Sorry I was so terse! Let's ignore guard band, for now. Our rasterization surface is a rectangle. We don't need to "geometrically clip" a triangle to the rectangle's surface. Instead, we just walk the surface of the rectangle and ask two questions: (1) does the triangle capture this (sub)sample; and, (2) what's the interpolated value of the attributes at this (sub)sample. In practice, for software rasterizers, we're working on tiny subrectangles (the tile), e.g., 4x4 or 2x8, whatever. So, we can be a little "inefficient" with our walking with respect to the edge testing for interiority. (This is roughly how HW works at the 2x2 level, as well.) Because the (sub)sample is "pulling" the attribute, we don't need to geometrically "clip" the triangle to the tile: the tile's (x,y) subsamples do that "for free".
On the flip side, if a triangle is 'really big' we need a guard band to either reject or subdivide triangles. The first one is fairly cheap -- we're throwing away the triangle! -- the second one is a better user experience, but requires synthesizing primitives. (The worst case is that a single triangle becomes 5 triangles, I think.) Each of those triangles needs its Z and 1/Z calculated in fixed precision. The precision of that fixed precision (though) can be clamped to the local tile; so, even though the global precision might need to be 25.25 (or whatever), the tile-local precision is only 4.9 (or whatever), with an intermediate 24.24 that can be handled with a float-float patch-up. The computation should all occur in the triangle's barycentric space: that means you need the inverted barycentric mapping to invert the guard band into the triangle's barycentric space. You do that because it lets you control the fixed point calculations better. (You can leave off the inverted determinant multiplication until the last moment.)
When I say "deferred attribute synthesis" I mean that we don't calculate attributes in the vertex shader. Instead, we calculate the barycentric, Z, and 1/Z values and pass those along. When we fire up the tile walker for the triangle (in general we only need 1-3 tiles), we calculate the attributes "on the fly, as they're used" and then let the compiler do CSE to fold down the replicated constructions.
You only need to clip triangles is you're worried about attribute interpolation for very large triangles. There's two ways to handle this: (1) discard (fast but not a great user experience); or, (2) primitive synthesis. Just frustum clipping is enabled by point picking in the local tile. Primitive synthesis requires some FP kung fu; but, is easiest done in barycentric space against a reverse transformed clipping rectangle. This lets you carefully control clip rounding error using either doubles or (better) fixed point. Abrash likes to use integer fixed point, but that is historical — modern fixed point can be handled with careful control of the fp unit in the mantissa. The major issue is regenerating the Z and the 1/Z values for the new vertices of the synthesized primitives. Everything else should flow down the pipe naturally, assuming a deferred attribute synthesis rasterizer.
There are examples in the open source version of my rasterizer: OpenSWR.org.
I want to be able to take a conversation and ask for subconversations as red pen annotations "on the side". The linear nature of the context tends to frustrate this.
I'm no intelligence researcher or philosopher; but, I think LLMs make us confront the (IMO, now clear) distinction between cleverness (intuition), reasoning (rational argument), and consciousness. I suspect that we think of "intelligence" as either of the first two welded to the latter. In that vein, I'd say that consciousness may be just another emotion: happiness, sadness, egoness.
Races are virtually uncompetitive; it means politicians only need to pander to the 40% bloc of the 10–20% of voters that show up in the primary. Once elected, the chance of losing their office is nearly 0. Gerrymandering absolutely reduces effective voting power. That's the whole point.
This is why gerrymandering should be unconstitutional, and why corporations should have their rights explicitly curtailed: they're not citizens or the people.
I know your threw an "etc" in there; but, all fingers point to my home state: Texas. We need two legislative changes at the federal level: (1) uncap the house from 435 to at least cube-root or (better) max 500k; and, (2) you can't be sworn in unless your district was from an ICRC or statistically equivalent object.
I'm responding to a random comment: I was in molecular biology, but >20 years ago. Your article immediately presents as someone who's acquired reading expertise in a biological/medical subfield. Second, your initial survey presents as a "brittle x": AB is the proximal cause all by itself; but, it can also be the secondary cause from many vectors. Diseases like that are (essentially) impossible to explain to the public. Also, the biological principle function is a standard trope for "good for X in the short run, bad for the person in the long run".
A ten hour wait doesn't really strike me as a pancake? You should have a "it's 730am, there's four screaming girls, only two of which are related to me, the dogs are begging for scraps, and the demand for pancakes has crossed into Veblen goods territory."