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Fun fact. Take 4 points representing the vertices of a tetrahedron. Put them in a 4x4 matrix, using 1 as the 4th element then invert the matrix. The 4 row vecto
by phkahler 3y ago
Fun fact. Take 4 points representing the vertices of a tetrahedron. Put them in a 4x4 matrix, using 1 as the 4th element then invert the matrix. The 4 row vectors of the result will be the coefficients for the plane equations of the faces of the tetrahedron.
They'll be scaled such that the point not on a plane will evaluate to 1 when plugged into the equation. You can see this easily because multiplying the planes matrix by the points matrix is just plugging each of the 4 points into each of the 4 plane equations, and you get the identity matrix by definition.
- nbcomplete 3y ago[flagged]
- radarsat1 3y agoEven though it's well intended, I feel like pasting in responses from ChatGPT should be against HN guidelines, if it's not yet. Reason is, if I want that type of explanation, I can go and get it myself. I come here for people's personal comments, not to read them regurgitate what they had an LLM generate. And I use ChatGPT all the time so don't get me wrong, I just think it doesn't add a lot to the discussion here and takes up a lot of room.
- Terr_ 3y agoI'm torn on this, because I don't want to have LLM stuff gunking everything up either, but I think there's a general case to be made for comments like: "For anyone who is confused about X like I was, I found this explanation." In other words, how would one exclude LLM regurgitation but permit Wikipedia quotes?
- amelius 3y agoAsk the LLM to cite a source, then use that.
- deleted 3y ago[deleted]
- robswc 3y agoI agree on principal and instinct... but then I realize how often people add quotes from Wikipedia or 1st or 2nd results from a google search. Maybe most of the bad vibe comes from the "wall of text" and "tone" ChatGPT outputs.
- radarsat1 3y agoAgreed.
- thechao 3y ago> They'll be scaled such that the point not on a plane will evaluate to 1 when plugged into the equation. Evaluating a plane equation with a point will give a signed distance from the point to the plane. However, unless the equation is normalized, the distance could be scaled in unusual ways that are less than useful. I think a better way to say this is that a point who's shortest straight line distance to the line is 1 will evaluate to 1, after taking the absolute value. The LRBni ISA had a whole set of instructions designed to take advantage of signed distance fields defined in both plane equation & barycentric forms. (That's what the bit mask for the lanes was for, in part.)
- a1369209993 3y ago> However, unless the equation is normalized, the distance could be scaled in unusual ways that are less than useful. > > []the[] point not on a plane will evaluate to 1 They mean the vertex (of the tetrahedron). The signed distance function is scaled such that the (single remaining) vertex that isn't at distance 0 (by construction) will instead be at distance 1. So the distance is always scaled in a unique well-defined way (assuming not all four points are coplanar). Whether that way of scaling is useful depends on your use case, of course.