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Projection

Projection. v. VP. u. VPN. n. Projection. v. VRP. u. VRP. n. Eye Point. Camera & World. Up Vector. Look At Vector. Orthographic Projection. View Plane. Back Clipping Plane. VPN. Front Clipping Plane. In OpenGL. glOrtho (GLdouble left, GLdouble right, GLdouble bottom,

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Projection

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  1. Projection v VP u VPN n

  2. Projection v VRP u VRP n Eye Point

  3. Camera & World Up Vector Look At Vector

  4. Orthographic Projection View Plane Back Clipping Plane VPN Front Clipping Plane

  5. In OpenGL glOrtho(GLdouble left,GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far) far The direction of projection is parallel to Z-axis. Looking at the negative direction near top left Back Clipping Plane VPN right bottom Front Clipping Plane

  6. Perspective Projection View Plane Back Clipping Plane VPN Front Clipping Plane

  7. In OpenGL glFrustum(GLdouble left,GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far) far The direction of projection is parallel to Z-axis. Looking at the negative direction near top left VPN right Back Clipping Plane bottom Front Clipping Plane

  8. In OpenGL gluPerspective(GLdouble fovy,GLdouble aspect, GLdouble near, GLdouble far) far The direction of projection is parallel to Z-axis. Looking at the negative direction. Aspect = w/h near w VPN Back Clipping Plane h fovy Front Clipping Plane

  9. gluLookAt gluLookAt(GLdouble eyex,GLdouble eyey, GLdouble eyez, GLdouble latx,GLdouble laty, GLdouble latz, GLdouble upx,GLdouble upy, GLdouble upz) The direction of projection is parallel to Z-axis. Looking at the negative direction. Aspect = w/h far near up w VPN Back Clipping Plane h fovy lat Front Clipping Plane

  10. Parallel Projection

  11. y x z Parallel Projection (x,y,d) (x,y,z) d (x,y,z) (x,y,d)

  12. Perspective Projection

  13. Perspective Projection xp=x(zprp – zvp)/ (zprp – z) View Plane yp=y(zprp – zvp)/ (zprp – z) (x,y,z) dp=(zprp – zvp) (xp,yp,zvp) zprp dp

  14. Perspective Projection xp=x(zprp – zvp)/ (zprp – z) yp=y(zprp – zvp)/ (zprp – z) dp=(zprp – zvp) x y z 1 1 1 0 0 0 1 0 0 0 0 -zvp/dp zvp(zprp/dp) 0 0 -1/dp zprp/dp xh yh zh h = h = (zprp-z/dp) xp=xh/h yp=yh/h

  15. Graphics Pipeline Modeling Coordinates World Coordinates Modeling Transformation Viewing Transformation Viewing Coordinates Projection Coordinates Projection Transformation Normalization Transformation Normalized Projection Coordinates Device Coordinates Workstation Transformation

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