I do have this working now using the Eigen library and it is pretty fast. Let me know if anyone would like the c++ code posted.
I think I am still unsure about calculating the distance between P and pi, P and B, and pi and B. Normally I would just take the vector between each pair of points and...
Hello Again,
If I have point B in an orthogonal n-space and point C at the origin of the same space,
point_B = 0.03299720 0.00585822 -0.36979000 -0.43413200 -0.60787700 0.61335300 0.76003400
point_C = 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000...
I have been trying to code this up with the Eigen library but I seem to be misunderstanding the order of operations.
This expression,
$$ (M^TM)^{-1}M^T \mathbf v_3% $$
seems to involve either the product,
$$ ( (M^TM)^{-1}*M^T )* \mathbf v_3% $$
or the product,
$$ (M^TM)^{-1}*(M^T* \mathbf v_3)%...
So Octave will automatically evaluate M \ v3' with an inverse, pseudo inverse, or possibly some other appropriate solver, depending on what is efficient/possible based on the properties of M? Does Octave have a verbose output format that might explain more completely what it has done for a...
Hello Again,
I am in the process of writing this algorithm into c++ code to test and I have another question.
I have taken the transpose of the three vector matrix v1, v2, v (M=[v1' v2' v'])
B=[ -0.0700177 0.382249 -0.289338 0.00349957 ];
A=[ 1.13388 1.77602 -0.679365 -0.729256 ]...
Thanks for the explanations. I am going to code this up and see what results I can get but I have a few more clarification questions.
I am not sure what the single quote means in the Octave code you posted, such as,
M=[v1' v2' v']
parm = M \ (B-A)'
This looks like M is defined as a matrix of...
Thanks, my understanding always gets a bit fuzzy after R3.
I have a few clarification questions if you don't mind.
Question 1:
In the expression for the point we are looking for,
$$ \pi = \mathbf B - \xi \mathbf v $$
$$ \xi \text{ = some linear multiplier of } \vec {v} \text { that extends...
Thanks, I'm often a bit unsure about the best place to post.
I am not entirely sure about this. In my understanding, providing the space is orthogonal (which it is in this case) any three points can be considered to lie in a Euclidean plane, regardless of the dimensionality of the point...
Hello,
I believe that this is the correct forum for this post but please let me know if otherwise.
I have the following data in R4,
id x y z a
B -0.0700177 0.382249 -0.289338 0.00349957
A 1.13388 1.77602 -0.679365...
I am going to re-write the entire problem now because I think I made some errors in my original post. I apologize for the post being long, but I think it is best to do these problems out completely for the benefit of others who may be reading along.
For the following original data,
id x...
Hello,
This algorithm overall is probably more complicated than is correct for the pre-university forum but this question is about a relatively simple aspect of the calculations so I hope that this will be the proper place to ask.
I am writing a little program to do some computational geometry...
Looking at the equation above,
does the numerator refer to the cross product of vectors (p2-p1) and (p1-p0)? Since the resulting distance Dmin is a scalar, it seems as if this should be a simple product, but "x" often means cross product when vectors are concerned so I thought I should ask...