Rendering Lecture 3 - Monte Carlo Integration I

This lecture belongs to the computer graphics rendering course at TU Wien. It starts with a recap of calculus and statistics. Then, we discuss how to generate samples from a custom PDF. And finally, we explain Monte Carlo Integration and importance sampling.

[vaniaduartes]

This has been the best tutorial and explanation I've ever seen about Monte Carlo. Thank you so much!

[gehtsiegarnixan]

Thanks so much for making this public. I'm coming from the Two Minute Papers Channel

[dhawals]

I think there is a typo at 32:30 in the integral where where c_x and c_y should be {\int}_{2}^{4}(2 v)dv, instead v dv is written in it.

[AinurEru]

29:22 The plot doesn't seem to match the code - it's plotting with X_i and Y_i as the coordinate-pairs of each dot. X_i is not being modulated in any way in the code, so the density of dots along the X axis should be uniform. Y_i is actually the coordinate that is being modulated, so the dots should appear on the plot with some varying density along the Y axis. Instead the plot shows the inverse of that.

[dhawals]

26:31 Can you point to a resource why there isn't much difference in the behavior of Sampling from the Exponential function vs the Finding inverse of CDF from the points obtained from Uniform Distribution? Or maybe a brief explanation would be nice

[AinurEru]

5:43 Shouldn't the first derivative be square root of x qubed instead of qube-root of x squared?