Our next topic is Dynamic Illustrations. And the work we introduce here, is called sketch-based dynamic illustration of fluid systems. And the problem we want to address here, is that it is tedious to illustrate fluid flow. Suppose you have a engineering system or architecture. Or organic shapes or a river system. There is a lot of fluid systems, and you may want to describe how the fluid flow in these kind of systems. And then you want to get these kinds of results. And it's very tedious to draw them manually. So, our idea is to use automatic flow simulation to automatically synthesize this kind of detailed flow illustrations. So here, the simulation is not used for prediction, but this is used for enrich your illustration. So let me show you a video [BLANK_AUDIO] So this is basically a drawing system. You draw something, and the system continuously runs fluid simulation behind the scene. And they add fluid flow visualizations automatically. So you draw something, a region. And then you draw pipes. And then as soon as you finish drawing a system, system starts flow simulation behind the scene. So it visualize a, a detailed flow, and also shows the result of fluid mixtures. [BLANK_AUDIO] So this tool is very useful for explaining fluid phenomenons. [BLANK_AUDIO] So you can interactively edit the shape by deformation tools. [BLANK_AUDIO] Okay. So an, our motivating example is here [BLANK_AUDIO] So here we use these two for explaining surgical operations for a defected heart. So here is an example. So here this heart has very specific configuration. And not very ideal. And here ideally blue blood come from the body, should directly go to the lung, and then from the lung, fresh blood, red blood comes into the heart, and then red one should go to the body in red, however here blue blood is mixed together with red one. And then purple one go to the body. So, doctors will perform a surgical operation to fix this. However, before that, they need to explain what they do to their patients, or their patients' parents. However, it's very difficult to describe this with standard tools, currently, they use standard pen and ink, Black and white illustration to describe them, however, it's very difficult to understand it. But preparing this kind of beautiful illustration using computer system, is too time consuming, and more importantly, this kind of heart disease has different configuration for each patient, so it's not possible to prepare a template beforehand. So, this kind of tool can be very useful. To explain and understand complicated flow phenomenon. And then let me show you how it works. So first, the operation start with connecting the locations, and then they will change the configuration here. So doctor cuts here and then connect them. So, as soon as the configuration changes, the fluid simulation changes the flow prediction. [BLANK_AUDIO] So next one is the most important one. The doctor stops here, cut here, and then connect here. And then, blood flow suddenly changes. [BLANK_AUDIO] And finally, closing this hole and then let blood directly go to the body, in red. [BLANK_AUDIO] And this kind of technique can be very useful for various fluid phenomena inside of your body, like blood circulation and others. [BLANK_AUDIO] And also this technique is, can be used for engineering systems. Like this one. [BLANK_AUDIO] And this is another example in architecture so you can see how cold air and let- warm air mix together and flow. And you can test many different configurations. [BLANK_AUDIO] And this tool can be also used for, for explanation of pollution of rivers, and so. And so now let me describe the algorithm briefly. So what we use is a hybrid fluid simulation system. So user draws a global network with local regions. And we apply different simulation algorithm for different scale. Because single scale simulation can be very slow. So, for global network simulation, we use simple hydraulic simulation. And then for individual local region, we use hydrodynamic simulations. And so, the user specifies a node inflow, and then from the global network structure, hydraulics compute each pipe flow and then node pressure, and then from this node pipe flow and node pressure, hydrodynamics computes a detailed, computes detailed flow, inside of each region. So this is a little bit in too involved, but let me describe the way. The first one is hydraulics simulation for a global network. Here, input is node inflow Qn, so how much flow comes in from the node. And then what we compute is pipe flow from node inflow. And hydraulics is a simplified computational method directly computed from compute from node inflow, and to get a pipe flow. And after pipe flow, we can compute a pressure, pressure drop at each pipe. And then from pipe pressure drop, we can compute the node pressure inside of each node. And you can get these all information by solving a linear global system once. It's very fast and it's very efficient. And after computing pressure node, and pre- pipe flow, we now switch to the regional details. So for each local region. We compute, we divide into a lots of grid cells like this one, and for each grid cell, we compute pressure and velocity, and in order to compute individual pressure and velocity, we use a very standard established fluid equation called Navier-Stokes Equation. So this one is a little bit complicated, but essentially this just explains the relationship with fluid velocity and fluid pressure, you know, if there's a huge difference in fluid pressure, and it causes velocity, and so. And this step basically just solved this equation times step, each time step on this grid cells inside each region, to get an animation. So the original paper was published as Sketch-based Dynamic Illustration of Fluid Systems. And if you learn more about fluid Simulation, I recommend you to read some text books. One example is Fluid Simulation for Computer Graphics by Bridson. And this work is an example of illustrative animation for facilitating understanding. And interesting early dated work is, MathPad, which takes mathematical written expression, and they automatically generates animation, based on the mathematical expression. So that's, this is the end of our second week of this Interactive Computer Graphics course. We described dia- diagram beautification. And Pen-and-Ink Texture synthesis, shape manipulation, and also dynamic illustration with a fluid simulation. Thank you.
