Skip to main content

Converting a rotation matrix to a quaternion


I found a very good link about quaternions in Mathematica , but I don't know how to create a quaternion from a rotation matrix. Can anyone help me, please?


Update


I need this:




A rotation may be converted back to a quaternion through the use of the following algorithm. The process is performed in the following stages, which are as follows:


Calculate the trace of the matrix T from the equation:



  T = 4 - 4x^2  - 4y^2  - 4z^2
    = 4( 1 - x^2  - y^2  - z^2 )
    = mat[0] + mat[5] + mat[10] + 1


If the trace of the matrix is greater than zero, then perform an "instant" calculation.




  S = 0.5 / sqrt(T)
  W = 0.25 / S
  X = ( mat[9] - mat[6] ) * S
  Y = ( mat[2] - mat[8] ) * S
  Z = ( mat[4] - mat[1] ) * S


If the trace of the matrix is less than or equal to zero then identify which major diagonal element has the greatest value.


Depending on this value, calculate the following:


Column 0:




    S  = sqrt( 1.0 + mr[0] - mr[5] - mr[10] ) * 2;
    Qx = 0.5 / S;
    Qy = (mr[1] + mr[4] ) / S;
    Qz = (mr[2] + mr[8] ) / S;
    Qw = (mr[6] + mr[9] ) / S;


Column 1:




    S  = sqrt( 1.0 + mr[5] - mr[0] - mr[10] ) * 2;
    Qx = (mr[1] + mr[4] ) / S;
    Qy = 0.5 / S;
    Qz = (mr[6] + mr[9] ) / S;
    Qw = (mr[2] + mr[8] ) / S;


Column 2:



    S  = sqrt( 1.0 + mr[10] - mr[0] - mr[5] ) * 2;

    Qx = (mr[2] + mr[8] ) / S;
    Qy = (mr[6] + mr[9] ) / S;
    Qz = 0.5 / S;
    Qw = (mr[1] + mr[4] ) / S;


The quaternion is then defined as:



   Q = | Qx Qy Qz Qw |


Comments

Post a Comment

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more