Viewing in 3D

BASICS

3D Viewing: Positioning the planes

VIEW/PROJECTION WINDOW• A rectangular window in view-plane is used to

decide as to how much of the scene is caught and displayed.

• Edges of the window are parallel to the Xᵥ, and Yᵥ axes.

• Window boundary positions are described using viewing coordinates.

• View window can be placed any where on the view-plane.

• View volume is setup using window boundary.

VIEW/PROJECTION WINDOW

View Volume:• Four sides of view volume are planes that pass

through the edges of the window.• Object falling with in the view volume appear in

the generated display on output device, all others are clipped off.

• Size of the view volume depends on the view-window, its shape depends on the projection to be used.

VIEW/PROJECTION WINDOW

• For parallel projection, four sides of the view volume form an infinite parallelepiped.

• For perspective projection, the view volume is a pyramid with apex at the Projection Reference Point(PRP).

• Zᵥ boundary planes are introduced for limiting the extent of view volume. These are called front plane and back plane.

Projection Reference Point

VIEWING COORDINAT SYSTEM

3D Viewing: Positioning the planes

• Both, front and back planes must be on the same side of the PRP. Back-plane must be farther from PRP than the front-plane.

• The front and the back planes can be any position relative to the view plane, as long as the PRP is not between the front and the back planes.

Viewing: Positioning the planes

yₐ = d . (y/z)

ₐ

3D Viewing: Positioning the planes

Normalizing the Viewing Frustum:Transform frustum to a cube before clipping

• We can think of the synthetic camera as a pinhole.– As you look through the pinhole, you see a

certain volume of space.– Rays of light reflect off objects and

converge to the pinhole to let you see the scene

– Similar to the ideas we’ve discussed earlier

• In this model:– Pinhole = camera position– Volume of space = view volume– Create a projection plane that is the screen

The Pinhole model

Pinhole

Object

Image projectedon image plane

FilmPlane

Look Vector

Positioning the Planes

Back plane

View plane

Front plane

View plane

Back plane

Front plane

View planeBack plane

Front plane

Zᵥ Zᵥ Zᵥ

Orthographic parallel projections are not affected by view plane positioning, because the projection lines are perpendicular to the view plane regard less of its positioning.

Front and back clipping planes allow us to eliminate parts of the scene from the viewing operations based on depth.

Front clipping planeBack clipping plane

Width angle

Height angle Pinhole

Object

Image projectedon image plane

Perspective affects depth on the positioning of the PRP relative to the view plane

View Window View Window View Window

PRP

PRPPRP at Infinity

Positioning effects in Perspective Projections

• If view plane is in front of the object, near PRP, then the projected size will be smaller.

• When view plane is behind the object then the projected size is increased.

• For static view of a scene, view plane is placed at the viewing coordinate origin, then by adjusting the size of the window, to include all parts of the scene, becomes easier.

• In an animation sequence place the PRP at the viewing coordinate origin and place the view plane in front of the scene, move through the scene by moving the viewing reference frame.

PRP is at the origin