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Simulating drops of ink is probably one of the best applications of the Vorton Method. Unlike fluid solvers based on the velocity form of the Navier-Stokes equations, which track the density and velocity of a fluid, the Vorton Method tracks vorticity instead. It does so by simulating a large number of vortons, each carrying a small amount of vorticity; you ...


8

The notation $\delta_{i,j}$ is the Kronecker delta, a notation commonly used in physics. It's defined as: $$\delta_{i,j} \equiv \begin{cases}1,&i=j\\0,&i\neq j\end{cases}$$ So, as you suspected, it's essentially a shorthand for the identity matrix. The notation $\mathbf{S}_i \in \mathrm{R}^s$ means that each $\mathbf{S}_i$ is an $s$-dimensional ...


4

For rendering of gases, I think the usual approach is to simply render each particle as a tiny disc. Gases don't really coalesce into surfaces like liquids do, so this should produce acceptable results. You could perhaps apply a light blur over the gas layer afterwards to soften it and hide the fact that it is made of discrete elements. Liquids, on the ...


4

The shape you’re trying to draw is called a catenary: it’s the shape that a cable/cord of constant density takes when supported at each end. You’ll have to do some research to find a parametric equation for its shape—this page has a start, though it doesn’t let you substitute in the endpoints so you’ll need some additional work there. Once you have an ...


4

Yes, it looks like a sign error in the paper. It looks like it was introduced in equation (4) and then carried through the following ones. Probably the authors wrote the source code first and the paper after, so did not notice that their equations did not match what their code was doing. Ideally it should have been caught in the paper review, but, mistakes ...


3

user1118321's suggestion is the correct one but i'll elaborate a bit. You run your simulation giving it a fixed time step between frames. This time step would be 1/30th of a second (33.3333 ms) for instance if you wanted a 30 fps movie. You let your simulation calculations and your rendering run, taking as long as they need to, and then write the rendered ...


3

Baraff and Witkin propose to incorporate constraints by modifying the linear system by the constraints matrices $\mathbf S_i$. As they state in the beginning of Section 5.2, the resulting system is not symmetric anymore. Therefore, the modified linear system must be computed with a linear solver that can treat non-symmetric systems (as - if I got you ...


3

The curve you are seeking is just the intersection of a plane (the back of the camera) and a right circular cone. This is not really a question about the earth, or views of planets from space; it's just plain simple 3D coordinate geometry. To find a reference, I'd recommend searching for "intersection of a plane and a cone" or "plane section of a cone", or "...


3

Based on the comment of "ratchet freak" I researched Transform Feedback Buffers and solved my problem that way. I now generate the simulated points on the CPU and put them into a VertexBufferObject. I generate a second VBO for the points (along with some others for velocity). The connectivity of the cloth is given as an vertex-attribute in ivec4. Using the ...


2

From your code snippet and your result for 2x2 example, I can see that you are actually simulating a domain with only Neumann boundary conditions (slip wall). In this case, the system contains a null space and your matrix is singular. If this is the simulation configuration you want (i.e. no Dirichlet(pressure) BC), you will need to project out the null ...


2

Compare it with someone else's software. Run some standardized test and find out if you get roughly the same answer as others. If you get the same answer, than the probability of having your code right is quite high. Some tests: Flow past cylinder. In 2d take rectangular domain, cylinder in the middle, inflow on the left, outflow on the fight and calculate ...


2

As @AnnoyinC already mentioned in his comment, we are simply lacking computational power and storage requirements (RAM). For the visual effects, you need to calculate every ray of light that somehow ends up in the observer's eye after an arbitrary number of reflections on different surfaces. The reflections depend on the surface's microstructure. This alone ...


1

I found the problem. Maybe this answer helps someone since there isn't much discussion on the topic. I was doing the following change of coordinates in the frequency domain to fit the values on the 256x256 matrix: (n, m) = (x-N/2, y-N/2) where N, n and m appear in the ocean waves' paper and x, y are the coordinates of the matrix. Then I modified the change ...


1

Solution: Check for the minimum x,y,z value for all points. Add these values multiplied by (-1) to all points in order to guarantee that all points are not negative. Then take the largest point and subtract with the minimum point (max and minimum x y z) in order to get a cube-like bound for the object. Then divide this cube by an arbitrary size constant ...


1

There are a couple of companies doing middleware cloud simulation and rendering. It might have been SilverLining by Sundog, or trueSKY by Simul.


1

The rigid body simulation is very similar to the point mass case except for that we have to handle rotational motion (orientation and angular momentum). In addition to common particle attributes such as mass, position, and linear velocity, we will need to store initial moment of inertia $\mathbf{\hat{I}}$, current angular momentum $\mathbf{L}^n$, and ...


1

The damping force you mentioned $f=-k \frac{\dot{l} \cdot l}{|l|} \frac{l}{|l|}$ is a special case of $f=-k \dot{C} \frac{\partial C}{\partial \mathbf{x}}$. Let $$ \begin{align} C(\mathbf{x}) &= \lVert\mathbf{l}\rVert-l_0 \\ \mathbf{l} &= \mathbf{x}_1 - \mathbf{x}_2 \\ \mathbf{\dot{l}} &= \mathbf{v}_1 - \mathbf{v}_2 \\ \mathbf{v} &= \dot{\...


1

You could always write each frame out as an image and then use another tool to compress it into a movie that you playback. You don't say what type of system you're running on, but I believe that ffmpeg could do it for you, as it's a cross-platform tool. It's hard to estimate how long the compression will take since it will depend on the content you're ...


1

I use Nvidia OptiX for Ray casting and tracing purposes. It is based on CUDA and gives you a library that runs on GPU and is capable of building and traversing efficient acceleration structures. You just supply a few programs such as intersection tests and shading and OptiX does the rest. I personally think it is really easy to work with it but your milage ...


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