Maths: Determining angle in 3D space

Posted by 742 on Stack Overflow See other posts from Stack Overflow or by 742
Published on 2010-06-17T19:44:38Z Indexed on 2010/06/17 19:53 UTC
Read the original article Hit count: 330

Filed under:

math

|

3dgraphics

|

euler-angles

I hope this is the proper location to ask this question which is the same as this one, but expressed as pure math instead of graphically (at least I hope I translated the problem to math correctly).

Considering:

two vectors that are orthogonal: Up (ux, uy, uz) and Look (lx, ly, lz)
a plane P which is perpendicular to Look (hence including Up)
Y1 which is the projection of Y (vertical axis) along Look onto P

Question: what is the value of the angle between Y1 and Up?

As mathematicians will agree, this is a very basic question, but I've been scratching my head on walls now for at least two weeks without being able to visualize the solution... maybe now too old for finding solutions to school exercises.

I'm looking for the scalar trigonometric solution, not a solution using a matrix. Thanks.

© Stack Overflow or respective owner

Related posts about math

how to make a function recursive

as seen on Stack Overflow - Search for 'Stack Overflow'
i have this huge function and i am wondering how to make it recursive. i have the base case which should never come true, so it should always go to else and keep calling itself with the variable t increases. any help would be great thanks def draw(x, y, t, planets): if 'Satellites' in planets["Moon"]: … >>> More
Sunrise / set calculations

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm trying to calculate the sunset / rise times using python based on the link provided below. My results done through excel and python do not match the real values. Any ideas on what I could be doing wrong? My Excel sheet can be found under .. http://transpotools.com/sun_time.xls # Created on… >>> More
Android-Java: Constructing a triangle based on Coordinates on a map and your bearing

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi Guys, I'm constructing a geolocation based application and I'm trying to figure out a way to make my application realise when a user is facing the direction of the given location (a particular long / lat co-ord). I've got the math figured, I just have the triangle to construct. //UPDATE So… >>> More
Math.max and Math.min outputting highest and lowest values allowed

as seen on Stack Overflow - Search for 'Stack Overflow'
so I'm trying to make a program that will output the sum, average, and smallest and largest values. I have everything basically figured out except the smallest and largest values are outputting 2147483647 and -2147483647, which I believe are the absolute smallest and largest values that Java will… >>> More
Is Programming == Math?

as seen on Stack Overflow - Search for 'Stack Overflow'
I've heard many times that all programming is really a subset of math. Some suggest that OO, at its roots, is mathematically based. I don't get the connection. Aside from some obvious examples: using induction to prove a recursive algorithm formal correctness proofs functional languages lambda calculus asymptotic… >>> More

Related posts about 3dgraphics

Using 3D photos in silverlight?

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi all. I want use photos captured by 3D cameras in Silverlight 3 or 4. I want use that photos like in maps.google.com. Is it possible to do with silverlight and if yes is there any book, tutorial, video or anything alse, from which I can learn how to use tham. Thanks. >>> More
Calculate volume based on STL file

as seen on Stack Overflow - Search for 'Stack Overflow'
Just wondering if anyone had a simple, efficient way of calculating the volume of a stereolithographic file (STL)? And rendering this in a Windows Form Control? >>> More
Debugging a working program on Mathematica 5 with Mathematica 7

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi everybody, I'm currently reading the Mathematica Guidebooks for Programming and I was trying to work out one of the very first program of the book. Basically, when I run the following program: Plot3D[{Re[Exp[1/(x + I y)]]}, {x, -0.02, 0.022}, {y, -0.04, 0.042}, PlotRange -> {-1, 8}, PlotPoints… >>> More
Introduction to 3D Graphics Programming

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi everyone! I'm a self-taught programmer with absolutely nil 3D programming experience. A client of mine has related to me an idea for an iPhone app that requires OpenGL ES 2.0 for it's inherently complex 3D structure and animations. Where do I start on this ( albeit long ) journey toward OpenGL… >>> More
Getting started with OpenGL

as seen on Stack Overflow - Search for 'Stack Overflow'
As you can see here I'm about to start work on a 3d project for class. Do you have any useful resources/websites/tips/etc. on someone getting started with OpenGL for the first time? The project will be in C++ and accessing OpenGL via GLUT. Thanks! >>> More