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1. EA Has Officially Ruined Dungeon Keeper !

there's something called keeperfx. it works quite well.
2. Linear wavelets

maybe Daubechies D4 wavelet would do the trick? http://en.wikipedia.org/wiki/Daubechies_wavelet#The_scaling_sequences_of_lowest_approximation_order

unless you are doing perfect portal clipping you can just use rectangular frustrum on every level. just calculate AABB of the resulting portal and go on with that.
4. Raytracer: Generating rays for importance sampling?

maybe you should try metropolis sampling.?
5. Clipping frustum to portal

few tips on implementing portals. 1) don't use 2d approach, doing it in 3d is easier and less messy 2) you will always get problems when camera is very close to portal, treat this case separately, for example give each portal bounding box that adds some space around portal, and when camera is inside box, render both cells on both sides of portal using original frustum 3) don't use near and far clipping planes for portal processing 4) do portal processing as follows: 1. check bounding box of portal, if invisible - done 2. check if camera is inside box , if it is, render cells on both sides of portal using original frustum 3. clip portal to 4 frustum planes 4. for each vertex of clipped portal find distances to frustum planes calculatr 't' for each vertex and pick minimum and maximum value of 't' for example if distances to horizontal clip planes are d1 and d2 t=d1/(d1+d2) - this tells you position left - right of vertex 5. shrink frustum using calculated t-min and t-max again if horizontal frustum planes are P1 and P2 P1' = P1*(1-tmin) - P2*tmin P2' = P2*(tmax-1)+P2*tmax 6. render stuff behind portal using new frustum' that way you will get new set of 4 clipping planes that project to rectangle on the screen and without all that 2d crap i hope it helps
6. [Help] Software Rasterizer - Rasterizing Triangles

did you check the file i posted?

8. Unusual usages of linear algebra

hmm could page rank algorithm used by google count as 'unusual use of linear algebra' ?
9. What is a good algorithm to test whether a triangle intersects cube

here is how i do it. 1. test box with triangles bounding box. if no intersection return 'false' 2. test box agains triangle plane. if no intersection return 'false' 3. perform 3 2d overlap tests in xy, yz, zx planes if no overlap of triangle projection with box projection is found in any plane return 'false' 4. return 'true' this thing is equivalent to minkowski sum method but can be coded a bit easier.
10. I don't believe that this is the smartest man in the world...

Quote:Original post by JoeCooper Sounds like the IQTest.com thing that gave me and my friends 170+ scores before offering to sell us a certificate. actually megatest was quite interesting, trully difficult problems to solve and normed using quite large group of people, also as far as i remember they allowed only single attempt (that's why he used fake names)
11. I don't believe that this is the smartest man in the world...

a little info. the IQ test on which langan claims to have scored so high is Mega Test. it's not professional test used by psychologists. also he took it multiple times using fake IDs until he got score he wanted. My silly conspiracy theory is that american creationists needed poster boy so they created one, and now they can say 'hey look smartest man in the world believes in our stuff, now bend over!' i mean, that guy isn't dumb, he is above average, but score he boasts about in media is pulled out of ass, if i were looking for a smartest man in the world i would start here http://www.math.ucla.edu/~tao/, maybe here http://en.wikipedia.org/wiki/Grigori_Perleman and probably here http://en.wikipedia.org/wiki/Andrew_Wiles