Assignment 1 – Sampling
For this assignment I sampled a function over x and y and used the results as the brightness for the corresponding points in the image. The high frequency function used is: L(x, y) = ½ ( 1 + sin( (x^2 + y^2) / 100 ) ). The size of the picture I used was 512 X 384 pixels.
Each of the images is a thumb nail using only a fourth of the real image. I didn’t shrink the images to prevent more aliasing from occurring. To see the full image, click on the corresponding picture.
For the first Image I used one sample in the center to show the same aliasing affect seen in the notes. So the lower left corner uses x=0, y=0 and so on for the other pixels, incrementing one in x to the right and one in y upwards.
The next two are done using a box filter. The first one is done using 1 sample, so it’s really just one random sample taken over the entire pixel. The second image was done using 16 samples, so the image was divided up into 16 regions and one sample was taken randomly in each region of the pixel.
The next two pictures were done using a box filter, but this time with 128 and 512 samples. You’ll notice there isn’t much difference between the two, so this is the best that this filtering algorithm could do for aliasing on this function.
For these next images I used a tent filter, which takes samples from -1 to 1 with more samples taken towards zero. The image on the left was done with just random sampling and the image on the right was done with stratified sampling.
These last images were created by using a cubic spline filter. The cubic spline takes samples from pixels surrounding the current pixel just like the tent filter. The cubic filter takes samples from a larger area and also takes samples in a distribution pattern like what is visually displayed by a cubic basis function.