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Lemke's algorithm runtime complexity
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I'm trying to figure out the runtime complexity of Lemke's algorithm for solving linear complementarity problems (LCPs). I've got a simple implementation going from the paper Linear Complementarity and Mathematical (Non-linear) Programming.
In ge... |
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Posted December 31, 2010 5:20:50 PM
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2D vector graphics using shaders
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I'm working on a 2D vector graphics engine that will (hopefully) draw anti-aliased circles, quads, and bezier curves using pixel shaders. So vertex-wise everything is a quad. So for a circle, the pixel shader just checks to see how much of the... |
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Posted November 12, 2010 6:09:51 PM
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Area of overlap of parallelogram and square
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I have a parallelogram, for which I have the "half width" vectors (that is, this was a unit square that has had an arbitrary affine transformation applied to it). I have another square, which we can arbitrarily say is the axis aligned unit square.
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Posted November 16, 2010 1:33:37 PM
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Pixel coordinates
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When a pixel is rasterized to be sent to the pixel shader, are the coordinates of the pixel in the top left corner, the center, or some other corner? Does it depend on any flags or options?
That is, given a pixel at (4, 5), is the pixel's bo... |
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Posted November 11, 2010 7:20:34 PM
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Mapping animation skeletons
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Suppose I have a high-res skeleton (say, the display mesh) and a low-res skeleton (say, a ragdoll), and I want to map between them. I basically want to build up a bi-directional mapping of which bones in the low res skeleton correspond to which bone... |
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Posted November 9, 2010 6:37:40 PM
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Jacobian + QR decomposition
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I'm hoping someone can show me why I can't do the following:
Given a constraint Jacobian "J", where each row in the Jacobian is a different constraint.
Also given a diagonal mass Matrix M where the diagonal entries are mass and moment of inerti... |
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Posted May 17, 2010 12:47:52 AM
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LaTeX - math equations support?
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Could LaTeX support be added to the forums? Especially the math forum; it becomes a real pain to try and present complex math using ascii. |
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Posted June 4, 2009 11:03:06 PM
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Recentering polynomials
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Suppose I have a polynomial with real coefficients. I want to bound the roots of it. My goal is to do so using Cauchy bounds.
Which is basically: assuming the first coefficient of the polynomial is 1 (so: x^3 instead of 20 x^3), the absolute val... |
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Posted December 17, 2009 8:53:11 PM
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Offloading multiple-frame calculations to GPU
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Suppose I have some crazy large computations that I expect to take several seconds, even with the GPU's raw horsepower. I can do it on the CPU as a background thread of some sort. But the CPU can only really manage something in the ~1-10... |
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Posted December 10, 2009 6:36:04 PM
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Responsive UI programming
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I have a CPU heavy task that needs doing in a UI app. I want to provide a visual feedback to the user of how close the task is to completion, and still respond properly to normal events during that time.
This is the code I want to write:
pri... |
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Posted December 10, 2009 1:53:28 AM
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| Some recent replies made on our forums |
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Looking for a good book - Collision, Physics
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Hecker's Rigid Body articles are a good first step. Not all the links in that thread are thesis. Some are quite basic. |
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Posted January 2, 2011 7:20:52 PM
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Looking for a good book - Collision, Physics
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This not doing it for you? It's stickied right at the top of the forum.
If you're looking for an actual hard bound book, there's also Game Physics by David Eberly. I'm not sure I'd categorize it as "introductory" though. |
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Posted January 2, 2011 5:04:23 PM
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random number generation based on time in HLSL
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You might be able to leverage noise. Though that's not really suited for that purpose.
Any actually good random number generator is going to burn through too much instruction count to be of any good.
You can also write a bunch of random number... |
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Posted January 2, 2011 4:59:51 PM
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Optimization library
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You can turn a constrained LLS problem into a linear complementarity problem. See Linear least squares and quadratic programming. Basically you solve the unconstrained LLS problem first, then formulate the error into a LCP.
Once in LCP form, you... |
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Posted January 1, 2011 2:18:49 PM
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Multiple contact points in rigid body dynamics
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You'll get a system of equations, where each equation is one of the contacts taken in isolation. You'd solve for all contacts simultaneously, or solve them all sequentially a few times (an "iterative" solution) and hope the result converges to... |
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Posted December 31, 2010 6:01:39 PM
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Modeling stellar orbits
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The issue is that when you numerically integrate the motion (ie: when you turn acceleration into velocity into changes in position), there's some error involved. The tiny bit of error either adds or removes a bit of energy from the system, and the r... |
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Posted November 16, 2010 1:52:02 PM
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2D vector graphics using shaders
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Quote:Original post by apatriarca
But, how much translucent overlapping objects do you want to support? Have you verified this is actually a problem?
For things like circles, I'm basically creating a procedural texture in the pixel shader. So ju... |
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Posted November 15, 2010 1:35:33 PM
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2D vector graphics using shaders
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Quote:Original post by Relfos
I don't see a better way, if you want alpha blending and zsorting.
Actually I only care about alpha blending. I have to sort all the quads anyway, and go back to front to prevent artifacts, so I can't use the... |
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Posted November 14, 2010 2:45:30 PM
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2D vector graphics using shaders
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Quote:Original post by Relfos
Why don't you use just one shader for everything? This way you can batch draw calls easily, pass the 'shape' type as a uniform to the shader.
Quote:Original post by Numsgil
Which would seem to imply I need to w... |
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Posted November 13, 2010 4:00:47 PM
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2D vector graphics using shaders
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Depends how 'large' large is.
Let's take something simple like an eye:
You have a circle for the eyeball itself. You have a circle for the iris. You have a circle for the pupil. And you have a circle for the light shine. And maybe another e... |
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Posted November 13, 2010 1:05:52 PM
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View All Replies Made By This User
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