![]() ![]() It’s a different type of projection than spatial without this kind of depth mapping, in that the layers which would normally be hidden due to being obfuscated by other surfaces could still be made visible. You’d be able to “see” the 3D projection even strictly within a 2D space. ![]() Giving more color and saturation to something that has a greater volume. ![]() For example, I could see projecting 3D onto 2D by perhaps having a depth map projected onto the 2D surface by colorization. I’m not sure how though, just an intuitive hunch while watching your videos. It seems to me that we should be able to project 4D onto 3D by the use of color or possibly even space-warping somehow. In n-dimensional space, we actually have extra dimensions (they are not spatial though) due to sensory input. – reach out to friends and us random internet fans if you ever need to bounce thoughts off us, whether about Miegakure or otherwise (don’t let that monumental project weigh on you alone, that’s too much pressure / expectation)įorgive my potential ignorance, but is there a way that the 4th dimension could be projected onto the third dimension, similar to how we project 3-dimensions onto 2d space? – get exercise and eat fruits and vegetables – stay careful and safe during the Covid pandemic derivation of the double reflection formula and history. We don’t expect you to do all things, especially when Miegakure alone is a lifetime achievement award already.Īnyway, yours was one of the gentlest and most accessible introductions, and I appreciate especially all the detail in the “Asides” where needed, e.g. I don’t know how someone like 3Blue1Brown dude can keep up with life, work, and such a video production schedule as what he has, because it is clear putting together such a video (and accompanying article, and fancy interactive widgets) is an entire project in itself. Speaking of which, thank you immensely for doing the video on GA and rotors! SO many seemingly contrived concepts like determinants and cross products suddenly have a natural and visual motivation. You can follow any responses to this entry through the RSS 2.0 feed.īoth comments and pings are currently closed.Ģ5 Responses to “SIGGRAPH 2020 Technical Paper: N-Dimensional Rigid Body Dynamics” On Thursday, May 7th, 2020 at 6:04 pm and is filed under 4D Toys, Mathematics, Miegakure, Tech. Many thanks to them for helping me greatly improve the paper. Most of this work (including writing the paper) is from ~2012, but I added a section on the (4D) Dzhanibekov effect at the suggestion of the reviewers. One reviewer called the work “whimsical,” and they’re not wrong, ahah. ![]() The paper is full of really fun and beautiful math (obviously Geometric Algebra based, see my recent article) that makes me happy. I allow the user to manipulate these bodies in real-time.ītw I believe it is basically unheard of to have work from an indie game presented in the SIGGRAPH technical papers track? I display these four-dimensional rigid bodies by taking a three-dimensional slice through them. My implementation is 4D, but the techniques described here apply to any number of dimensions. Using collision detection algorithms extended to nD I resolve collisions and contact between bodies. I describe the state and equations of motion of rigid bodies using geometric algebra. I present a formulation for Rigid Body Dynamics that is independent of the dimension of the space. Here is the link to the paper and the abstract: Excited to announce that my technical paper “ N-Dimensional Rigid Body Dynamics” was accepted to SIGGRAPH 2020! Very proud to present research developed for 4D Toys & Miegakure at such a prestigious conference. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |