Questions tagged [linear-algebra]
37 questions
6
votes
1 answer
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 follow the math and picture the operations.
Then…
Joseph Garvin
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5
votes
1 answer
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 understand that this matrix multiplication is still a
…
MatriXcel
- 51
- 1
4
votes
1 answer
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 transformation to that image, identifying the top…
Lincoln Bergeson
- 171
- 4
4
votes
1 answer
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 a mesh (MeshA) which has 4 primitives, i'm…
Gangula
- 143
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3
votes
1 answer
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 remains constant in screen space (it becomes bigger…
Makogan
- 1,584
- 8
- 27
3
votes
0 answers
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-Splines of degree 3. The author describes the…
Felipe Gutierrez
- 278
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3
votes
1 answer
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.
Root
Bone A
Bone B
Bone C
Let's say we have a hierarchy like above. To…
Manh Nguyen
- 309
- 3
- 8
2
votes
3 answers
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 pixels - this rectangle is perpendicular to line…
Kamil Kiełczewski
- 155
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- 6
2
votes
1 answer
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 and add comments on what I think it's trying to…
theunseen
- 23
- 5
2
votes
1 answer
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), $f$(far) defining the…
Manh Nguyen Huu
- 207
- 1
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2
votes
1 answer
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 control the kinematic model such as encouraging joint…
shashack
- 523
- 4
- 13
2
votes
1 answer
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". Can someone explain its usages in CG (not physics) as…
PentaKon
- 123
- 2
1
vote
0 answers
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 say, the matrix transformation for such a zoom is…
Makogan
- 1,584
- 8
- 27
1
vote
1 answer
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 calculate this? Thank you!
P.S.: I need to implement that…
Dmitrii C.
- 23
- 3
1
vote
1 answer
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 shader.
bonePoseToWorldPose(Joint * joint, glm::mat4 & parentTransform, glm::mat4 &…
Manh Nguyen
- 309
- 3
- 8