I really liked this particular slide. It stresses that once the system of equations has been set up, we're basically done, we just need to sit back and let the computer work its magic. With this as a motivation, it is really exciting to think about how easy it is to model, say, a liquid flow by using a flurry of particles, and solving said equations for each of them, so that when we put the solutions together, we can model even complex flows. Sweet!
keenan
once the system of equations has been set up, we're basically done, we just need to sit back and let the computer work its magic
Yes, exactly—numerical linear algebra is a powerful abstraction, which will get you very far. However, I would be misleading you if I said it was always easy! There are substantial challenges in modeling the problem (e.g., expressing it as a PDE), discretizing the equations (e.g., turning a differential equation into numerical linear algebra problem), and also often in doing geometric calculations to determine quantities that show up in these equations. But, we'll get there—that's what this class is all about!
hyperion
Sure, I agree. Thanks for the feedback! I do imagine that setting up the model must be a challenging task in and of itself, and the very fact that, say for example, the animation industry, seems to be coming up with more and more realistic and organic representations of entities (bodies or surfaces), points to the fact that this is still very much a work in progress.
sclaure
Adding on to the comments above, I would imagine that real world physical limitations prevent a perfect implementation of ideal modeling equations. One issue that comes to mind involves the IEEE floating point standards and how decimals are approximated instead of being perfectly represented. I imagine this would cause inconsistencies in the calculations involved in physics engines and animations (more specifically in collision detection). Either way, it is great to see all of the progress made in spite of these obstacles.
I really liked this particular slide. It stresses that once the system of equations has been set up, we're basically done, we just need to sit back and let the computer work its magic. With this as a motivation, it is really exciting to think about how easy it is to model, say, a liquid flow by using a flurry of particles, and solving said equations for each of them, so that when we put the solutions together, we can model even complex flows. Sweet!
Yes, exactly—numerical linear algebra is a powerful abstraction, which will get you very far. However, I would be misleading you if I said it was always easy! There are substantial challenges in modeling the problem (e.g., expressing it as a PDE), discretizing the equations (e.g., turning a differential equation into numerical linear algebra problem), and also often in doing geometric calculations to determine quantities that show up in these equations. But, we'll get there—that's what this class is all about!
Sure, I agree. Thanks for the feedback! I do imagine that setting up the model must be a challenging task in and of itself, and the very fact that, say for example, the animation industry, seems to be coming up with more and more realistic and organic representations of entities (bodies or surfaces), points to the fact that this is still very much a work in progress.
Adding on to the comments above, I would imagine that real world physical limitations prevent a perfect implementation of ideal modeling equations. One issue that comes to mind involves the IEEE floating point standards and how decimals are approximated instead of being perfectly represented. I imagine this would cause inconsistencies in the calculations involved in physics engines and animations (more specifically in collision detection). Either way, it is great to see all of the progress made in spite of these obstacles.