Are there any rendering alternatives to rasterisation or ray tracing? - graphics

Question

Rasterisation (triangles) and ray tracing are the only methods I've ever come across to render a 3D scene. Are there any others? Also, I'd love to know of any other really "out there" ways of doing 3D, such as not using polygons.

Answer 1

Aagh! These answers are very uninformed!
Of course, it doesn't help that the question is imprecise.
OK, "rendering" is a really wide topic. One issue within rendering is camera visibility or "hidden surface algorithms" -- figuring out what objects are seen in each pixel. There are various categorizations of visibility algorithms. That's probably what the poster was asking about (given that they thought of it as a dichotomy between "rasterization" and "ray tracing").
A classic (though now somewhat dated) categorization reference is Sutherland et al "A Characterization of Ten Hidden-Surface Algorithms", ACM Computer Surveys 1974. It's very outdated, but it's still excellent for providing a framework for thinking about how to categorize such algorithms.
One class of hidden surface algorithms involves "ray casting", which is computing the intersection of the line from the camera through each pixel with objects (which can have various representations, including triangles, algebraic surfaces, NURBS, etc.).
Other classes of hidden surface algorithms include "z-buffer", "scanline techniques", "list priority algorithms", and so on. They were pretty darned creative with algorithms back in the days when there weren't many compute cycles and not enough memory to store a z-buffer.
These days, both compute and memory are cheap, and so three techniques have pretty much won out: (1) dicing everything into triangles and using a z-buffer; (2) ray casting; (3) Reyes-like algorithms that uses an extended z-buffer to handle transparency and the like. Modern graphics cards do #1; high-end software rendering usually does #2 or #3 or a combination. Though various ray tracing hardware has been proposed, and sometimes built, but never caught on, and also modern GPUs are now programmable enough to actually ray trace, though at a severe speed disadvantage to their hard-coded rasterization techniques. Other more exotic algorithms have mostly fallen by the wayside over the years. (Although various sorting/splatting algorithms can be used for volume rendering or other special purposes.)
"Rasterizing" really just means "figuring out which pixels an object lies on." Convention dictates that it excludes ray tracing, but this is shaky. I suppose you could justify that rasterization answers "which pixels does this shape overlap" whereas ray tracing answers "which object is behind this pixel", if you see the difference.
Now then, hidden surface removal is not the only problem to be solved in the field of "rendering." Knowing what object is visible in each pixel is only a start; you also need to know what color it is, which means having some method of computing how light propagates around the scene. There are a whole bunch of techniques, usually broken down into dealing with shadows, reflections, and "global illumination" (that which bounces between objects, as opposed to coming directly from lights).
"Ray tracing" means applying the ray casting technique to also determine visibility for shadows, reflections, global illumination, etc. It's possible to use ray tracing for everything, or to use various rasterization methods for camera visibility and ray tracing for shadows, reflections, and GI. "Photon mapping" and "path tracing" are techniques for calculating certain kinds of light propagation (using ray tracing, so it's just wrong to say they are somehow fundamentally a different rendering technique). There are also global illumination techniques that don't use ray tracing, such as "radiosity" methods (which is a finite element approach to solving global light propagation, but in most parts of the field have fallen out of favor lately). But using radiosity or photon mapping for light propagation STILL requires you to make a final picture somehow, generally with one of the standard techniques (ray casting, z buffer/rasterization, etc.).
People who mention specific shape representations (NURBS, volumes, triangles) are also a little confused. This is an orthogonal problem to ray trace vs rasterization. For example, you can ray trace nurbs directly, or you can dice the nurbs into triangles and trace them. You can directly rasterize triangles into a z-buffer, but you can also directly rasterize high-order parametric surfaces in scanline order (c.f. Lane/Carpenter/etc CACM 1980).

Answer 2

There's a technique called photon mapping that is actually quite similar to ray tracing, but provides various advantages in complex scenes. In fact, it's the only method (at least of which I know) that provides truly realistic (i.e. all the laws of optics are obeyed) rendering if done properly. It's a technique that's used sparingly as far as I know, since it's performance is hugely worse than even ray tracing (given that it effectively does the opposite and simulates the paths taken by photons from the light sources to the camera) - yet this is it's only disadvantage. It's certainly an interesting algorithm, though you're not going to see it in widescale use until well after ray tracing (if ever).

Answer 3

The Rendering article on Wikipedia covers various techniques.
Intro paragraph:
Many rendering algorithms have been
researched, and software used for
rendering may employ a number of
different techniques to obtain a final
image.
Tracing every ray of light in a scene
is impractical and would take an
enormous amount of time. Even tracing
a portion large enough to produce an
image takes an inordinate amount of
time if the sampling is not
intelligently restricted.
Therefore, four loose families of
more-efficient light transport
modelling techniques have emerged:
rasterisation, including scanline
rendering, geometrically projects
objects in the scene to an image
plane, without advanced optical
effects; ray casting considers the
scene as observed from a specific
point-of-view, calculating the
observed image based only on geometry
and very basic optical laws of
reflection intensity, and perhaps
using Monte Carlo techniques to reduce
artifacts; radiosity uses finite
element mathematics to simulate
diffuse spreading of light from
surfaces; and ray tracing is similar
to ray casting, but employs more
advanced optical simulation, and
usually uses Monte Carlo techniques to
obtain more realistic results at a
speed that is often orders of
magnitude slower.
Most advanced software combines two or
more of the techniques to obtain
good-enough results at reasonable
cost.
Another distinction is between image
order algorithms, which iterate over
pixels of the image plane, and object
order algorithms, which iterate over
objects in the scene. Generally object
order is more efficient, as there are
usually fewer objects in a scene than
pixels.
From those descriptions, only radiosity seems different in concept to me.