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Thanks, folks. That was all quite helpful. Given these unfortunate circumstances, it sounds like I'm better off prototyping with the Match3 mechanic. I do wonder: How did TetriNET get away with it? That game is still around and it's still free.

[color=#000000][font=Verdana, Helvetica, sansserif][size=3]I got an idea for a game that builds on top of Tetris. It will be pretty clear that it's not just a Tetris clone, and it's even more unlike Tetris than, say, Tetrinet (which is awesome!!). But, the influence will be obvious and a huge part of the game. So, should I expect any legal issues to arise if I might make some money off of this, or am I OK? Maybe I'm better off adopting the Match3 mechanic, which could work for my idea as well.[/size][/font][/color] [color=#000000][font=Verdana, Helvetica, sansserif][size=3]Also, what would be the legal implications of actually using "Tetris" or a part of that word in the title? Would I be forced to release it for free, etc.?[/size][/font][/color]

A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
UPDATE: I implemented a linear programming formulation (along with a Simplex solver in JavaScript..heh), and it works quite well! There are some issues which I need to investigate, but it's quite robust 90% of the time. I'll post some videos and some code soon if there is interest.. 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
Update: The problem has changed slightly. Instead of maximizing a square inside a cloud of points, now I have a set of planes (or oriented lines to use 2D terms) that restrict the square. And the cool thing is, it now becomes an instance of linear programming! The 3 variables are X and Y for the location of the center and L for the width/height of the square. Each plane defines four constraints, one for each corner. And our objective function is simply L. It's a fairly small problem with only 3 variables and probably 20 constraints tops, so I'm hoping this will be doable on a perframe basis when necessary. I'm gonna implement Simplex in JavaScript (heh) and see how it goes... 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
Sorry, should be max(abs(...)) up there again. 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
@clb  Ah yes, I think it would work then. It's essentially the same as splitting up the points into 4 diagonallydelineated regions, but the max(abs(...)) formulation is certainly cleaner The only ingredient missing from the solution is that the square should be allowed to move around, ie. it doesn't need to be centered at any point. So if it can shift up and get even larger, it should do that. I think this can be done using the following iteration:  Grow the square using the algo above for a single given center point, call it s0  Note which side is "touching" a point in s0, and "fix" it.  Repeat the algo above, except instead now pretend that you're growing a 1:2 aspect rectangle centered at the midpoint of the fixed edge. So, instead of min(abs(dx), abs(dy)), it'd be min( abs(dx), 2*abs(dy) ) if the bottom edge was fixed. And you would also ignore all points atandbelow the bottom edge. That's probably a bit confusing to just read...but I'll try implementing it soon and see how it goes. 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
@clb  wow thanks for taking the time to write that! Unfortunately I think it suffers from the same issue as I mentioned above: [quote name='stevesan' timestamp='1328805147' post='4911350'] Furthermore, unless I'm misunderstanding your suggestion, I don't see how that would work for my drawing here: http://www.makeitsha...om/drawing/8753 The minimum distance point from the red center would be the black point furthest to the right  it is closest to the center in the Y direction, and using that distance would make the square too small. I also assume you don't mean the Euclidian distance, as that would make the square too big. Am I misunderstanding? [/quote] 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
After some digging, it is [i]similar[/i] although not quite this problem here: [url="http://chaoxuprime.com/2011/02/anopenproblemaxisalignedrectanglepackingdensity"]http://chaoxuprime.com/2011/02/anopenproblemaxisalignedrectanglepackingdensity[/url] Humm...I hope this doesn't end up being some NPcomplete or highorder polynomial algorithm where I have to brute force it (ie. try placing edges at every point and enumerating..??)... 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
I don't need the square to actually be centered about the central point. So it should be allowed to move around, as long as it still [i]contains [/i]the central point. Furthermore, unless I'm misunderstanding your suggestion, I don't see how that would work for my drawing here: [url="http://www.makeitshareit.com/drawing/8753"]http://www.makeitsha...om/drawing/8753[/url] The minimum distance point from the red center would be the black point furthest to the right  it is closest to the center in the Y direction, and using that distance would make the square too small. I also assume you don't mean the Euclidian distance, as that would make the square too big. Am I misunderstanding? EDIT: Hmm I think for the fixedcenter case, you can split up the points into 4 regions delineated by the 2 diagonals of the square. So all points in the "top" and "bottom" regions, you consider their "grow distance" to be the Y distance to the center, and for the "left" and "right" region you consider it the X distance. Then, you can find the point with the minimum "grow distance" and use that as your halfwidth. Still thinking about the movable case..perhaps applying this iteratively would work... Thanks for taking the time to reply! 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
[quote name='jjd' timestamp='1328793072' post='4911282'] Does the box need to be axisaligned or oriented? [/quote] Yes, it needs to be axisaligned. Not sure if oriented would be any easier...? [quote name='Waterlimon' timestamp='1328796165' post='4911299'] Get the farthest point relative to the center point on both x and y axis and resize the rectangle to those values? [/quote] I need the square to NOT contain any of the points (except for the center one, to avoid the trivial solution where you just put the square outside the point cloud). 
A simple problem: Growing a square in a cloud of points
stevesan replied to stevesan's topic in Math and Physics
And in case you're curious, here's the [url="http://pupilgame.wordpress.com"]dev blog for the game[/url]. 
I've encountered a problem in a 2d game I'm working on right now that seems super simple, but I can't seem to find an optimal solution for it. I want to have a box that's as large as possible, which contains a single point (let's assume the middle) but does not contain any other points. [url="http://www.makeitshareit.com/drawing/8753"]A drawing here[/url] I need the solution to [i]keep it a square[/i], and while I don't need global optimality, I do need the edge to go right up to the points. Any thoughts? I haven't had much sleep..so maybe my brain just isn't working and it's actually a really easy problem...

State of the Art in rendering massively detailed geometry?
stevesan replied to stevesan's topic in Graphics and GPU Programming
[quote name='sk8beast' timestamp='1310688337' post='4835490'] [quote name='CirdanValen' timestamp='1310670957' post='4835392'] I recall seeing a video where someone was able to do what you describe by basically culling out the interior of the building when the player is too far away to notice, and as they get closer it will make the windows transparent and allow the user to see within the building. I doubt I will be able to find it tho [/quote] "Interior mapping"? [/quote] It's a geometry shader trick that gets some cool looking results. Google it 
State of the Art in rendering massively detailed geometry?
stevesan posted a topic in Graphics and GPU Programming
I know plenty of work on rendering terrain, but what about general 3D geometry? Do we have the technology to render stuff like this: [img]http://img2.chinatraveldepotstatic.com/Bossimages//packageimages/PicDisplay/20090511/34a535420ea2499fb0dfe14e10b1647c.jpg[/img] ..and also allow the player to fly to and enter one of those buildings? What's the closest we can get to achieving that? 
Existing vehicle damage tech?
stevesan replied to GraphicsDude's topic in Graphics and GPU Programming
I have no real experience with this, so consider this just an educated guess based on the Blur slides: The "morph target" is just an artist's modeling of a fully banged up car. The "damage volume" is a very lowres, crude FEM simulation of some overall volumepreserving material with plasticity. Each cell in your damage volume is assigned to a part of the car model, and as a cell loses volume, you blend into the morph target. You also blend into dent/crunch textures for further effects. Maybe you also deform the geometry a little using the damage volume as a deformer using meanvalue coordinates? All sorts of things you could do for some cool effects.