3D graphics eBook - Course Materials Repository

Image plane 65
Image plane
In 3D computer graphics, the image plane is that plane in the world which is identified with the plane of the
monitor. If one makes the analogy of taking a photograph to rendering a 3D image, the surface of the film is the
image plane. In this case, the viewing transformation is a projection that maps the world onto the image plane. A
rectangular region of this plane, called the viewing window or viewport, maps to the monitor. This establishes the
mapping between pixels on the monitor and points (or rather, rays) in the 3D world.
In optics, the image plane is the plane that contains the object's projected image, and lies beyond the back focal
plane.
Irregular Z-buffer
The irregular Z-buffer is an algorithm designed to solve the visibility problem in real-time 3-d computer graphics.
It is related to the classical Z-buffer in that it maintains a depth value for each image sample and uses these to
determine which geometric elements of a scene are visible. The key difference, however, between the classical
Z-buffer and the irregular Z-buffer is that the latter allows arbitrary placement of image samples in the image plane,
whereas the former requires samples to be arranged in a regular grid.
These depth samples are explicitly stored in a two-dimensional spatial data structure. During rasterization, triangles
are projected onto the image plane as usual, and the data structure is queried to determine which samples overlap
each projected triangle. Finally, for each overlapping sample, the standard Z-compare and (conditional) frame buffer
update are performed.
Implementation
The classical rasterization algorithm projects each polygon onto the image plane, and determines which sample
points from a regularly spaced set lie inside the projected polygon. Since the locations of these samples (i.e. pixels)
are implicit, this determination can be made by testing the edges against the implicit grid of sample points. If,
however the locations of the sample points are irregularly spaced and cannot be computed from a formula, then this
approach does not work. The irregular Z-buffer solves this problem by storing sample locations explicitly in a
two-dimensional spatial data structure, and later querying this structure to determine which samples lie within a
projected triangle. This latter step is referred to as "irregular rasterization".
Although the particular data structure used may vary from implementation to implementation, the two studied
approaches are the kd-tree, and a grid of linked lists. A balanced kd-tree implementation has the advantage that it
guarantees O(log(N)) access. Its chief disadvantage is that parallel construction of the kd-tree may be difficult, and
traversal requires expensive branch instructions. The grid of lists has the advantage that it can be implemented more
effectively on GPU hardware, which is designed primarily for the classical Z-buffer.
With the appearance of CUDA, the programmability of current graphics hardware has been drastically improved.
The Master Thesis, "Fast Triangle Rasterization using irregular Z-buffer on CUDA", provide a complete description
to an irregular Z-Buffer based shadow mapping software implementation on CUDA. The rendering system is
running completely on GPUs. It is capable of generating aliasing-free shadows at a throughput of dozens of million
triangles per second.