Questions tagged [linear-algebra]

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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. ...
e7min's user avatar
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Different basis from spherical harmonics to represent light?

There's a lot of research being done in 3D shape analysis when it comes to PDE methods. Recently I've been reading quite a bit of literature on this subject and recent trends in this subject propose ...
user8469759's user avatar
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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 ...
Makogan's user avatar
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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 ...
Joseph Vargas's user avatar
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1 answer
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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 ...
ytrox's user avatar
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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 ...
Makogan's user avatar
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2 votes
1 answer
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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 ...
Makogan's user avatar
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4 votes
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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 ...
Gangula's user avatar
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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} + ...
James B's user avatar
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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 ...
Jimmy Yang's user avatar
2 votes
1 answer
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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&...
PentaKon's user avatar
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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 ...
exrhizo's user avatar
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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 ...
Makogan's user avatar
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1 answer
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Plotting points along a 3D line segment

I'm trying to plot some points along a 3D line segment and could really use some help. In 2D, I've found success getting the angle of the line, the sine & cosine of the angle, and then adding the ...
Dr. Pontchartrain's user avatar
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Changing Coordinate Frames with Affine Transformations

Stuck with this questions could I get some help. where uA and vA are two orthonormal vectors indicating the two axes, and oA is the origin. Suppose that all three frames of reference shown in ...
gmjasonx's user avatar
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2 answers
445 views

Why negate z when constructing projection matrix OpenGL

I constructed an orthographic projection matrix from this article on scratchpixel.com: ...
Lenny White's user avatar
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1 answer
2k views

How to keep an object constant in screen space?

If you open the modern Blender UI and select for example scaling, and then you use the scroll wheel to "zoom" (move the camera along the radial axis). You will notice that the size of the 3D widget ...
Makogan's user avatar
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Apply Projective Transformation 2D Rectangle

I want to write code from scratch about Projective Transformation in order to apply this transformation to 2d rectangular. I searched about this transformation, but I could not figure out completely. ...
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Mathematics in Computer Graphics

Can you please recommend some topic for research work related to mathematics in CG? (Maybe something like "Affine transformations in CG")
FlyMeToTheMoon's user avatar
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Transformation for aligning 3D object with reference frame of 3D turtle graphics

The problem I'm using a 3D extension of the well-known "Turtle graphics" to draw plants. My system works by maintaining a position $\vec{p}$ and three vectors: The heading $\vec{H}$ The "up" ...
Katharina's user avatar
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How to Pan Zoom a spherical camera?

I asked this in regular SO but I think people are not understanding the question so i will try here: So, for anyone familiar with Google Maps, when you zoom, it does it around the cursor. That is to ...
Makogan's user avatar
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Want to study computer graphics

I want to study computer graphics but I don't have a strong foundation in mathematics. I am doing a computer science degree that doesn't cover computer vision, image processing or computer graphics, ...
Vektor's user avatar
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How to find matrix that projects 3d points into 2d plane centered in the origin?

I have a list of 3D points defined by Cartesian coordinates, i.e. [(x1,y1,z1), (x2,y2,z2), ..., (xn,yn,zn)]. I want to project them to a 2D plane which has origin in the center (0,0,0) but which is ...
slobodan.blazeski's user avatar
3 votes
0 answers
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NURBS Weights De Boor's Algorithm

I am having trouble implementing an algorithm for 3rd degree NURBS. I have been able to program 2nd degree ones from the equations described here but I am not able to derive an equation for Rational B-...
Felipe Gutierrez's user avatar
2 votes
3 answers
7k views

How to calculate ray

In ray-tracing technique critical point is to calculate rays which came out from eye $E$ to target $T$ through pixel $P_{ij}$ on viewport. The "viewport" is represented as rectangle divided to square ...
Kamil Kiełczewski's user avatar
1 vote
1 answer
844 views

Project vertex onto plane

What I have: a plane given by its normal$\ n $ and a point on the plane$\ p $. a 3D-point$\ v $. a direction$\ d$. What I need: the projection of$\ v$ along$\ d$ onto the plane. How can I ...
Dmitrii C.'s user avatar
2 votes
1 answer
234 views

Deciphering Affine/Projective Transformation Code

I've spent about 2 days trying to understand this piece of code (from here) that applies an affine/projective transformation to an image. I will link bits of the code that I'm struggling to understand ...
theunseen's user avatar
0 votes
0 answers
262 views

Changing coordinate system from texelFetch to textureLod is breaking the algebra

I have a scene rendered using texelFetch() and I am trying to modify the shader to use textureLod() instead. This is the image generated with texelFetch: When I try to change the shader to use ...
Makogan's user avatar
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1 vote
1 answer
735 views

Skeletal animation: What is the purpose of multiplying interpolated bone matrix with parent's matrix?

Let's say I have the following hierarchy: Bone A Bone B Bone C Here's how most tutorial is telling me how to calculate the finalMatrix to be sent to ...
Manh Nguyen's user avatar
3 votes
1 answer
4k views

Confusion about how inverse bind pose is actually calculated and used?

I am trying to do skeletal animation using Assimp and the inverse bind pose matrix just trips me up. I will give a little example to illustrate my point. ...
Manh Nguyen's user avatar
2 votes
1 answer
15k views

How to derive a perspective projection matrix from its components?

This has been haunting me for several days now. I want to find the component that makes up of this 4x4 perspective projection matrix, with $l$(left), $r$(right), $b$(bottom), $t$(top), $n$(near), $f$(...
Manh Nguyen Huu's user avatar
5 votes
1 answer
957 views

why is translating in 3D space the same as shearing in 4D space?

I was reading "3D Math Primer for Computer Graphics and Game Development" and there was something the author had said that I thought was particularly interesting, he stated It is important to ...
MatriXcel's user avatar
4 votes
1 answer
398 views

Why does an affine transform work only on three of the corners?

I am trying to use a linear transformation to straighten out the camera angle on this image: In other words, I want to transform the image into a head-on view of the whiteboard. I applied an affine ...
Lincoln Bergeson's user avatar
1 vote
0 answers
1k views

360 degrees rotation around x axis

How do we rotate the camera around x axis 360 degrees, without having to flip the axis, meaning without having the strange flip after we go over +-90 degrees on <...
Test's user avatar
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2 votes
1 answer
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pseudoinverse Jacobian and adding more control in computer animation

I am studying inverse kinematics. But I wonder the suggested equations. (The following equations are taken from 'Computer Animation Algorithms and Techniques Third Edition Page, 181') To better ...
shashack's user avatar
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6 votes
1 answer
2k views

What does it *mean* to scale in an arbitrary direction?

My graphics text explains rotating along the cardinal axes, then generalizes the math to show how to make a rotation matrix for rotating around an arbitrary vector. That all makes sense and I can both ...
Joseph Garvin's user avatar
1 vote
1 answer
388 views

Final transformation matrix to transform world coordinate into vrc [duplicate]

For a 3D scene in the world coordinates, its View Reference Point $\mathrm{VRP}$ is at $(5,2,1)$, and a viewer is looking towards point $A=(1,1,1)$. Construct a transform matrix which will map world ...
S.A's user avatar
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1 vote
1 answer
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Building view transform matrices

For a 3D scene in the world coordinates, its View Reference Point $\mathrm{VRP}$ is at $(5,-2,1)$, and a viewer is looking towards point $A=(1,1,1)$. Construct a transform matrix which will map world ...
S.A's user avatar
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