Applied Spatial Hash
Function in Ray Tracing
By : Jaruwan Mesit
Optimized ray tracing
In class, we have learned two methods
• Bounding Volume Hierarchy
• Grid
New method
• Spatial Hash function (My project)
Bounding Volume
Hierarchy
– Sort all objects in the scene
– Create the tree from sorted objects
– Create the bounding boxes to bound the
objects in the same leave
– Find the intersection between ray and
bounding volume
Grid (1)
• Create grid from the scene
• Create bounding box in every object in
scene
• Create the list of the object in the grid by
comparing minimum and maximum points of
bounded objects and grid (complex)
• If ray pass through the grid
– Check if the ray also pass the objects
Some case is better than Bounding Volume
Hierarchy but some case not.
******** We can do something easier********
Grid (2)
Spatial Hash Function (1)
• Simple and no comparison
• Using hash function and hash table
Spatial Hash Function (2)
• Create grid
• Give the index to grid by using spatial hash function which
hashes to minimum point of Grid
Index = ( floor(Grid.min.x / length) * xprime+
floor(Grid.min.y / height) * yprime +
floor(Grid.min.z / width) * zprime) % bucketsize;
length = Grid length
height = Grid height
width = Grid width
xprime, yprime, zprime = any prime number for x, y, and z
• Now we have Grid with the index.
Spatial Hash Function (3)
Grid 1
Index 1
Grid 2
Index 2
Grid 3
Index 3
Grid 4
Index 4
Grid 5
Index 5
Spatial Hash Function (4)
• Create the bounding box to bound
every object in scene
• Create hash table by using the same
hash function
Spatial Hash Function (5)
= point[1..8]
HashIndex = ( floor(point[1..8].min.x /length)
* xprime+
floor(point[1..8].min.y /height)
* yprime +
floor(point[1...8].min.z /width)
* zprime) % bucketsize;
• Put the object name into the hash index
Spatial Hash Function (6)
Hash Index
Now We have
1) Hash table
2) List of Grid
and Index
Grid 1
Index 1
1
Object 1 Object 2 Object4
2
Object 1 Object 4
3
Object 3
4
Object 4
Grid 2
Index 2
Grid 3
Index 3
Grid 4
Index 4
Grid 5
Index 5
Spatial Hash Function (7)
Ray Pass Through
Grid 1
Grid 1
Index 1
Grid 2
Index 2
Grid 3
Index 3
Grid 4
Index 4
Grid 5
Index 5
Hash Index
1
Object 1 Object 2 Object4
Find Intersection with object 1, 2, and 4
Spatial Hash Function (8)
Experiments
# of objects
Without any
technique
Bounding
Volume
Hierarchy (5)
Grid (3)
Spatial Hash
Function with
(3, 1001 bz)
30 spheres
5544 ms.
3654 ms.
5264 ms.
6420 ms.
50 spheres
8649 ms.
8560 ms.
6908 ms.
7770 ms.
100 spheres
25093 ms.
21314 ms.
21014 ms.
18966 ms.
Problem
Grid and hashing function
These two girds have to be compute
for intersection. This is the problem
why hashing function and grid spend time
more than bounding volume hierarchy
in some case.
Distributed objects
If the objects are distributed among grid, hashing function
and grid are better than bounding volume hierarchy.
Images
End
• Question?