如何将 4D 坐标转换/投影为 3D 坐标
有很多漂亮的 4D 投影演示，展示了超立方体和其他奇妙的形状。我正在尝试对超正方体进行可视化，但在 google 上找不到任何明确描述所涉及数学的内容...
如何（最好用伪代码）将 4D 空间中的一个点投影到 3D 空间中？
提前致谢！
theres a lot of nice looking demonstrations of 4D projection showing tesseracts and other wonderful shapes. I'm trying to make a visualisation of a tesseract and I couldn't find anything explicitly describing the maths involved on google...
How (preferably in pseudo code) does one project a point in 4D space into 3D space?
thanks in advance!
如果你对这篇内容有疑问，欢迎到本站社区发帖提问 参与讨论，获取更多帮助，或者扫码二维码加入 Web 技术交流群。
绑定邮箱获取回复消息
由于您还没有绑定你的真实邮箱，如果其他用户或者作者回复了您的评论，将不能在第一时间通知您！
发布评论
评论（1）
直接的答案是：在 N 空间中定义一个 3D 矩形段作为视口和焦点，然后对于感兴趣的点向焦点发射光线，它们与视口（如果有）的交点是投影位置...
然而，出于可视化的目的，这可能不是最简单或最好的事情。您可以自由选择任意映射，并且您可能希望对高维对象施加某种对称性并以某种方式利用它（假设对象的 CM 必须位于原点，并且您将映射将前三个维度直接转换为 3 空间，然后将所得向量缩放到第四个维度（顺便说一句，不知道这是否看起来不错，但我认为这就是通常的牙签立方体立方体建模的结果一个超立方体））。
The straight ahead answer is: define a 3D rectangular segment in your N space to be the view-port and focus and then for points of interest shoot rays toward the focus, their intersection with the view-port (if any) is the projected location...
However for the purposes of a visualization this may not be the easiest or best thing to do. You have the freedom to choose an arbitrary mapping, and you may want to impose some kind of symmetry on the high dimensional object and take advantage of that somehow (say the CM of the object must be located at the origin, and you will map the first three dimensions directly into 3-space and then scale the resulting vector by the fourth dimension (no idea if this will look good, BTW, but I think that's what would result in the usual toothpick-cube-in-a-cube modeling of a tesseract)).