Questions tagged [linear-algebra]
The linear-algebra tag has no summary.
40 questions
0 votes
0 answers
43 views
Practical applications of messing with the $w$ coordinate with affine transformation matrices?
Suppose we're using augmented coordinates to represent affine transformations (matrix transformations + translations) in space. If a vector has a $w$ coordinate of, say, $2$, it will be twice as ...
- 251
0 votes
1 answer
132 views
Manifold harmonics vectors not working?
I am trying to implement manifold harmonics. To see if I am doing things right I am visualizing the Fiedler eigenvector, which is the eigenvector associated with the second smallest eigenvalue. On my ...
- 1,891
0 votes
2 answers
97 views
Finding vertices of a polytope?
Assume that in 3D we have a polytope defined by the intersection of halfspaces. A half space is the set of all solutions of a linear inequality $P = N \cdot x + c \leq 0$ Where $N$ is the normal to ...
- 1,891
1 vote
1 answer
138 views
convert right handed matrix into left handed forward/up/right vectors
I have an openGL style matrix (column major, right handed ) that needs to be converted into two vectors (forward and up) I've managed to find, in a weird way, a solution that matches the the ...
- 31
2 votes
1 answer
282 views
Can you encode a reflection in a quaternion?
Say we have the transformation: \begin{bmatrix} 1 & 0 & 0\\ 0 & 0 & 1\\ 0 & 1 & 0\\ \end{bmatrix} i.e. the matrix that encodes swapping the z and y axes. This is equivalent to ...
- 1,891
1 vote
1 answer
144 views
Determinants as another way to multiply two vectors
I'm reading section 6.1 (Determinants) of the book Fundamentals of Computer Graphics (5th Ed), in regards to the definition of the determinant: \begin{align} |\textbf{ab}| &= |(x_a \textbf{x} + ...
- 67
2 votes
1 answer
226 views
Usage of Jacobi transformation in computer graphics
I have been going through scratchapixel.com lessons. Unfortunately some of the lessons are incomplete and one of the missing chapters is titled "Jacobi Transformation and Eigenvalue Algorithm&...
- 123
0 votes
1 answer
66 views
Computing heat diffusion creates weird results
I am trying to model heat diffusion on the surface of a mesh. I annexed the most important bits of theory about this topic as screenshots on the question see the bottom. The crux of the issue is we ...
- 1,891