1 Ray Tracing - Bounding Volumes Ray Tracing - Bounding Volumes - - PDF document

1

Ray Tracing: Intersection

Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

Ray Tracing: Intersection

• We only talked about ray intersection with spheres

and planes

• What about?

– Boxes – Cylinders – Cones – Triangles – Spline surfaces – Irregular shapes

Ray Tracing - Object - Ray Intersection

• For each ray, intersection test needs to be

made for each object

– This could costly if you have many

• bjects…consider if object has n polygons, n

very large! – Solutions

• Adaptive Depth Control
• Bounding Volume
• Spatial Subdivision

Ray Tracing – Adaptive Depth Control

• Indices of diffuse/reflection/refraction get

multiplied together as the ray tracer recurses

• Depending on material properties, this

attenuation can get very small

• Keep running product and stop when below

a threshold

Ray Tracing - Bounding Volumes

• Place simple objects (i.e., sphere or box)

around complex objects

– Suitability depends on object being enclosed!

• Do initial intersection tests on bounding
• bjects.
• If ray intersects bounding volume, then test

complex bounded object

• Can be nested

2

Ray Tracing - Bounding Volumes

[Watt/Watt,235]

Ray Tracing - Bounding Volumes

[Watt/Watt,236]

Ray Tracing - Spatial Subdivision

• Motivation

– Without spatial subdivision, for each ray, you will need to query all objects/polygons and test for intersection – With spatial subdivision, you know which

• bjects are in each volume so you only test
• bjects that are in the volumes where a ray is

traveling.

Ray Tracing - Spatial Subdivision

• Subdivide your scene volume into hierarchical

regions

– Octrees – BSP Trees

• Create a tree structure that indicates for each region:

– if the region is empty – the object present at that particular region

• Test ray intersection with region volume

Ray Tracing - Octrees

• Recursively subdivide volume into equal

regions.

• If subregion is empty or contains a single
• bject, then stop
• Otherwise, further subdivide.
• Continue until each subregion is empty or

contains a single object.

Ray Tracing - Octrees

[Foley/Van Dam]

3

Ray Tracing – Oct(quad)trees

• Subdivisions represented as a tree

[Watt/Watt,244]

Ray Tracing - Oct(quad)trees

• Quadtree applet

http://njord.umiacs.umd.edu:1601/users/brabec/qu adtree/points/pointquad.html

Ray Tracing -- Octrees

• Images from

http://www.flipcode.com/tutorials/tut_octrees.shtml

Ray Tracing -- Octrees Ray Tracing -- Octrees Ray Tracing -- Octrees

Shows viewing frustum and which “octants” need to be checked.

4

Ray Tracing - BSP Trees

• Binary Space Partitioning Trees (BSP

Trees)

– Like Octrees but divides space into a pair of subregions – Subregions need not be equally spaced – Planes separating regions can be placed at

• bject boundaries.

Ray Tracing - Spatial Subdivision

• Octrees vs BSP Trees

[Watt/Watt,246]

Ray Tracing - BSP Trees

• BSP Trees – Each non-terminal node represents a single

partitioning plane that divides space in two

[Watt/Watt,247]

Ray Tracing - BSP Trees

• BSPTree applet

http://symbolcraft.com/graphics/bsp/index.html

Ray Tracing - Spatial Subdivision

• Advantages

– Efficient means for finding objects within your space – Compact representation

• Disadvantages

– Preprocessing required – If scene changes, must rebuild your tree – Not foolproof

Ray Tracing - Spatial Subdivision

• Potential Problems - can double testing or miss small items

[Watt/Watt,247]

5

Ray Tracing - Spatial Subdivision

• Octrees vs BSP trees

– BSP Trees are generally more balanced than Octrees – BSP Traversal more efficient – BSP Trees have additional storage overhead as must store subdivision planes