# Projection v VP u VPN n Projection v

• Slides: 15

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 Open. GL gl. Ortho(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 botto right m Front Clipping Plane Back Clipping Plane

Perspective Projection View Plane Back Clipping Plane VPN Front Clipping Plane

In Open. GL gl. Frustum(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 VPN top left botto m right Front Clipping Plane Back Clipping Plane

In Open. GL glu. Perspective(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 fovy h Front Clipping Plane Back Clipping Plane

glu. Look. At(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 lat fovy h Front Clipping Plane Back Clipping Plane

Parallel Projection

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

Perspective Projection

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

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

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