Just for funsies:
* What are some shadow-volume algorithms? When would you use shadow-volumes over shadow-maps?
'Shadow volume algorithms' is a bit ambiguous. In terms of shading calculation, I've looked into the bog-standard Crow 1977 paper and Forest's Penumbra Wedges idea, but it's not something I've really investigated much. (see later) In terms of masking you have the standard Z-pass and Z-fail/Carmack's Reverse.
Second part: In practice, never. Shadow maps are superior in pretty much every conceivable way these days. Filtering's better, you get free support for alpha-tested surfaces, you can amortize a lot of the cost over several frames, etc. Translucent surfaces can also receive shadow maps, too, which is something shadow volumes are flat-out incapable of. Point lights are a little more difficult to do, but there exist methods like dual-paraboloid and cube projection that can work pretty effectively.
Lastly, I figured out how F.E.A.R./F.E.A.R. 2 got such nice shadow edge transitions not that long ago. They actually apply a depth bias to the shadow boundary geometry so you don't get that ugly faceting artifact near silhouette edges. It's so unbelievably stupid, it's brilliant. If you must use shadow volumes, give that a whirl.
* What are some ways that you can filter shadow maps? What other techniques can you use to get better results from shadow-mapping?
This could probably be rephrased as 'how *can't* you filter shadow maps, and the answer is 'there aren't any ways'
Percentage-closer filtering is the oldest (I think) and works pretty well for the general case. Variance shadow maps and friends are rather popular these days, though I think exponential variance shadow maps in particular are the flavor of choice. Shadow maps for area lights seem to be pretty in vogue for CG research, and most of them seem to involve microfacet back-projection, though there are some more interesting VSM-like approaches I know of (the rather underutilized interpolation-friendly soft shadow maps seems promising, but I haven't yet got around to implementing it so I can't speak with total authority) Crytek's also experimented with using some sampling noise to get softer shadows for marginal performance cost, and this looks really good if you render the contribution into a God of War-style white buffer and blur it a bit. I won't tell if you won't ;)
Better's also a vague term. If you want to avoid acne, generating the shadow map by way of using backfaces for map generation works fairly well, as does using midpoint shadow maps (though the latter is a lot more expensive and is NOT compatible with all filtering methods, at least not to the extent that backface maps usually are)
Improving effective resolution also has scads of research. You've got perspective shadow maps, trapezoidal shadow maps, the irregular Z-buffer idea, adaptive shadow maps, cascaded shadow maps and the new, very promising adaptive shadow maps by way of rectilinear shadow map warping. That doesn't really even begin to scratch the surface.
* What are some techniques for rendering reflective materials?
Reflective in the sense of 'analytical lights' would mean your standard rogue's gallery of BRDF models. Image-based reflection is a little less broad in scope and is really constrained by the capabilities of your target hardware more than anything. You have your cubemaps, spheremaps, esoteric-projection maps and even some raytracing done in screen space if you want to get really fancy.
* How would you implement DOF on SM3? What about SM5?
Rendering budget would play a larger role in determining the algorithm(s) used rather than shader model, IMHO. Bokeh DOF by way of scads of billboards has been receiving some attention by Epic and friends, inelegant as it may be. While they make use of D3D10+ hardware features, I think you could probably cook up something pretty similar using vertex texture fetch/render to vertex buffer and point sprites on D3D9-equivalent feature levels. Probably wouldn't be as fast due to the rather inexpressive API, though.
If you want cheap and are doing bloom, you can also do things the Unreal Way™ and repurpose your bloom buffer. You don't get out-of-focus bleed, but if your game involves a lot of fast motion the artifacts probably won't be too noticeable. Infinity Ward also details some tricks to work around that problem that mostly involves blurring your circle of confusion, but that's not quite perfect either.
Also, if you want bokeh DOF but don't want to commit performance seppuku DICE details how to do a separable blur with a hexagonal shape. Whoever thought that up needs to get a pay hike; it's brilliant and involves decomposing the shape down into a series of skewed box blurs.
* Give an overview of how skinned meshes are drawn.
Animate bones, collect/weight influences, project to screen(?) This seems a little too easy.
Note that I don't include things like tangent transformation since there are some more modern bump mapping approaches (thinking primarily of Mikkelsen's stuff here) that don't actually need it. You could also use quaternions or even dual quaternions if you want to save some memory/interpolators and preserve volume across deformations, respectively.
* What's the difference between forward and deferred shading schemes?
Forward shading considers lighting as an object-space query, deferred shading opts for a more screen-space approach. There's so much futzing around with G-buffer design I don't consider going into detail about the various data designs useful due to their fluidity. I'm actually working on expanding some of the ideas behind light-indexed deferred rendering to try and get some of the best from both worlds.
* What are some different lighting models, and what's special about them?
Isotropic microfacet BRDFs like Phong/Blinn-Phong consider the surface to have lots of bits pointing every-which-way, and are a good fit for most surfaces.
Anisotropic BRDFs, like the Ashikmin-Shirley and Kajiya-Kay models, are designed to simulate the effects of surfaces where the little bits are instead usually facing along a single direction, and are practical for things like hair or brushed metal.
BSSRDFs are probably the most expressive/expensive, so you don't see them much in games, though there's some new research by d'Eon, Jimenez and Mikkelsen about efficiently implementing them on a GPU. (Blur kernels say hello) Eric Penner's got some really cool stuff that calculates the scattering ahead of time and examines the curvature of the surface to try and fit what you've got to what you precomputed. Hacky, but extremely fast and surprisingly effective.
I consider things like energy conservation to be subtopics of the above three items, and if you aren't paying attention to this, then your graphics programmer license is revoked until you do
In short, you'll need to adjust the approximate models like Blinn-Phong so that they reflect the amount of light they receive based on the properties of the surface, (tl; dr BRDF normalization) and for extra credit adjusting the diffuse reflection such that it only accounts for light that was NOT reflected based on the specular component of your shading model.
* What are the pros/cons of performing lighting in tangent space vs view or world space?
Precision reasons and being able to reuse tangent-space normal maps for different objects, though the latter is sort of a non-feature these days. World-space shading can also make handling scads of lights easier as there's less transforming to be done/interpolators that need to be used. Object-space shading (conspicuously absent, I note
) can end up being the best of both worlds, actually. Contrary to popular belief, it can also play nice with skinned meshes.
clb: At the end of 2012, the positions of jupiter, saturn, mercury, and deimos are aligned so as to cause a denormalized flush-to-zero bug when computing earth's gravitational force, slinging it to the sun.
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