw ambient component into color and depth buffer view = camera.GetViewMatrix(); projection = glm::perspective(glm::radians(camera.Zoom), (float)SCR_WIDTH / (float)SCR_HEIGHT, 0.1f, 100.0f); // setting up lighting shader for ambient pass [...] // render the cubes glBindVertexArray(cubeVAO); for (unsigned int i = 0; i < 10; i++) { //position cube [...] glDrawArrays(GL_TRIANGLES, 0, 36); } //------------------------------------------------------------------------------------------------------------------------ glDepthMask(GL_FALSE); //disable depth writing glEnable(GL_BLEND); glBlendFunc(GL_ONE, GL_ONE); //additive blending glEnable(GL_STENCIL_TEST); //setting up shadowShader and lightingShader [...] for (int light = 0; light < lightsused; light++) { glDepthFunc(GL_LESS); glClear(GL_STENCIL_BUFFER_BIT); //configure stencil ops for front- and backface to write according to z-fail glStencilOpSeparate(GL_FRONT, GL_KEEP, GL_DECR_WRAP, GL_KEEP); //-1 for front-facing glStencilOpSeparate(GL_BACK, GL_KEEP, GL_INCR_WRAP, GL_KEEP); //+1 for back-facing glStencilFunc(GL_ALWAYS, 0, GL_TRUE); //stencil test always passes if(hidevolumes) glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE); //disable writing to the color buffer glDisable(GL_CULL_FACE); glEnable(GL_DEPTH_CLAMP); //necessary to render SVs into infinity //draw SV------------------- shadowShader.use(); shadowShader.setInt("lightnr", light); int nr; if (onecaster) nr = 1; else nr = 10; for (int i = 0; i < nr; i++) { //position cube[...] glDrawArrays(GL_TRIANGLES, 0, 36); } //-------------------------- glDisable(GL_DEPTH_CLAMP); glEnable(GL_CULL_FACE); glStencilFunc(GL_EQUAL, 0, GL_TRUE); //stencil test passes for ==0 so only for non shadowed areas glStencilOp(GL_KEEP, GL_KEEP, GL_KEEP); //keep stencil values for illumination glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE); //enable writing to the color buffer glDepthFunc(GL_LEQUAL); //avoid z-fighting //draw diffuse and specular pass lightingShader.use(); lightingShader.setInt("lightnr", light); // render the cubes for (unsigned int i = 0; i < 10; i++) { //position cube[...] glDrawArrays(GL_TRIANGLES, 0, 36); } } glDisable(GL_BLEND); glDepthMask(GL_TRUE); //enable depth writing glDisable(GL_STENCIL_TEST); //------------------------------------------------------------------------------------------------------------------------ // also draw the lamp object(s) [...] // glfw: swap buffers and poll IO events (keys pressed/released, mouse moved etc.) // ------------------------------------------------------------------------------- glfwSwapBuffers(window); glfwP } // optional: de-allocate all resources once they've outlived their purpose: // ------------------------------------------------------------------------ glDeleteVertexArrays(1, &cubeVAO); glDeleteVertexArrays(1, &lightVAO); glDeleteBuffers(1, &VBO); // glfw: terminate, clearing all previously allocated GLFW resources. // ------------------------------------------------------------------ glfwTerminate(); return 0;  
    • By Green_Baron
      i am self teaching me graphics and oo programming and came upon this:
      My Window class creates an input handler instance, the glfw user pointer is redirected to that object and methods there do the input handling for keyboard and mouse. That works. Now as part of the input handling i have an orbiting camera that is controlled by mouse movement. GLFW_CURSOR_DISABLED is set as proposed in the glfw manual. The manual says that in this case the cursor is automagically reset to the window's center. But if i don't reset it manually with glfwSetCursorPos( center ) mouse values seem to add up until the scene is locked up.
      Here are some code snippets, mostly standard from tutorials:
      // EventHandler m_eventHandler = new EventHandler( this, glm::vec3( 0.0f, 5.0f, 0.0f ), glm::vec3( 0.0f, 1.0f, 0.0f ) ); glfwSetWindowUserPointer( m_window, m_eventHandler ); m_eventHandler->setCallbacks(); Creation of the input handler during window creation. For now, the camera is part of the input handler, hence the two vectors (position, up-vector).  In future i'll take that functionally out into an own class that inherits from the event handler.
      void EventHandler::setCallbacks() { glfwSetCursorPosCallback( m_window->getWindow(), cursorPosCallback ); glfwSetKeyCallback( m_window->getWindow(), keyCallback ); glfwSetScrollCallback( m_window->getWindow(), scrollCallback ); glfwSetMouseButtonCallback( m_window->getWindow(), mouseButtonCallback ); } Set callbacks in the input handler.
      // static void EventHandler::cursorPosCallback( GLFWwindow *w, double x, double y ) { EventHandler *c = reinterpret_cast<EventHandler *>( glfwGetWindowUserPointer( w ) ); c->onMouseMove( (float)x, (float)y ); } Example for the cursor pos callback redirection to a class method.
      // virtual void EventHandler::onMouseMove( float x, float y ) { if( x != 0 || y != 0 ) { // @todo cursor should be set automatically, according to doc if( m_window->isCursorDisabled() ) glfwSetCursorPos( m_window->getWindow(), m_center.x, m_center.y ); // switch up/down because its more intuitive m_yaw += m_mouseSensitivity * ( m_center.x - x ); m_pitch += m_mouseSensitivity * ( m_center.y - y ); // to avoid locking if( m_pitch > 89.0f ) m_pitch = 89.0f; if( m_pitch < -89.0f ) m_pitch = -89.0f; // Update Front, Right and Up Vectors updateCameraVectors(); } } // onMouseMove() Mouse movement processor method. The interesting part is the manual reset of the mouse position that made the thing work ...
      // straight line distance between the camera and look at point, here (0,0,0) float distance = glm::length( m_target - m_position ); // Calculate the camera position using the distance and angles float camX = distance * -std::sin( glm::radians( m_yaw ) ) * std::cos( glm::radians( m_pitch) ); float camY = distance * -std::sin( glm::radians( m_pitch) ); float camZ = -distance * std::cos( glm::radians( m_yaw ) ) * std::cos( glm::radians( m_pitch) ); // Set the camera position and perspective vectors m_position = glm::vec3( camX, camY, camZ ); m_front = glm::vec3( 0.0, 0.0, 0.0 ) - m_position; m_up = m_worldUp; m_right = glm::normalize( glm::cross( m_front, m_worldUp ) ); glm::lookAt( m_position, m_front, m_up ); Orbiting camera vectors calculation in updateCameraVectors().
      Now, for my understanding, as the glfw manual explicitly states that if cursor is disabled then it is reset to the center, but my code only works if it is reset manually, i fear i am doing something wrong. It is not world moving (only if there is a world to render :-)), but somehow i am curious what i am missing.
      I am not a professional programmer, just a hobbyist, so it may well be that i got something principally wrong :-)
      And thanks for any hints and so ...
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