# OpenGL setting up a perspective matrix

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Hi everyone, this is my first post here so be gentle :) I am currently working on a small project which involves representing large datasets in multiple ways. One of the ways is going to be a 3D scatter chart. I am using OpenGL via Tao in C# with multiple contexts held in child windows in an MDI application. My problem is setting up my viewing matrix. Im afraid im a bit new to OpenGL. Basically I have a set of points which translate to my cartesian co ordinates and what I need is for the chart to always "fill" the GL context regardless of its upper and lower limits. I have values for x/y/zMin and x/y/zMax. I was hoping someone could push me in the right direction for calculating a field of view which will always encompass the whole of my chart. I have been reading the red book and have tried a few techniques from in there, including one which required I calculated a "bounding sphere" and then calculated the FOV from that. Whether I was doing it wrong im not sure but I found if all three max and mins were the same I always got an angle of 90 and if they wernt then the angle generated was close to being correct but not quite big enough. Any help anyone could give would be much appreciated! (or alternative suggestions, I dont mind even using an Ortho projection matrix as perspective isnt imperative, but im struggling to produce a 3d chart in an ortho view)

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Look at the mathematical definition of a perspective matrix found here:

http://pyopengl.sourceforge.net/documentation/manual/gluPerspective.3G.html

Create that same matrix yourself.

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What follows is not optimal, but it will give you a field of view that guarantees that no point of your chart is outside the view.

- Take the center of your box
- compute the radius of the sphere containing your box
- make your camera look at the center of the sphere
- if the perspective angle is set to a constant value a, you can compute the distance from your camera to the sphere with tan(a) = radius/distance ; to be sure that ALL points of your chart are in the view, distance must be the closest distance from camera to sphere surface (not center), otherwise the cone of the camera could intersect the sphere and some points might be outside ; so the distance from the camera to the center of the box should be distance + radius
- finally, the near clipping plane must be at distance and the far clipping plane at distance + 2*radius

- enter these parameters into the perspective matrix

Again, it's not optimal and your chart may not be centered and will not completely fill the view. I believe it would be quite complex to go beyond that in perspective mode, as perspective projection introduces non-linear behaviour, so my guess is that you would have to use some kind of iterative method. But with ortho view, things are much easier ! Just compute the transformed (screen) coordinates of the 8 points of the box, take the min and max X and Y values, then move and scale your camera so that all points are in the view. If ortho is OK, use ortho !

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Ok thanks for that guys, much appreciated.

I'll have a go at your suggestions and get back later to say how I got on :)

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I will be glad for help!

Here is part of my PlayerAxis class:

//player coordinate float x[] = new float[3]; float y[] = new float[3]; float z[] = new float[3]; public PlayerAxis(float move_step, float angle_move) { x[0] = 1; y[1] = 1﻿; z[2] = -1; step = move_step; angle = angle_move; setTransMatrix(); } public void cameraMoving(float angle_step, String axis) { float[] new_x = x; float[] new_y = y; float[] new_z = z; float alfa = angle_step * angle; switch(axis) { case "x": new_z = addVectors(multScalar(z, COS(alfa)), multScalar(y, SIN(alfa))); new_y = subVectors(multScalar(y, COS(alfa)), multScalar(z, SIN(alfa))); break; case "y": new_x = addVectors(multScalar(x, COS(alfa)), multScalar(z, SIN(alfa))); new_z = subVectors(multScalar(z, COS(alfa)), multScalar(x, SIN(alfa))); break; case "z": new_x = addVectors(multScalar(x, COS(alfa)), multScalar(y, SIN(alfa))); new_y = subVectors(multScalar(y, COS(alfa)), multScalar(x, SIN(alfa))); }﻿ x = new_x; y = new_y; z = new_z; normalization(); } public void playerMoving(float x_move, float y_move, float z_move) { float[] move = new float[3]; move[0] = x_move; move[1] = y_move; move[2] = z_move; setTransMatrix(); float[] trans_move = transVector(move); position[0] = position[0] + step*trans_move[0]; position[1] = position[1] + step*trans_move[1]; position[2] = position[2] + step*trans_move[2]; } public void setTransMat﻿rix() { for (int i = 0; i < 3; i++) { coordiTrans[0][i] = x[i]; coordiTrans[1][i] = y[i]; ﻿coordiTrans[2][i] = z[i]; } } public float[] transVector(float[] v) { return multiplyMatrixInVector(coordiTrans, v); }
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public void keyPressed(KeyEvent e) { if (e.getKeyCode()== KeyEvent.VK_ESCAPE) { System.exit(0); //player move } else if (e.getKeyCode()== KeyEvent.VK_W) { //front //moveAmount[2] += -0.1f; player.playerMoving(0, 0, 1); } else if (e.getKeyCode()== KeyEvent.VK_S) { //back //moveAmount[2] += 0.1f; player.playerMoving(0, 0, -1); } else if (e.getKeyCode()== KeyEvent.VK_A) { //left //moveAmount[0] += -0.1f; player.playerMoving(-1, 0, 0); } else if (e.getKeyCode()== KeyEvent.VK_D) { //right //moveAmount[0] += 0.1f; player.playerMoving(1, 0, 0); } else if (e.getKeyCode()== KeyEvent.VK_E) { //moveAmount[0] += 0.1f; player.playerMoving(0, 1, 0); } else if (e.getKeyCode()== KeyEvent.VK_Q) { //moveAmount[0] += 0.1f; player.playerMoving(0, -1, 0); //camera move } else if (e.getKeyCode()== KeyEvent.VK_I) { //up player.cameraMoving(1, "x"); } else if (e.getKeyCode()== KeyEvent.VK_K) { //down player.cameraMoving(-1, "x"); } else if (e.getKeyCode()== KeyEvent.VK_L) { //right player.cameraMoving(-1, "y"); } else if (e.getKeyCode()== KeyEvent.VK_J) { //left player.cameraMoving(1, "y"); } else if (e.getKeyCode()== KeyEvent.VK_O) { //right round player.cameraMoving(-1, "z"); } else if (e.getKeyCode()== KeyEvent.VK_U) { //left round player.cameraMoving(1, "z"); } }
finallt found it.... i confused with the transformation matrix row and col. thanks anyway!
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To check if a wrong stencil buffer value caused this problem i decided to change the stencil function for the diffuse pass to only render if the stencil is equal to 2. As i repeated this approach with different values for the stencil function i found out that if i set the value equal to 1 or any other uneven value the lit and shadowed areas are inverted and if i set it to 0 or any other even value i get the results shown above.
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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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