And we'd like its plane to be roughly parallel to \$\triangle ABC\$, so we don't lose precision to a shallow oblique projection. Ideally we want to find a \$\triangle PMN\$ that's reasonably close to \$\triangle ABC\$ - otherwise when we do the subtractions we could get catastrophic cancellation that lowers our precision. If you continue this search to check all candidate \$P\$ vertices in your mesh, then it scales as \$O(n)\$, a major improvement over \$O(n^3)\$ checking every possible triangle.Īnd you can restrict this search to a subset of promising candidates \$P\$ for further savings. Choose the candidate with the least error. If you find multiple candidates, you can score them by computing the UVs each candidate triangle assigns to \$A\$, \$B\$, and \$C\$, and summing the squared error. If both check out, then you have a candidate \$\triangle PMN\$. M = M_0 t (P - P_0) \quad \textĬheck a small sphere or box around these points to see if you have a suitable vertex in your mesh. We can use that to find the positions where \$M\$ and \$N\$ would need to be: This forms our projection axis, the normal to the plane of \$\triangle PMN\$. If we don't have a good candidate there, then we can look at each candidate point P that's not in \$\triangle ABC\$'s plane.įor each such candidate \$P\$, take the vector \$P - P_0\$. If you already have a vertex in all three spots (maybe even the vertices of \$\triangle ABC\$ itself) then we can just use those and skip any wider search. We can use this as the starting point of our search for other \$\triangle PMN\$ candidates.įirst, check a small sphere or box around \$P_0\$, \$M_0\$, and \$N_0\$. My answer to the earlier question shows how to find a particular choice of \$\triangle PMN\$ in the plane of \$\triangle ABC\$ itself. Then we project that UV space along the normal perpendicular to the plane of \$\triangle PMN\$, onto \$\triangle ABC\$. Point \$N\$ corresponds to (u, v) = (0, 1).Point \$M\$ corresponds to (u, v) = (1, 0).Point \$P\$ corresponds to (u, v) = (0, 0). ![]() ![]() We define a 2D UV space using the \$PMN\$ points to form our origin and basis vectors: You can read the full text of the rules here.First, it's helpful to develop some geometric intuition about how this UV projection algorithm works. General discussion on Treasure Hunter and other MTX is allowed. Posts created with the sole intent to share rewards received from Treasure Hunter, Umbral Chests, or other microtransactions ("MTX") will be removed. Additionally, do not ask for charity or free items/gold/membership. We do not allow users to advertise, host or operate giveaways, competitions, or events which offer prizes for winners/participants. Do not advertise trades, giveaways, or ask for free items or cash. Instead of posting about it, check here for the official methods of contacting Jagex to resolve these issues.Ĩ. This includes, but is not limited to, bans, mutes, locks, hacks, billing, and rollbacks. The /r/runescape moderators, and the J-Mods who browse this subreddit, cannot help you with account issues. However, any post or comment that specifically names or links to bot or private server websites or software will be removed. General discussion on the topics of bots and private servers is permitted. Posting content and linking the source is perfectly fine, spamming it is not. Do not submit advertisements or clan recruitment posts.ĭo not submit posts which are solely for the purpose of promoting or advertising a content source, such as a YouTube channel, or clan recruitment. Call outs and witch hunts are not allowed.ĥ. Posts or comments which directly target, name, or harass players or groups of players will be removed. Attempting to annoy, troll, harass, or otherwise participate in bad faith will result in your content being removed. If a post is not directly related to RuneScape, it will be removed.ĭo not flame, troll, or harass users on this subreddit.
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