Questions tagged [linear-algebra]
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40 questions
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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
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Applications of the outer product in shaders
I've been reading through the specification of OpenGL ES 3.20 and found a built-in "outerProduct" function for computing the outer product of two vectors, specifically, outerProduct(a,b) = $...
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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
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How is a system for parametrizing a triangular mesh obtained?
I am analyzing the article Parameterization of triangular meshes (Michael S. Floater November 10, 2009) and have reached the point where the uniqueness of the solution to a system of linear equations.
...
- 11
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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
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Custom LookAt and Perspective Matrix functions not rendering in Vulkan
I am trying to create a custom math library for a renderer. The renderer works when using glm but for educational purposes as well as for the sake of having a custom library to support multiple ...
- 109
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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
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A fresh perspective confusion about a paragraph
I am trying to re-implement the paper "A fresh perspective"
In this paper there is one paragraph on secion 2 that reads:
Usually, $z_s = z$
is the depth value of the point $P$, unchanged by ...
- 1,891
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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
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How to apply transformation matrices from multiple primitives on a mesh
I'm working on some code to convert a 3d geometry from IFC to gltf/glb. One of the challenges I'm facing with this is that - IFC provides transformations for each primitive separately i.e., if I have ...
- 143
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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
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What are viewport transformation matrixes for this coordinate system?
I have a set of vertexes (x, y, z) in normalized device coordinates. Its x, y, and z values are in the range (-1, 1). Normalized device coordinates use the left-handed coordinate system, as shown ...
- 167
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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
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Using the HTML canvas and colors to track objects
I need to rewrite a short utility library, to get it working with the Brave browser (My actual question isn't about brave per se.)
canvas-color-tracker - example of it being used and src/index.js is ...
- 11
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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