Why does paths determined by a sequence of random values in [0, 1]? Still don't quite understand this unit hypercube view.
qiqinl
Each value is the turning angle of the path. In 2D, with all turning angle determined and the fact that the camera position is fixed, the path is uniquely determined.
am1
I'm not too sure I understand the plot on the right. So the white is when we hit a window and black is everything else?
WJM
@am1 You are correct, the chart on the right is white when random variables ?1, ?2 relate to the traced ray hitting a window, black for walls. Each ? is the random variable used to determine the ? value of each bounce. Note: ?1, ?2: so only two bounces are being traced. The point of the right chart is to illustrate how we estimate the total brightness of the image (the integral of it).
(I think it would be worth placing the example (?1, ?2) in the white since the image on the left did hit a window).
WJM
@am1 you are correct, the plot on the right shows black for walls and white for windows (doors unknown).
The chart plots random variables: epsilon1 and epsilon2 (which relate to theta: the bounce angle) for the first and second bounce. (Only plotting two bounces). The point of having this chart is to show how you would estimate the total brightness of this image--the integral of the image. (Essentially this is showing an example where we are given the ray from the eye, and then considering possible 2-bounce results, too estimate the total brightness).
(It is worth noting that the point (epsilon1, epsilon2) should be in the white to match the image on the left).
Why does paths determined by a sequence of random values in [0, 1]? Still don't quite understand this unit hypercube view.
Each value is the turning angle of the path. In 2D, with all turning angle determined and the fact that the camera position is fixed, the path is uniquely determined.
I'm not too sure I understand the plot on the right. So the white is when we hit a window and black is everything else?
@am1 You are correct, the chart on the right is white when random variables ?1, ?2 relate to the traced ray hitting a window, black for walls. Each ? is the random variable used to determine the ? value of each bounce. Note: ?1, ?2: so only two bounces are being traced. The point of the right chart is to illustrate how we estimate the total brightness of the image (the integral of it).
(I think it would be worth placing the example (?1, ?2) in the white since the image on the left did hit a window).
@am1 you are correct, the plot on the right shows black for walls and white for windows (doors unknown).
The chart plots random variables: epsilon1 and epsilon2 (which relate to theta: the bounce angle) for the first and second bounce. (Only plotting two bounces). The point of having this chart is to show how you would estimate the total brightness of this image--the integral of the image. (Essentially this is showing an example where we are given the ray from the eye, and then considering possible 2-bounce results, too estimate the total brightness).
(It is worth noting that the point (epsilon1, epsilon2) should be in the white to match the image on the left).