Visible Surface Detection

A. K. Biswas, Dept. Of Computer Apllication, B.I.T., Durg 1
COMPUTER GRAPHICSCOMPUTER GRAPHICS
Visible SurfaceVisible Surface
DetectionDetection

CONTENTCONTENT
Surface Detection Methods
 Back face detection
 Depth-buffer method
 A-buffer method
 Scan-line method
 Depth Sorting
 Area Sub-Division

Why Surface Detection?Why Surface Detection?
Given a set of 3D objects and a viewing specification, we
wish to determine which lines or surfaces are visible, so
that we do not needlessly calculate and draw surfaces,
which will not ultimately be seen by the viewer, or which
might confuse the viewer.
For 3D worlds this is known as Visible Surface Detection
or Hidden Surface Elimination
Visible Surface Detection or Hidden Surface
Elimination, refer to the methods and algorithms to
determine which parts of which surfaces of a scene are
visible from a chosen viewing position.

Simple Example…….Simple Example…….
With all lines drawn, it is
not easy to determine
the front and back of the
box.
Is this the front face of
the cube or the rear?

DEFINITIONSDEFINITIONS
Visibility Culling
Refers to the detection of which surfaces
are completely Visible with respect to the
camera.
Hidden-Surface Elimination
Refers to the elimination of the parts of the
surfaces which are hidden with respect to
the camera.
Shadows
Refer to the determination of the parts of the
surfaces which are hidden with respect to
the light sources

DIFFERENT APPROACHESDIFFERENT APPROACHES
Visible Surface Detection or Hidden Surface
Elimination 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 more common
Pixel Space

OBJECT SPACEOBJECT SPACE
Object space algorithms do their work on the
objects themselves before they are converted to
pixels in the frame buffer.
Pseudo code…
 for each object A in the scene
•determine which parts of object A are
visible
•draw these parts in the appropriate
color
Comparing the polygons in object A to other
polygons in A and to polygons in every other object
in the scene.

IMAGE SPACEIMAGE SPACE
Image space algorithms, the objects are being
converted to pixels in the frame buffer.
Pseudo code…
 for each pixel in the frame buffer
•Determine which polygon is closest to
the viewer at that pixel location
•Color the pixel with the color of that
polygon at that location

OBJECT SPACE VS IMAGE SPACEOBJECT SPACE VS IMAGE SPACE
Object Space:
 Consider each object only once - draw its
pixels and move on to the next object
 Might draw the same pixel multiple times
Image Space:
 Consider each pixel only once - draw part of
an object and move on to the next pixel
 Might compute relationships between
objects multiple times
Square Box
indicate Frame
Buffer

ALGORITHMSALGORITHMS
Object space
– Back-Face Detection / Culling
Image space
– z-Buffer / Depth Buffer Algorithm
– A-Buffer
– Scan Line
Hybrid
– Depth-Sort / Painter
– Area Sub-division
– Binary Space Partitioning (BSP)

BACK-FACE DETECTION / CULLINGBACK-FACE DETECTION / CULLING
Back-face culling (an object space algorithm) works
on 'solid' objects which you are looking at from the
outside. That is, the polygons of the surface of the
object completely enclose the object.
The simplest thing we can do is find the faces on the
backs of polyhedra and discard them

 Which way does a surface point?
 Vector mathematics defines the concept of
a surface’s normal vector.
 A surface’s normal vector is simply an
arrow that is perpendicular to that surface.
 Every planar polygon has a surface
normal, that is, a vector that is normal to
the surface of the polygon.
– Actually every planar polygon has two normals.
 Given that this polygon is part of a 'solid'
object we are interested in the normal that
points OUT, rather than the normal that
points in.

 Consider the 2 faces (Surface) of a cube and their normal
vectors.
 Vectors N1 and N2 are the normal to surfaces 1 and 2
respectively.
 Vector L points from surface 1 to the viewpoint.
 Depending on the angle between L, and N1 & N2, they may or
may not be visible to the viewer.
N2
N1L
surface1
surface2

•If we define θ to be the angle between L and N.
•Then a surface is visible from the position given by L if:
•Can calculate Cos θ using the formula:
°≤≤ 900 θ 1cos0 ≤≤ θor
θcos... NLNL =

Determining N:
• Use cross product to calculate N
• N = A × B
–Vertices are given a counter clockwise order when
looking at visible side.
A
B
E
D
N
N

We know from before that a point (x, y, z) is behind
a polygon surface if:
where A, B, C & D are the plane parameters for the
surface
This can actually be made even easier if we
organise things to suit ourselves
0<+++ DCzByAx

 If Object description have been converted to projection coordinates
and our viewing direction is parallel to the viewing zv axis, then V=(0,
0, Vz) and
V . N = Vz * C
Depend on the sign of C (the z component of the normal vector N
 In a right handed system with the viewing direction along the
negative z-axis, the polygon is a back face if C < 0 and C=0 (Normal
has z component C=0, since our viewing direction is grazing that
polygon.
 Now we can simply say that if the z component of the polygon’s
normal (N) is less than zero the surface cannot be seen.

Limitations:
 Requires a lot of memory
 It can only be used on solid objects…
• Remove the top or front face of the cube, and
suddenly we can see inside, and our algorithm falls
over.
 It works fine for convex polyhedra but not
necessarily for concave polyhedra.
• example of a partially hidden face, that will not be
eliminated by Back-face removal.

DEPTH-BUFFER METHODDEPTH-BUFFER METHOD
 Compares surface depth values throughout a scene
for each pixel position on the projection plane
 Usually applied to scenes only containing polygons
 Fast approach due to easy depth values computation
 Also often called the z-buffer method
(x2, y2) & z2
(x3, y3) & z3
(x1, y1) & z1
 (x1, y1), (x2, y2) & (x3,
y3) are the pixel
positions of surfaces
S1, S2, and S3
respectively.
 z1, z2 and z3 defines the
depth values (distance)
of surfaces S1, S2, and
S3 respectively from
the View Plane

DEPTH-BUFFER METHOD (Cont…)DEPTH-BUFFER METHOD (Cont…)
1. Initialise the depth buffer and frame buffer so that for
all buffer positions (x, y)
depthBuff(x, y) = 1.0
frameBuff(x, y) = bgColour
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

DEPTH CALCULATIONDEPTH CALCULATION

Iterative Calculations (cont…)Iterative Calculations (cont…)
top scan line
bottom scan line
y scan line
y - 1 scan line
x x’

DISADVANTAGES: DEPTH BUFFERDISADVANTAGES: DEPTH BUFFER
This method only find out one visible surface
at each pixel position that means it deals
with only Opaque surface.
1
2
3
4
5
6
1 Red
2 Red
3 Green
4 Blue
5 Green
6 Red

A-BUFFER METHODA-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)

A-BUFFER METHOD (Cont…)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

(a) If depth >= 0, then the surface data field stores the
depth of that pixel position as before
(b) If depth < 0, then the data filed stores a pointer to
a linked list of surface data

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

SCAN-LINE METHODSCAN-LINE METHOD
An image space method for identifying visible surfaces
Computes and compares depth values to create an
image one scan line at a time.
This algorithm is similar to polygon scan conversion
algorithm, but deal with a set of polygons.
Two important tables are maintained:
 The Edge Table (ET)
 The Polygon Table (PT)

Edge TableEdge Table
 Create an Edge Table (ET) for all non-horizontal edges of all
polygons projected on the view plane.
 Edge Table Process:
– Entries in the ET are sorted into bucket based on each edge’s smaller
y coordinates and within bucket are ordered by increasing x
coordinate.
 Edge Table fields:
– The x-coordinate of the end with the smaller y coordinate.
– The y-coordinate of the edge’s other end.
– The x Increment, ∆x used in stepping from one scan line to the
next.
– Polygon Identification no., indicating the polygon to shich the
edge belongs.
– Pointers into the surface facet table to connect edges to
surfaces.
x ymax ∆x ID

Polygon TablePolygon Table
Polygon Table fields:
– Polygon ID
– The coefficients of the plane equation
– Shading or Color information for the Polygon
– An ‘in-out’ Boolean flag, initiated to false and used
during Scan-line processing.
ID Plane Equation Shading Information In-out

Scan-Line MethodScan-Line Method
 To facilitate the search for surfaces crossing a given scan-line
an active list of edges is formed for each scan-line as it is
processed
 The active list stores only those edges that cross the scan-line
in order of increasing x
 Also a flag is set for each surface to indicate whether a position
along a scan-line is either inside or outside the surface
 To facilitate the search for surfaces crossing a given scan-line
an active list of edges is formed for each scan-line as it is
processed
 The active list stores only those edges that cross the scan-line
in order of increasing x
 Also a flag is set for each surface to indicate whether a position
along a scan-line is either inside or outside the surface

Scan-Line Method: ExampleScan-Line Method: Example
Sorted Edges Are: AD, CD, GH, FG, HE, BC, AB and EF
Polygon Table has entries for ABCD and EFGH
Prepare a Active Edge Table (AET):
Active Edge Table (AET)
Scan Line Entries
1 AB, BC, HE, FG
2 AD, HE, BC, FG
3 AD, HE, BC, FG
4 AD, DC, GH, FG Scan Line 4

Scan-Line Method LimitationsScan-Line Method Limitations
The scan-line method runs into trouble when
surfaces cut through each other or otherwise
cyclically overlap
Such surfaces need to be divided

Depth-Sorting MethodDepth-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

Depth-Sorting Method: ProblemDepth-Sorting Method: Problem
Look at cases where it doesn't work correctly. S has a
greater depth than S' and so will be drawn first. But S'
should be drawn first since it is obscured by S. We
must somehow reorder S and S'.
S
S’
X
Z

Depth-Sorting MethodDepth-Sorting Method
First, assume that we are viewing along the z
direction
All surfaces in the scene are ordered according to the
smallest z value on each surface
The surface S at the end of the list is then compared
against all other surfaces to see if there are any
depth overlaps
If no overlaps occur then the surface is scan
converted and the process is then repeated for the
next surface in the list.
If depth overlap is detected at any point in the list,
then need some additional comparisons to determine
whether any of the surface should be reordered.

Depth-Sorting Method (cont…)Depth-Sorting Method (cont…)
Test for depth overlap:
– The bounding rectangles for the two surfaces do not
overlap.
– Surface S is completely behind the overlapping surface
relative to the viewing position.
– The overlapping surface is completely in front of S relative
to the viewing position.
– The boundary edge projections of the two surfaces onto
the view plane do not overlap
The tests are performed in the order listed and as
soon as one is true we move on to the next surface
If all tests fail then we swap the orders of the surfaces

Depth OverlappingDepth Overlapping
S
Pz’max
z’min
zmax
zmin
x
z
No Depth Overlap
S
P
z’max
z’min
zmax
zmin
x
z
Depth Overlap

Polygon Reordering TestPolygon Reordering Test
Perform a series of test for reordering the polygons.
If the polygons fails all the test one after another, then
the polygons are reorder.
The initial tests are computationally cheap, but the
later tests are more expensive.
 Test Requirements:
– Store Zmax, Zmin for each Polygon
– Sort on Zmax
– Start with polygon with greatest depth (S)

Depth-OverlappingDepth-Overlapping
Compare S with all other polygons (P) to see if there
is any depth overlap.
If S.Zmin <= P.Zmax then have depth overlap (as in
below figures), Test-2 will perform
S.Zmax
S.Zmin
P.Zmax
P.Zmin
S
P
S.Zmax
S.Zmin
P.Zmax
P.Zmin
S
P
Depth
Overlap
No Depth
Overlap
Z
X
Z
X

Depth-Overlapping: Test – 1Depth-Overlapping: Test – 1
 Check to see if polygons overlap in xy plane (use bounding
rectangles)
S.XrS.Xl P.Xl P.Xr
S
P
Depth Overlap, check for
xy overlap
Case-1
S.XrS.Xl P.Xl P.Xr
S P
Bounding rectangle of P is
Completely inside of S i. e. overlap
Case-2
S P
Partially obscured
Problem
Case-3
 For Case-1 and Case-2, Test-2
is Passed
 For Case-3, Test-2 is Failed
Z Z
Z
X X
X

Depth-Overlapping: Test – 2 (1/2)Depth-Overlapping: Test – 2 (1/2)
Test if surface S is “inside" of polygon P (relative to
view plane)
Remember: a point (x, y, z) is "outside" of a plane if
we put that point into the plane equation and get:
Ax + By + Cz + D > 0
Suppose plane equation for P is
Ax + By + Cz + D
So to test for S outside of P, put all vertices of S into
the plane equation for P and check that all vertices
give a result that is > 0.
i.e. Ax' + By' + Cz' + D > 0 x', y', z' are S vertices

Depth-Overlapping: Test – 2 (2/2)Depth-Overlapping: Test – 2 (2/2)
 Choose Normal away from the view plane since define
“inside" with respect to the view plane
S P
N
S completely Inside of P,
so scan convert S
SP
N
S is not Inside of P
XX
ZZ

 If the test of S “inside" of P fails, then test to see if P is “outside" of S
(again with respect to the view plane) (Test 2).
 Compute plane equation of S and put in all vertices of P, if all vertices of
P inside of S then P inside.
 Inside Test: Ax' + By' + Cz' + D & lt 0 where x', y', z' are coordinates of P
vertices
S
P
N
P is outside of S, so scan
Convert S
X
Z
S
P
Bounding Rectangles overlap
S not inside of P
P is not inside of S
X
Z

 Check for overlap for actual projections in xy plane since may have
bounding rectangles overlap but not actual overlap
 For example: Look at projection of two polygons in the xy plane
X
Z
• Bounding Rectangle Overlap, But Projection Don’t
• Use Line eq. and test for Intersection
• No intersection, scan convert S
X
Z

Ordering S and S’Ordering S and S’
 If all previous tests fail, interchange S and S’ in the list
x
z
S
S’

DrawbacksDrawbacks
Gets into infinite loop if surfaces alternately obscure each other

Area Sub-Division methodArea Sub-Division method
 This method is essentially an image space method but used
Object Space operations for reordering of surfaces according
to depth.
 The method makes use of area coherence in a scene by
collecting those areas that form part of a single surface.
 Successively subdivide the total viewing area into small
rectangles until each small is the projection of part of a single
visible surface or no surface at all.
 Identify whether the area is part of a single surface or a
complex surface by mean of visibility tests.
 The visibility of a single surface within a specified area is
determined by comparing it against the specified area
boundary.

Area Sub-Division methodArea Sub-Division method
Start with the total view
Apply tests to see whether area should be subdivided
If view sufficiently complex, subdivide it
Continue testing and subdivision
…
Until subdivisions are easy or reach the resolution
limit

Area – Surface RelationshipsArea – Surface Relationships
The relative surface characteristics of test surface and
the specified area are as follows:
– Surrounding Surface:
The test surface that completely enclose the area.
– Overlapping Surface:
The Test surface that is partially inside and partially
outside the area.
– Inside Surface:
The Test surface that is completely inside the area.
– Outside Surface:
The Test surface that is completely outside the area.

Area – Surface RelationshipsArea – Surface Relationships
Surrounding
surface
Overlapping
surface
Inside
surface
Outside
surface

Conditions for Stopping SubdivisionConditions for Stopping Subdivision
 All surfaces are outside the specified area.
 There is only one overlapping surface or only one inside surface. In this
case, the area is filled with the background color, and then the part of the
surface inside the area is scan converted .
 There is a single surrounding surface but no overlapping or inside
surface. In this case, the area is filled with the color of surrounding
surface.
 A surrounding surface obscures all other surfaces within the specified
area boundary. If there is more that one surface which is overlapping,
inside or surrounding the specified area, then there may be atleast one
surface which is front of all others. It is easy to determine such surface
by computing the z-coordinates of the planes of all surfaces al the four
corner of the specified area. The surface whose four whose four corner
z-coordinates are closer to the view point than those of the other surface
obscures all other surfaces. So the entire area is filled with the color of
this surrounding surface.

Subdivision ConditionsSubdivision Conditions
Conditions for stopping subdivision:
– All surfaces are outside an area
– An area has only one inside, overlapping, or surrounding
surface
– An area has one surrounding surface that obscures all
other surfaces within the area boundaries:

Area-Subdivision MethodArea-Subdivision Method
 Conditions for stopping subdivision:
1.All surfaces are outside an area
2.An area has only one inside, overlapping, or surrounding
surface
3.An area has one surrounding surface that obscures all
other surfaces within the area boundaries:

Ray Tracing MethodRay Tracing Method
Ray tracing method
– Traces a ray for every
pixel
– Objects intersecting this
ray are visible
– If ray intersects multiple
objects, take the closest
– Only shades each pixel
once
– Algorithm is slow

RaytracingRaytracing

Binary Space PartitioningBinary Space Partitioning
Goal: build a structure that captures some relative
depth information between objects. Use it to draw
objects in the right order from any viewpoint.
Called the binary space partitioning tree, or BSP tree
Key observation: The polygons in the scene are
painted in the correct order if for each polygon P,
– Polygons on the far side of P are painted first
– P is painted next
– Polygons in front of P are painted last

Visible Surface Detection

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