multidimensional vector rotation and angle computation -- how?

Posted by macias on Stack Overflow See other posts from Stack Overflow or by macias
Published on 2010-04-08T11:14:27Z Indexed on 2010/04/08 15:53 UTC
Read the original article Hit count: 296

Filed under:

math

|

rotation

|

vector

|

multidimensional

|

equation

Input: two multidimensional (for example dim=8) vectors a and b.

I need to find out the "directed" angle (0-2*Pi, not 0-Pi) between those vectors a and b. And if they are not parallel I need to rotate vector b in plane a,b by "directed" angle L. If they are parallel, plane does not matter, but angle of rotation is still the same L.

For 2d and 3d this is quite easy, but for more dimensions I am lost, I didn't find anything on google, and I prefer using some already proved&tested equations (avoiding errors introduced by my calculations :-D).

Thank you in advance for tips, links, etc.

Edit: dimension of the space is the same as dimension of the vectors.

© 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 rotation

Pygame surface rotation, rect rotation or sprite rotation?

as seen on Game Development - Search for 'Game Development'
i seem to have a conceptual misunderstanding of the surface and rect object in pygame. I currently observe these objects this way: Surface Just the loaded image rect the 'hard' representation of the ingame object (sprite). Used for simplifying object moment and collision detection sprite rect… >>> More
Need to translate a Rotation Matrix to Rotation y, x, z OpenGL & Jitter for 3D Game

as seen on Game Development - Search for 'Game Development'
I am using the Jitter Physics engine which gives a rotation matrix: M11 M12 M13 M21 M22 M23 M21 M32 M33 And I need it so OpenGL can use it for rotation GL.Rotate(xr, 1, 0, 0) GL.Rotate(yr, 0, 1, 0) GL.Rotate(zr, 0, 0, 1) Initially I Tried xr = M11 yr = M22 zr = M33 [1 0 0] [0 1 0] [0 0 1] Which… >>> More
Finetuning movement based on gradual rotation towards a target

as seen on Game Development - Search for 'Game Development'
I have an object which moves towards a target destination by gradually adjusting its facing while moving forwards. If the target destination is in a "blind spot", then the object is incapable of reaching it. This problem is ilustrated in the picture below. When the arrow is ordered to move to point… >>> More
2d movement solution

as seen on Game Development - Search for 'Game Development'
Hi! I'm making a simple top-down tank game on the ipad where the user controls the movement of the tank with the left "joystick" and the rotation of the turret with the right one. I've spent several hours just trying to get it to work decently but now I turn to the pros :) I have two referencial… >>> More
2d tank movement and turret solution

as seen on Game Development - Search for 'Game Development'
Hi! I'm making a simple top-down tank game on the ipad where the user controls the movement of the tank with the left "joystick" and the rotation of the turret with the right one. I've spent several hours just trying to get it to work decently but now I turn to the pros :) I have two referencial… >>> More