Specifying an Arbitrary 3D View

Creation of a 3D View

• specifying a projection model

• specifying viewing parameters

• 3d clipping

Mapping a 3D view onto a 2D screen requires:

• projection and display

• specifying viewing parameters

Creation of a 3D View

View Reference Point (VRP) - a point on the view plane

View Plane Normal (VPN) - a vector normal to the view plane

View-Up Vector (VUP) - defines the v axis direction. (indicates which way is up.)

Creation of a 3D View

u

v

n

PROJECTION PLANE

VRP

View Reference Point

VIEW PLANE

View Plane Normal

VPN

VUP

View-Up Vector

Creation of a 3D View

Coordinate Systems:

Viewing Reference Coordinate System

World Coordinate System

Creation of a 3D View

Viewing Reference Coordinate System

origin - the VRP

n axis - the VPN

v axis - coincident with the projection of the VUP onto the view plane

u axis - perpendicular to n and v axes, and defined such that u, v, and n form a right-handed coordinate system.

Creation of a 3D View

u

v

n

VIEW PLANE

x

y

z x

y

z

x

y

z

x

y

z

x

y

z

u

v

n

Viewing Reference (Camera) Coordinate Systemx

y

z

World (Object) Coordinate System x

y

z

Creation of a 3D View

VIEW PLANE

u

v

VRP

n

VPN

(Umax,Vmax)

(Umin,Vmin)

CW

Creation of a 3D View

Viewing Reference Coordinate System

The center and direction of projection are defined by : - a projection reference point PRP - the projection type (perspective/parallel)

Creation of a 3D View: parallel

VIEW PLANE

u

v

VRP

n

VPN

CW

PRP

Projection Reference Point - defines direction of projection

Creation of a 3D View: perspective

VIEW PLANE

u

v

VRP

n

VPN

PRP

Projection Reference Point = center of projection

• 3D clipping• 3D clipping

Creation of a 3D View

• specifying a projection model

• specifying viewing parameters

Mapping a 3D view onto a 2D screen requires:

• projection and display

Creation of a 3D View

View Volume:

defines the bounds of the world coordinate system that is to be clipped and projected onto the view plane.

Creation of a 3D View: parallel

VIEW PLANE

u

v

VRP

n

VPN

CW

PRP

Projection Reference Point - defines direction of projection

Creation of a 3D View: parallel

VIEW PLANE

u

v

VRP

n

VPN

CW

BACK CLIPPING PLANE

FRONT CLIPPING

PLANE

Creation of a 3D View: perspective

VIEW PLANE

u

v

VRP

n

VPN

PRP

Projection Reference Point = center of projection

Creation of a 3D View: perspective

u

v

VRP

n

VPN

PRP

VIEW PLANE

FRONT CLIPPING

PLANE

BACK CLIPPING PLANE

Creation of a 3D View

3D Clipping for the parallel view volume:extension of the 2D Cohen-Sutherland clipping algorithm

6 bit outcodes:100000 point is above view volume y > 1010000 point is below view volume y < -1001000 point is right of view volume x > 1000100 point is left of view volume x < -1000010 point is behind view volume z < -1000001 point is in front of view volume z > 1