Projection v VP u VPN n.

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Presentation transcript:

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, 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

Perspective Projection View Plane Back Clipping Plane VPN Front Clipping Plane

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

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 h Back Clipping Plane fovy Front Clipping Plane

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 h Back Clipping Plane fovy lat Front Clipping Plane

Parallel Projection

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

Perspective Projection

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

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

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