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Viewing (Part 1)

Viewing (Part 1). Projection types Positioning of the camera Defining the camera frame Simple perspective projection matrix Simple orthogonal projection matrix. Orthographic Projections of a Temple. Viewing. (Center of Projection). Perspective Viewing.

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Viewing (Part 1)

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  1. Viewing (Part 1) • Projection types • Positioning of the camera • Defining the camera frame • Simple perspective projection matrix • Simple orthogonal projection matrix

  2. Orthographic Projections of a Temple

  3. Viewing (Center of Projection)

  4. Perspective Viewing

  5. Movement of the COP to infinity:Orthographic Projections

  6. Orthographic Projections

  7. Initial Camera Position

  8. Positioning of the Camera • Specify the position indirectly by applying a sequence of rotations and translations to the model-view matrix (before adding objects to the scene). • Using OpenGL viewing APIs

  9. Movement of the Camera and World Frames Initial Configuration After change in model-view matrix glTranslate(0.0, 0.0, -d)

  10. Example of Positioning the Camera

  11. Example of Positioning the Camera glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glTranslatef(0.0, 0.0, -d); glRotatef(-90.0, 0.0, 1.0, 0.0);

  12. y x z Another example:Creating an isometric view of a cube Ry Rx

  13. y x z Rx Cube after Rotation about X-Axis

  14. Rx Rotation angles y M = T Rx Ry • Ry: 45 degrees • Rx: 35.26 degrees Ry x z

  15. Calculation of R

  16. Final transformation matrix

  17. How to specify in OpenGL? glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glTranslatef(0.0, 0.0, -d); glRotatef(35.26, 1.0, 0.0, 0.0); glRotatef(45.0, 0.0, 1.0, 0.0);

  18. Movement of the Camera Frame Initial Configuration After change in Camera Frame

  19. Defining the Camera Frame n: View-plane Normal (VPN) VUP: View-Up Vector VRP: View-Reference Point Projection plane u-v-n system Viewing coordinate system

  20. Defining the Camera Frame in OpenGL set_view_reference_point (x, y, z); set_view_plane_normal (nx, ny, nz); set_view_up (vup_x, vup_y, vup_z);

  21. Representing u-v-n in x-y-z

  22. Building the viewing transformation matrix RT=

  23. VPN Look-at Positioning At point VPN Eye point

  24. Look-at Positioning gluLookAt (eyex, eyey, eyez, atx, aty, atz, upx, upy, upz);

  25. Describing camera location usingRoll, Pitch, and Yaw Center of mass

  26. Describing camera location using Elevation and Azimuth Polar coordinate system

  27. Simple camera General camera -z -z Lens Projection plane Perspective projection matrix in case of simple camera

  28. Top view Side view (xp, - d) (yp, - d) z = -d z = -d Projection plane (z = -d) Perspective Projection

  29. (x, z) (xp, - d) zp = -d Transformation equations Division by z cases further objects to become smaller (non-uniform foreshortening)

  30. q Simple Perspective Projection Matrix

  31. Projection Pipeline

  32. Orthogonal Projection

  33. Simple Orthogonal Projection

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