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CS 4731: Computer Graphics Lecture 11: 3D Viewing

CS 4731: Computer Graphics Lecture 11: 3D Viewing. Emmanuel Agu. 3D Viewing. Similar to taking a photograph. Viewing Transformation. Control the “lens” of the camera Project the object from 3D world to 2D screen. (ex, ey, ez). world. view up vector (Up_x, Up_y, Up_z). (cx, cy, cz).

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CS 4731: Computer Graphics Lecture 11: 3D Viewing

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  1. CS 4731: Computer GraphicsLecture 11: 3D Viewing Emmanuel Agu

  2. 3D Viewing • Similar to taking a photograph

  3. Viewing Transformation • Control the “lens” of the camera • Project the object from 3D world to 2D screen

  4. (ex, ey, ez) world view up vector (Up_x, Up_y, Up_z) (cx, cy, cz) Viewing Transformation • Control the “lens” of the camera • Important camera parameters to specify • Camera (eye) position (Ex,Ey,Ez) in world coordinate system • Center of interest (coi) (cx, cy, cz) or lookAt point • Orientation (which way is up?): Up vector (Up_x, Up_y, Up_z)

  5. u v n y Eye coordinate frame coi world x z Viewing Transformation • Transformation? • Form a camera (eye) coordinate frame • Transform objects from world to eye space

  6. world Viewing Transformation • Eye space? • Transform to eye space can simplify many downstream operations (such as projection) in the pipeline (1,0,0) (0,1,0) u v (0,0,1) n y (0,0,0) coi x z

  7. Viewing Transformation • OpenGL way: • gluLookAt (Ex, Ey, Ez, cx, cy, cz, Up_x, Up_y, Up_z) • The view up vector is usually (0,1,0) • Remember to set the OpenGL matrix mode to GL_MODELVIEW first • Recall: OpenGL uses 3 matrices: • Modelview matrix: • Projection matrix: • Viewport matrix: • Modelview matrix: • combination of modeling matrix M and Camera transforms V

  8. Viewing Transformation • OpenGL Code: void display() { glClear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(0,0,1,0,0,0,0,1,0); display_all(); // your display routine }

  9. Projection Transformation • Different types of projection: parallel, perspective, orthographic, etc • Important to control • Projection type: perspective or orthographic, etc. • Field of view and image aspect ratio • Near and far clipping planes

  10. Perspective Projection • Similar to real world • Characterized by object foreshortening • Objects appear larger if they are closer to camera • Need: • Projection center • Projection plane • Projection: Connecting the object to the projection center camera projection plane

  11. Projection?

  12. Orthographic Projection • No foreshortening effect – distance from camera does not matter • The projection center is at infinite • Projection calculation – just drop z coordinates

  13. y y z z x Field of View • Determine how much of the world is taken into the picture • Larger field of view = smaller object projection size center of projection field of view (view angle) q

  14. Near and Far Clipping Planes • Only objects between near and far planes are drawn • Near plane + far plane + field of view = Viewing Frustum Near plane Far plane y z x

  15. Viewing Frustrum • 3D counterpart of 2D world clip window • Objects outside the frustum are clipped Near plane Far plane y z x Viewing Frustum

  16. Projection Transformation • In OpenGL: • Set the matrix mode to GL_PROJECTION • Perspective projection: use • gluPerspective(fovy, aspect, near, far) or • glFrustum(left, right, bottom, top, near, far) • Orthographic: • glOrtho(left, right, bottom, top, near, far)

  17. y y z z x gluPerspective(fovy, aspect, near, far) • Aspect ratio is used to calculate the window width w fovy h eye Aspect = w / h near far

  18. y z x glFrustum(left, right, bottom, top, near, far) • Can use this function in place of gluPerspective() left top right bottom near far

  19. y z glOrtho(left, right, bottom, top, near, far) • For orthographic projection top left x right bottom near far

  20. Example: Projection Transformation void display() { glClear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_PROJETION); glLoadIdentity(); gluPerspective(fove, aspect, near, far); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(0,0,1,0,0,0,0,1,0); display_all(); // your display routine }

  21. y f x pitch roll Flexible Camera Control • Sometimes, we want camera to move • Just like control a airplane’s orientation • Use aviation terms for this y d x q yaw

  22. Yaw, pitch, roll? • Think about being in an airplane • Pitch: nose up-down • Roll: roll body of plane • Yaw: move nose side to side

  23. y y f q x x pitch roll yaw Flexible Camera Control • Instead of provide COI, it is possible to just give camera orientation • Just like control a airplane’s orientation d

  24. Flexible Camera Control • How to compute the viewing vector (x,y,z) from pitch(f) and yaw(q) ? z = Rcos(f)cos(90-q) x = Rcos(f)cos(q) y y F = 0 q = 0 R f x x q R cos(f) z y = Rsin(f) z

  25. Flexible Camera Control • gluLookAt() does not let you to control pitch and yaw • you need to • User supplies ,  or roll angle • Compute/maintain the vector by yourself • Calculate COI = Eye + (x,y,z) • Then, call gluLookAt().

  26. References • Hill, chapter 7

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