Download Polygon Rendering

GR2
Advanced Computer Graphics
AGR
Lecture 8
Polygon Rendering
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The Story So Far

We now understand:
– how to model objects as a set of
polygonal facets and create a 3D world
(Lectures 1 & 2)
– how to view these worlds with a camera
model, projecting the facets to 2D
(Lectures 3 & 4)
– how to calculate reflection off a surface
(Lectures 5 & 6)
– how to shade a single projected facet
using the reflection calculation (Lecture 7)
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Next step: rendering a set of facets
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First a Word on Normals

A polygon has two normals
If the polygon is part of a solid object, one normal will
face out, one will face in. We need to have a way of
distinguishing them.
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Surface Normals
Each polygon facet is considered to
have an inside and an outside, and a
single normal
 This is determined by the order in
which vertices of facet are specified:

– look at object from outside
– if polygon vertices are specified in anticlockwise order, then normal points from
inside to outside
P3
P2
P4
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P1
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Rendering Polygons
We are now ready to consider
rendering a set of polygon facets
 For efficiency, we only want to render
those that are visible to the camera
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Back Face Culling

If the facets belong to a solid object (a
polyhedron) we do not need to render
back-facing polygons
Here only three
facets need to
be drawn - those
that face towards
the camera
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Back Face Culling

A polygon faces away from the viewer
if the angle between the surface
normal (N) and the viewing direction
(V) is less than 90 degrees
V.N > 0
N
V
camera
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Back Face Culling

It is efficient to carry this out in the
viewing coordinate system
– camera on z-axis pointing in negative zdirection
– so V = (0,0,-1)

Thus the V.N>0 test becomes a test
only on z-component of normal vector
Nz < 0
– ie test if z-component of normal points in
negative z-direction
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Back Face Culling
Back face culling is an extremely
important efficiency gain in rendering
and is typically the first step in visibility
processing
 We are left with a set of front facing
polygons...
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The Next Problem

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Some facets will be obscured by
others - we only want to draw (ie
shade) the visible polygons
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Solution - Z Buffer Algorithm

Suppose polygons have been passed
through the projection transformation,
with the z-co-ordinate retained (ie the
depth information) - suppose z
normalized to range 0 to 1
For each pixel
(x,y), we want
to draw the
polygon nearest
the camera, ie
0
largest z
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y
x
z
view plane window
1
camera
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Z Buffer Algorithm

We require two buffers:
– frame buffer to hold colour of each pixel
(in terms of RGB) ... typically 24 bits
– z-buffer to hold depth information for each
pixel ... typically 32 bits
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Initialize:
– frame buffer to the background colour of
the scene
colour (x,y) = (IRED, IGREEN, IBLUE)background
– z-buffer to zero (back clipping plane)
depth (x,y) = 0
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Z Buffer Algorithm

As each polygon is scan converted and
shaded using Gouraud or Phong shading:
– calculate depth z for each pixel (x,y) in
polygon
– if z > depth(x,y), then set:
depth (x,y) = z;
colour (x,y) = (IRED, IGREEN, IBLUE)gouraud/phong
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After all polygons processed, depth
buffer contains depth of visible surfaces,
and frame buffer the colour of these
surfaces
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Z Buffer - Strengths and
Weaknesses
A major advantage of the z-buffer
algorithm is its simplicity
 A weakness (of now decreasing
importance) is the amount of memory
required
 Limited precision for depth
calculations in complex scenes
(perspective effect again a problem)

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Transparency

Polygons in practice may be opaque
or semi-transparent
– in OpenGL a=1 represents opaque

Simple rendering:
– render opaque polygons first, generating
colour (x,y)
– for each semi-transparent polygon (with
opacity a, render into another buffer as
polygon (x,y)
– and combine using:
( 1 - a ) * colour (x,y) + a * polygon (x,y)
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Better Transparency
Better results by storing for each pixel
the depth and transparency of each
surface
 Surfaces can then be composited
back to front in order to give more
accurate images

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Shadows
Z buffers also give us a nice way of
doing shadows
 The z buffer is a way of determining
what is visible to the camera
 For shadows, we need a way of
determining what is visible to the light
source

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Shadow Z Buffer
We require a second z-buffer, called a
shadow z-buffer
 Two step algorithm:

– scene is ‘rendered’ from the light source
as viewpoint, with depth information
stored in the shadow z-buffer (no need to
calculate intensities)
– scene is rendered from the camera
position, using Gouraud or Phong shading
with a z-buffer algorithm ... but we need to
adjust colour if point is in shadow
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Shadow Z Buffer

To determine if point is in shadow:
– take its position (xO, yO, zO) in the camera
view, and transform it into the
corresponding position (xO’, yO’, zO’) in the
light source view
– look up the z value, say zL , in the shadow
z-buffer at the position (xO’, yO’)
– if zL is closer to the light than zO’, this
means some object is nearer the light and
therefore the point is in shadow... in this
case only the ambient reflection would be
shown at that point
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