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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. - PowerPoint PPT Presentation
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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
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