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Advanced Viewing

Advanced Viewing. Glenn G. Chappell CHAPPELLG@member.ams.org U. of Alaska Fairbanks CS 381 Lecture Notes Friday, October 31, 2003. Review: Projection in 3-D [1/3]. We use the projection to handle camera properties. Perspective or parallel (orthogonal) projection. Wide or narrow angle.

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Advanced Viewing

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  1. Advanced Viewing Glenn G. ChappellCHAPPELLG@member.ams.org U. of Alaska Fairbanks CS 381 Lecture Notes Friday, October 31, 2003

  2. Review:Projection in 3-D [1/3] • We use the projection to handle camera properties. • Perspective or parallel (orthogonal) projection. • Wide or narrow angle. • But not camera position & orientation. • How do we determine wide & narrow angle using glFrustum or gluPerspective? • With gluPerspective, change the 1st parameter (fovy). • With glFrustum, multiply left, right, bottom, top by some number. • Fancy projections can mess up screen text, buttons, etc. For these, use a separate gluOrtho2D projection. • See printmatrix.cpp, on the web page, for sample code. CS 381

  3. Review:Projection in 3-D [2/3] • Computing Perspective Projection • Based on the synthetic-camera model, we can find the coordinates of a projected point. • We use similar triangles (outlined in red). Screen Center of Projection (“eye”)(0, 0, 0) (x, y, z) –z (x/[–z/near],y/[–z/near],–near) z = –near View Frustum z = –far CS 381

  4. Review:Projection in 3-D [3/3] • We can perform this projection using the following matrix. • This matrix is not exactly what glFrustum produces, since it deals with right, left, top, bottom, far, too. • But this gives the general idea. CS 381

  5. Review:More on OpenGL Matrices [1/2] • We store an OpenGL matrix in an array of 16 GLdouble’s:GLdouble matrixd[16]; • To put the model/view matrix into this array:glGetDoublev(GL_MODELVIEW_MATRIX, matrixd); • This is column-major. 0..3 are the first column, not the first row. • To restore the saved model/view matrix:glLoadMatrixd(matrixd); // Mode must be GL_MODELVIEW! • More usefully, to multiply saved matrix by current matrix:glMultMatrixd(matrixd); // Mode must be GL_MODELVIEW! CS 381

  6. Review:More on OpenGL Matrices [2/2] • How would you write glTranslate* yourself? void myglTranslate(double x, double y, double z) { GLdouble m[16]; // The translation matrix m[ 0] = 1.; m[ 4] = 0.; m[ 8] = 0.; m[12] = x; m[ 1] = 0.; m[ 5] = 1.; m[ 9] = 0.; m[13] = y; m[ 2] = 0.; m[ 6] = 0.; m[10] = 1.; m[14] = z; m[ 3] = 0.; m[ 7] = 0.; m[11] = 0.; m[15] = 1.; glMultMatrixd(m); // Multiply it } • Why don’t I set GL_MODELVIEW mode in this function? CS 381

  7. Advanced Viewing:Problem & Solution • So far, we have always created the model/view transformation from scratch for each frame. • This can get unwieldy if an increasingly long sequence of transformations must be remembered. • Consider “flying”. • Solution • Keep the current state of a sequence of transformations in a matrix. • Modify the matrix appropriately when a new transformation is added. • In the display function, just do glMultMatrix*. CS 381

  8. Advanced Viewing:Example 1: “Zoom & Pan” [1/2] • In traditional zoom & pan (with a real camera): • Zoom means changing the wide/narrow-angle properties of the lens. • Pan means rotating the camera. • We will misuse these terms somewhat, in order to make a more helpful example. • Our “zoom” will scale the world. • Our “pan” will translate it. • We will use model/view for both of these. • Think: What is a problem with panning while zoomed in close? CS 381

  9. Advanced Viewing:Example 1: “Zoom & Pan” [2/2] • Suppose we handle “zoom & pan” with a saved viewing matrix. • What do we do to this matrix, in order to pan? • Translate, then do the saved transformations. Result is the new transformation. • What do we do to this matrix, in order to zoom? • Scale, then do the saved transformations. Result is the new transformation. • How do we use this matrix in the display function? • Load it (glLoadMatrixd). • Or do whatever else needs to be done first, then multiply by it (glMultMatrixd). CS 381

  10. Advanced Viewing:Handling the Saved Matrix • Don’t forget to initialize the saved matrix. glMatrixMode(GL_MODELVIEW); glPushMatrix(); ***** Transformation commands go here? ***** glGetDoublev(GL_MODELVIEW_MATRIX, your_matrix_variable); glPopMatrix(); • Whenever you do anything with the model/view transformation, use push & pop. • Changing the matrix alters the display. • So post a redisplay event whenever you change the matrix outside the display function. • Generally, to alter a saved model/view matrix outside the display function: glPushMatrix(); glLoadIdentity(); // May not be necessary ***** Transformation commands go here ***** glMultMatrixd(your_matrix_variable); // If this is appropriate glGetDoublev(GL_MODELVIEW_MATRIX, your_matrix_variable); glPopMatrix(); glutPostRedisplay(); CS 381

  11. Advanced Viewing:Example 2: A Driving Interface • Imagine a car at the center of the window, driving through the city streets. • How can we turn our zoom-pan interface into a 2-D driving-style interface (viewed from above) with only minimal modifications? • Change the pan-left and pan-right code to do rotations about the z-axis. CS 381

  12. Advanced Viewing:Example 3: Flying [1/2] • We implemented the first two examples using a saved matrix to hold viewing transformations. • Viewing transform’s = camera motions. • Okay, the “zoom” part didn’t quite fit this model … • The ultimate generality in camera motions is achieved in “flying”. • Flying = moving in the viewing direction & rotating about the camera. • How do we fly forward? • Put a +z translation before (in the code) all previous transformations. • How to we turn? • Put a y-axis (or x-axis, for going up & down) rotation before (in the code) all previous transformations. CS 381

  13. Advanced Viewing:Example 3: Flying [2/2] • Wouldn’t it be nicer to use the mouse? • Yes. We’ll talk about that next time. CS 381

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