What's Going On ant123 commented on slide_045 of Monte Carlo Ray Tracing ()

How do we decide what prr is Murrowow commented on slide_037 of Dynamics and Time Integration ()

How exactly is this better than forward/backward Euler? They seem similar enough that I find it hard to believe that one will produce a significantly better one over the other. Murrowow commented on slide_041 of Dynamics and Time Integration ()

Is this similar to aliasing where if the value you choose is too small/different, it would cause the values to be incorrect. jefftan commented on slide_011 of Numerical Integration ()

If these special weights are expensive to compute (for example if you need to compute square roots and division operations), might it be more computationally efficient to use a larger number of inexact sampling points that are easier to compute jefftan commented on slide_036 of Numerical Integration ()

Is there a better way to generalize rejection sampling to higher dimensional spheres? In 2D, pi * r^2 / (2r)^2 = pi/4 which is about 78.5% but in 3D, 4pi/3 * r^3 / (2r)^3 = pi/6 which is about 52.4% and I imagine it drops quite rapidly when you go up to 10D spheres jefftan commented on slide_044 of Partial Differential Equations ()

How different is it to solve the heat equation in a Lagrangian vs. Eulerian framework? I imagine in an Eulerian framework you could use a grid solver like you said in the slide, but in a Lagrangian framework the neighbors are in irregular positions which would require using a spatial data structure like a BVH or quadtree or something similar jefftan commented on slide_016 of Partial Differential Equations ()

Is there any geometric reason for why these equations are also called "elliptic", "parabolic", and "hyperbolic"? Like what does the wave equation have to do with a hyperbola? Mogician commented on slide_037 of Variance Reduction ()

Is there a mathematical explanation of the decreased variance? Mogician commented on slide_035 of Variance Reduction ()

This sounds to be biased. How can we decide the distribution density value of the chosen path? Mogician commented on slide_026 of Variance Reduction ()

After we switch our sample distribution, the biasness has not changed right? What about consistency? Mogician commented on slide_024 of Monte Carlo Ray Tracing ()

So we can combine as many distributions as we want into one distribution to do importance sampling? Mogician commented on slide_056 of The Rendering Equation ()

Does this scene looks darker because of loss of energy? Mogician commented on slide_027 of The Rendering Equation ()

The BRDF term looks quite abstract. Given any pair of direction, it produces a scalar. How would you store such a function? Mogician commented on slide_056 of Radiometry ()

Does radiometry related calculation always come with raytracing? Is there any practice to incorporate them into rasterization? Mogician commented on slide_051 of Radiometry ()

Does the "screen space" means this AO is not pre-baked but real-time calculated with information of screen space pixels? Mogician commented on slide_037 of Color ()

Is that possible to distinguish without measuring their physical properties between monochromatic colors and mixed colors? Mogician commented on slide_035 of Color ()

So are we sharing a fake commonsense of colors, and when we describe some color, we are actually talking about different perceptions or feelings? Mogician commented on slide_040 of Spatial Data Structures ()

Is the disadvantage compared to K-D Tree caused by inflexible division point decision? Mogician commented on slide_010 of Spatial Data Structures ()

Would bounding box not aligned to axis in some way performs better because of a tighter volume? How much is the benefit gain compared to the performance loss? superbluecat commented on slide_043 of Partial Differential Equations ()

Should the equivalent statement in 1D as 'two dirivatives are the same'? superbluecat commented on slide_036 of Partial Differential Equations ()

How to add boundary conditions to the linear system in the previous page? superbluecat commented on slide_028 of Optimization ()

Is it also necessary to optimize the positions of the joints, in addition to the IK we did in A4? superbluecat commented on slide_030 of Optimization ()

Can we view the calculation of p2 as a sequence of linear transformation, where (u0 + theta1 u1) is rotated as a whole by theta0? superbluecat commented on slide_037 of Dynamics and Time Integration ()

Is the backward euler evaluating the new velocity using next configuration? superbluecat commented on slide_034 of Dynamics and Time Integration ()

What do u stand for in this equation? BlueCat commented on slide_060 of Course Intro ()

This assignment is crazy. I am wondering why this picture's quality is much better than mine? How much samples are used in this result? spidey commented on slide_032 of Partial Differential Equations ()

How does the error play out in this method of approximating, as we are approximating twice would the errors compound? spidey commented on slide_024 of Partial Differential Equations ()

I understand how the Eulerian method would be calculated by just checking the flux at fixed locations but for the Lagrangian method, how would we keep track of all the moving particles and would that ever be efficient as supposed to the fixed locations? spidey commented on slide_020 of Optimization ()

What is the difference between strong and weak convexity and how does that affect how we can solve the problem? spidey commented on slide_008 of Optimization ()

Are more problems we deal with in computer graphics discrete or continuous? Is it better to leave a discrete problem as is or is converting it into a continuous problem better? spidey commented on slide_019 of Dynamics and Time Integration ()

How would we account for the error and collisions in such a large system of equations? spidey commented on slide_004 of Dynamics and Time Integration ()

Is the equation for animation actually this simple, how do other forces and changes in acceleration play a part in the animations? spidey commented on slide_051 of Intro to Animation ()

When animating for something big like a movie, do the animators do this individually for each character, or do common animation sequences like walking have a sort of template to work off of? spidey commented on slide_026 of Intro to Animation ()

What are some methods for generating inbetweens with a computer? How can we tell exactly how some parts are moving, for example the hook, in the keyframes to create the inbetweens? Bellala commented on slide_018 of Partial Differential Equations ()

How is this the same as laplace? Bellala commented on slide_034 of Partial Differential Equations ()

When is the numerical solution more preferable? Bellala commented on slide_024 of Optimization ()

how to look for local/global min and max in this situation Bellala commented on slide_030 of Optimization ()

Will FK and IK be in conflict with each other/form a cycle for one joint? Bellala commented on slide_023 of Dynamics and Time Integration ()

Other than particle based fluids, are there other algorithms/models for fluid simulation? Bellala commented on slide_030 of Dynamics and Time Integration ()

I heard that for curly hair, hair is simulated by the spring system. What would be the best physical system to simulate straight hair? Bellala commented on slide_018 of Intro to Animation ()

Does this use the similar algorithm with today's mesh? Bellala commented on slide_029 of Intro to Animation ()

Are there different principles for interpolations between keyframes? dshernan commented on slide_030 of Linear Algebra ()

What could be an inner product function for comparing images, like in the last slide? large_monkey commented on slide_035 of Partial Differential Equations ()

Are there substantial advantages in complexity when solving these problems on sparse matrices? My intuition is that some of the operations on sparse matrices (like finding eigenvalues) might not be easier than on dense matrices, but things like solving linear equations, for example, might be. large_monkey commented on slide_034 of Partial Differential Equations ()

This numerical solution (averaging with neighbors) seems to exhibit great parallelism; is there a usage where certain hardware could leverage this to make it more feasible? birb commented on slide_030 of Optimization ()

How practical is it to compute gradient descent every time someone is reaching for something for example? Are there quicker estimation algorithms? birb commented on slide_024 of Optimization ()

Is there a similar way to approach the problem when we need to find the global min/max instead of a local one? Is it practical to run this algorithm a bunch of times and take the min or max of all the local min/maxs found? corgo commented on slide_035 of Partial Differential Equations ()

It seems that this would be very costly in practice. Is there another alternative to store the sparse matrix information that is more efficient in terms of storage? L1TTLEM4N commented on slide_026 of Partial Differential Equations ()

By mixing the two methods, does that mean you would use the Lagrangian in some scenarios and Eulerian in others? L1TTLEM4N commented on slide_024 of Partial Differential Equations ()

Does the Eulerian take much less computing power in a scene with lots of particles since the variables that are stored are not dependent on the number of particles in the space?