2. 2
of
20
Why?
We must determine what is visible within a
scene from a chosen viewing position
For 3D worlds this is known as visible
surface detection or hidden surface
elimination
3. 3
of
20
Two Main Approaches
Visible surface detection algorithms are
broadly classified as:
– Object Space Methods: Compares objects
and parts of objects to each other within the
scene definition to determine which surfaces
are visible
– Image Space Methods: Visibility is decided
point-by-point at each pixel position on the
projection plane
Image space methods are by far the more
common
5. 5
of
20
Back-Face Detection Method
• A fast and simple object-space method for identifying
the back faces of a polyhedron is based on the "inside-
outside" tests. A point (x, y, z) is "inside" a polygon
surface with plane parameters A, B, C, and D if
• When an inside point is along the line of sight to the
surface, the polygon must be a back face (we are inside
that face and cannot see the front of it from our viewing
position).
0
D
Cz
By
Ax
D
Cz
By
Ax
S
6. 6
of
20
Back-Face Detection Method
• We can simplify this test by considering the
normal vector N to a polygon surface, which has
Cartesian components (A, B, C). In general, if V
is a vector in the viewing direction from the eye
(or "camera") position, as shown in Fig, then this
polygon is a back face if
V.N>0
7. 7
of
20
N calculation
P1(X1,Y1,Z1)
P2(X2,Y2,Z2)
P3(X3,Y3,Z3)
)
P
-
(P
)
P
-
(P
N 2
3
2
1
2
3
2
3
2
3
2
1
2
1
2
1
N
Z
Z
Y
Y
X
X
Z
Z
Y
Y
X
X
k
j
i
k
Y
Y
X
X
Y
Y
X
X
j
Z
Z
X
X
Z
Z
X
X
i
Z
Z
Y
Y
Z
Z
Y
Y
2
3
2
3
2
1
2
1
2
3
2
3
2
1
2
1
2
3
2
3
2
1
2
1
N
2
3
2
1
2
3
2
1
A *
N Y
Y
Z
Z
Z
Z
Y
Y
2
3
2
1
2
3
2
1
B *
N X
X
Z
Z
Z
Z
X
X
2
3
2
1
2
3
2
1
C *
N X
X
Y
Y
Y
Y
X
X
8. 8
of
20
Back-Face Detection Method
• Ensure we have a right handed system with the
viewing direction along the negative z-axis
Now we can simply say that if the z component
(C) of the polygon’s normal is less than zero the
surface cannot be seen
V = (0, 0, Vz) V.N=Vz.C
so that we only need to consider the sign of C,
the ; component of the normal vector N .
9. 9
of
20
Back-Face Detection Method
• In a right-handed viewing system with
viewing direction along the negative z,
axis, the polygon is a back face if C <= 0.
• In a Left-handed viewing system with
viewing direction along the positive z, axis,
the polygon is a back face if C > 0.
10. 10
of
20
Back-Face Detection (cont…)
In general back-face detection can be
expected to eliminate about half of the
polygon surfaces in a scene from further
visibility tests
More complicated surfaces
though scupper us!
We need better techniques
to handle these kind of
situations
11. 11
of
20
Depth-Buffer Method
Compares surface depth values throughout
a scene for each pixel position on the
projection plane
Usually applied to scenes only containing
polygons
As depth values can be computed easily,
this tends to be very fast
Also often called the z-buffer method
14. 14
of
20
Depth-Buffer Algorithm (cont…)
2. Process each polygon in a scene, one at
a time
– For each projected (x, y) pixel position of a
polygon, calculate the depth z (if not already
known)
– If z < depthBuff(x, y), compute the surface
colour at that position and set
depthBuff(x, y) = z
frameBuff(x, y) = surfColour(x, y)
After all surfaces are processed depthBuff
and frameBuff will store correct values
15. 15
of
20
A-Buffer Method
The A-buffer method is an extension of the
depth-buffer method
The A-buffer method is visibility detection
method developed at Lucasfilm Studios for
the rendering system REYES (Renders
Everything You Ever Saw)
16. 16
of
20
A-Buffer Method (cont…)
The A-buffer expands on the depth buffer
method to allow transparencies
The key data structure in the A-buffer is the
accumulation buffer
17. 17
of
20
A-Buffer Method (cont…)
If depth is >= 0, then the surface data field
stores the depth of that pixel position as
before
If depth < 0 then the data filed stores a
pointer to a linked list of surface data
18. 18
of
20
A-Buffer Method (cont…)
Surface information in the A-buffer includes:
– RGB intensity components
– Opacity parameter
– Depth
– Percent of area coverage
– Surface identifier
– Other surface rendering parameters
The algorithm proceeds just like the depth
buffer algorithm
The depth and opacity values are used to
determine the final colour of a pixel
19. 19
of
20
Scan-Line Method
An image space method for identifying
visible surfaces
Computes and compares depth values
along the various scan-lines for a scene
20. 20
of
20
Depth-Sorting Method
A visible surface detection method that uses
both image-space and object-space
operations
Basically, the following two operations are
performed
– Surfaces are sorted in order of decreasing
depth
– Surfaces are scan-converted in order, starting
with the surface of greatest depth
The depth-sorting method is often also known
as the painter’s method
