Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060128 07:48:07
3D AnglesThis may seem like a funny question but, I frequently use mathematics at my job and I have recently started working with 3D simulations. My question is, what exactly is meant by an angle in 3D? Say we have two vectors in a 3D coordinate system and we use the dot product method to figure out the angle between the two. Is this angle with respect to the xy, the xz, or is it some sort of average between the two? This simple concept is evasive to me for some reason. Thanks #2 20060128 23:49:45
Re: 3D AnglesIf you use the dot product to find this angle then this angle can be interpreted as the angle between them in the plane that they both lay on. #3 20060201 10:51:51
Re: 3D AnglesYes, I think it makes more sense. My interpretation of what you are saying is that it has nothing directly to do with the xy or xz, but more just a direct angle relationship between the two vectors in the plane that they both lay on. My knowledge of planes is limited. I am having difficulty comprehending planes in 3D and their relationship to vectors and math functions applied to them. To where as a simple projection from a point is quite simple using a bearing and magnitude in 2D, but when considering the 3rd dimension in 3D the whole game seems to change. #4 20060201 11:39:19
Re: 3D AnglesWhat I said before applies specifically to what you were talking about earlier. In other words, when dealing with the dot product of two vectors in x,y,z coordinates the angle between the two is only dealing with the angle between them. This angle is only related to their separation along their mutual plane. #5 20060202 04:27:48
Re: 3D AnglesThis sounds exactly what I was looking for. 2D angles only represent two coordinate systems. I did a little searching and reading and it looks like the steradian is a measure for a 3D angle by using an area of the surface of a sphere. (still not clear on it, but something like that) Thank you a bunch for the help. 