11–20 of 86 posts
Fantastic article, exactly my kinda thing :) One significant limitation here is that the polygon needs to have constant colour, unfortunately.
Earlier quoted context omitted.
I've been looking into how viable this is as a performant strategy. If you have non-overlapping areas, then contributions to a single pixel can be made independently (since it is just the sum of contributions). The usual approach (computing coverage and blending into the color) is more constrained, where the operations need to be done in back-to-front order.
I've been researching this field for 20 years (I'm one of the developers of AmanithVG). Unfortunately, no matter how fast they are made, all the algorithms to analytically decompose areas involve a step to find intersections and therefore sweepline approaches that are difficult to parallelize and therefore must be done in CPU. However, we are working on it for the next AmanithVG rasterizer, so I'm keeping my eyes ope…
> This is equivalent to applying a box filter to the polygon, which is the simplest form of filtering. Am I the only one who has trouble understanding what is meant by this? What is the exact operation that's referred to here? I know box filters in the context of 2D image filtering and they're straightforward but the concept of applying them to shapes just doesn't make any sense to me. Can someone clarify?
Earlier quoted context omitted.
I've been looking into how viable this is as a performant strategy. If you have non-overlapping areas, then contributions to a single pixel can be made independently (since it is just the sum of contributions). The usual approach (computing coverage and blending into the color) is more constrained, where the operations need to be done in back-to-front order.
I've been researching this field for 20 years (I'm one of the developers of AmanithVG). Unfortunately, no matter how fast they are made, all the algorithms to analytically decompose areas involve a step to find intersections and therefore sweepline approaches that are difficult to parallelize and therefore must be done in CPU. However, we are working on it for the next AmanithVG rasterizer, so I'm keeping my eyes ope…
> This is equivalent to applying a box filter to the polygon, which is the simplest form of filtering. Am I the only one who has trouble understanding what is meant by this? What is the exact operation that's referred to here? I know box filters in the context of 2D image filtering and they're straightforward but the concept of applying them to shapes just doesn't make any sense to me. Can someone clarify?
It is more similar to the convolution of the shape with the filter (you can take the product of the filter, at various offsets, with the polygon) Essentially if you have a polygon function p(x,y) => { 1 if inside the polygon, otherwise 0 }, and a filter function f(x,y) centered at the origin, then you can evaluate the filter at any point x_0,y_0 with the double-integral / total sum of f(x-x_0,y-y_0)*p(x,y).
> This is equivalent to applying a box filter to the polygon, which is the simplest form of filtering. Am I the only one who has trouble understanding what is meant by this? What is the exact operation that's referred to here? I know box filters in the context of 2D image filtering and they're straightforward but the concept of applying them to shapes just doesn't make any sense to me. Can someone clarify?
It literally means that you take a box-shaped piece of the polygon, ie. the intersection of the polygon and a box (a square, in this case the size of one pixel). And do this for each pixel as they’re processed by the rasterizer. If you think of a polygon as a function from R^2 to {0, 1}, where every point inside the polygon maps to 1, then it’s just a signal that you can apply filters to.
Earlier quoted context omitted.
It literally means that you take a box-shaped piece of the polygon, ie. the intersection of the polygon and a box (a square, in this case the size of one pixel). And do this for each pixel as they’re processed by the rasterizer. If you think of a polygon as a function from R^2 to {0, 1}, where every point inside the polygon maps to 1, then it’s just a signal that you can apply filters to.
But as I understand it, the article is about rasterization, so if we filter after rasterization, the sampling has already happened, no? In other words: Isn't this about using the intersection of polygon x square instead of single sample per pixel rasterization?
I am quite convinced that if the goal is the best possible output quality, then the best approach is to analytically compute the non-overlapping areas of each polygon within each pixel. Resolving all contributions (areas) together in the same single pass for each pixel.
In the given example (periodic checkerboard), that would be impossible because the pixels that touch the horizon intersect an infinite amount of polygons.
Not that TFA solves that problem either. As far as I know the exact rendering of a periodic pattern in perspective is an open problem.
Fantastic article, exactly my kinda thing :) One significant limitation here is that the polygon needs to have constant colour, unfortunately.