Questions tagged [mathematics]
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144
questions
2
votes
1answer
64 views
Determining Rational Quadratic Bezier Curve Weights for Circle
I am trying to create a spherical interpolation with 3 points. I'm currently using Quadratic Bezier Interpolation but have been told I should use Rational Quadratic Bezier Curve in order to get a ...
0
votes
0answers
27 views
Explanation of converting a look-at / direction vector to quaternion rotation?
Can someone please explain the math behind converting a direction-vector or lookAt-vector into a quaternion rotation?
What I am trying to do?
I am trying to create a custom aim-constraint for a DCC (...
0
votes
1answer
20 views
In place sorting of a half edge DS?
Cross posting from SO because I didn;t know where to put this question.
I have an implementation of the half edge and I am trying to sort the edges such that edge n+1 is the pair of edge n.
Setup
I ...
1
vote
1answer
31 views
Improve accuracy of mesh gradient?
So to make it simple. I currently use a method I found online to compute the gradient of a scalar field of a mesh.
To test how accurate this is, I made a sphere and followed the gradient direction of ...
1
vote
0answers
23 views
Finding a flat plane within iPhone depth data
I have real time depth data coming from an iPhone and I want to identify flat objects within the point cloud so that I can highlight the Hard edges in the images. The objects can be at any angle and I'...
3
votes
1answer
37 views
Mis understanding of the Heat Method
I have been trying to understand a paper in CG for a while, called the Heat Method by Ken
Many things have clicked but I don't fully understand it yet. In particular.
In the following $u$ is a vector ...
0
votes
0answers
54 views
Calculating of vectors in Phong Lighting Model
I'm learning about computer graphics and I have some questions about calculation of the vectors, so I will write the exercises that I have and I hope that someone can help me with the formulas that I ...
4
votes
1answer
48 views
Gradient descent (Not ML) on arbitrary meshes
So I am doing a gradient descent like algorithm on the surface of a mesh and I just noticed something:
The above is the geodesic gradient (the distance to a single vertex)
Look at where the ear ...
1
vote
2answers
61 views
Discrete Gradient?
I am trying to understand how to get the discrete gradient of a mesh that is being used as the input of some function $f$. In other words for every vertex $v$ there is a scalar quantity $s$ associated ...
1
vote
2answers
67 views
Heat Method (Crane et Al) How do we pick u?
The heat method is a very interesting paper for distance computation:
https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf
The idea behind the paper is that, heat travels along the ...
0
votes
1answer
30 views
Is the laplacian operator for meshes just the sum of the differences of neighbouring vertices?
I am starting to learn about the laplacian operator $\Delta = \nabla \cdot \nabla\phi(p)$
Which can be described as the divergence of the gradient of a scalar function $\phi$. This is equivalent to ...
0
votes
0answers
7 views
MMP algorithm, no metion of “in window” intersections
If you are familiar with the MMP algorithm for geodesic finding, you know an important part of the algorithm revolves around solving intersections of windows.
I am running into a case that I don't see ...
0
votes
0answers
34 views
Are there algorithms besides Canny edge detection that can create consistent width edges?
Sobel edge detection is pretty much the quintessential way to get edges out of an image. It however suffers from certain quirks.
One example is, because it's gradient, based certain surfaces exhibit ...
1
vote
1answer
73 views
Approximating Geodesics in a half edge DS, how can I refine my mesh to get good approximations
I implemented Djikstra's shortest path algorithm to approximate Geodesics on arbitrary meshes. Djikstra's works, but I noticed a problem inherent to the discretization of my meshes.
Consider the ...
0
votes
1answer
38 views
Fast and exact Geodesics on meshes, Backtracking confusion
The following is an excerpt from a 2005 paper on geodesics on triangular meshes, taken from section 3.5
In this case $p$ is a point on some arbitrary face in a mesh, $p'$ is a point on one of the 3 ...
1
vote
1answer
48 views
Finding geodesics on a mesh?
What are some state of the art methods/algorithms to find geodesics on arbitrary manifold meshes?
1
vote
0answers
78 views
Why does my self-written rendering engine make further away objects look larger?
I am writing a very simple rendering engine. I have already made a few tests, but somehow the images it creates look wrong. Objects that are further away from the camera look larger than objects ...
0
votes
1answer
39 views
Closest sphere on segment
I am trying to get a segment closest point on a surface and display a circle (or sphere in this case) at that position.
I actually get the correct position but I can't get a uniform sphere based on ...
2
votes
1answer
38 views
Interpreting Image Processing Math Equation
I am reading "Image Processing and Analysis" by Chan and Shen, c 2005 SIAM. They introduce some notation I'm not 100% sure how to interpret:
$$ u_0(x)=u(x)+n(x), x=(x_1,x_2) \in \Omega $$
They ...
0
votes
0answers
32 views
What are some uses for the vector triple product in computer graphics?
I have just learned about the vector triple product (Lagrange formula) from a math for computer graphics textbook, however the book does not mention any use cases for it beyond the fact that it's a ...
1
vote
0answers
34 views
What is the projection matrix of reverse (Byzantine) perspective?
I would like to construct a projection matrix for reverse perspective.
I'm using OpenGL and tried to modify concepts from this excelent tutorial.
I came up with:
$$
\begin{bmatrix}
2\frac{(near-M)}{...
0
votes
1answer
111 views
Prove radiance contributions of deeper paths fade away
When ray tracing, I find it intuitively clear that deeper paths have a lower contribution to the overal picture than shorter paths. This is the main reason why it is generally okay to render a picture ...
0
votes
0answers
50 views
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")
0
votes
1answer
46 views
How do you compute the winding number of a closed poly curve?
Pretty much the title, given a closed curve in 2D, defined by a set of points, and a point. What's the algorithm to calculate the winding number of that curve, point pair?
0
votes
1answer
62 views
Wrong reflection
Here is a youtube video showing my problem:
youtube.com/watch?v=y8J7VhS2pkM
I think I'm either doing the texture lookup on the reflection texture wrong, or the reflection or view matrix is somehow ...
0
votes
0answers
22 views
GIMP's Additional blending formula
I try to implement GIMP's the Additional blending mode for layers in my application.
I've found the formula:
E = min((M+I), 255)
I think, that if I blend ...
3
votes
0answers
92 views
Procedural Generation of 4D Shapes
I'm curious if anyone has any insight into how one might procedurally generate 4D objects, as showcased in Miegakure (or the developer's other game, 4D Toys ).
I built a program a while back to do ...
1
vote
1answer
85 views
How to handle Half edge boundary edge iteration from vertex?
Ok so let's say we have a portion of a mesh that looks somewhat like this:
A triangle fan with one of the triangles removed. If that triangles was not removed, we could get all the edges adjacent to ...
2
votes
1answer
99 views
How do people come up with subdivision schemes?
Be it chaikin subdivision, loop subdivision, catmull-clark subdivision...
How do people come up with the coefficients for an arbitrary subdivision scheme?
4
votes
1answer
57 views
Understanding distinct vs. not distinct knots in B-splines
In reading the wikipedia page about B-Splines https://en.wikipedia.org/wiki/B-spline, I am getting confused about the concept of knots.
If we have a spline of order $n$, with a knot vector ($t_0, \...
1
vote
0answers
122 views
Why does Schlick's approximation contain a \$(1-\cos\theta)^5\$ term?
The approximation writes the reflection coefficient as$$R(\theta)=R_0+(1-R_0)(1-\cos\theta)^5,\,R_0=\left(\frac{n_1-n_2}{n_1+n_2}\right)^2.$$Why is the exponent 5? Schlick 1994 introduces this ...
0
votes
1answer
87 views
Reading thesis on cone tracing, did the author make a mistake?
I am reading this document that talks about signed distance field rendering.
In that document section 6.3, on the topic of cone tracing, it says:
Cone tracing is an extension of the sphere tracing ...
0
votes
1answer
143 views
Confusion around Lambert's Cosine Law in Ray Tracing in One Weekend
Peter Shirely's Ray Tracing in One Weekend presents the following function to calculate the color of a lambertian material (See chapter's 7 and 8):
...
1
vote
0answers
76 views
GPU Procedural placement - Creating evenly distributed sampling points
I am working on a procedural placement system on the GPU, inspired by the work done by Guerrilla Games in Horizon Zero Dawn:
https://www.guerrilla-games.com/read/gpu-based-procedural-placement-in-...
2
votes
0answers
47 views
When should operations on 4D (homogeneous/projective) vectors use the w-coordinate?
Various operations on 2D vectors naturally generalise to 3D vectors simply by including the $z$-coordinate. The ones that come to mind are:
Vector sum and difference
Dot product
Magnitude (Euclidean ...
4
votes
1answer
80 views
Shader or formula that distorts inward
I am looking for a shader (or at least the right terminology) for crushing an image. It should be something very similar to barrel distortion, but instead of the center crushing outward to the edges, ...
1
vote
1answer
43 views
Mapping sample to a disk
So I have been reading this wonderful book on ray tracing by Kevin Suffern, Ray tracing from Ground Up. I am reading this book after finishing Peter Shirley's first two book on ray tracing & ...
4
votes
3answers
110 views
Visualize the interpolated unit quaternion on the surface of the unit sphere
My major is mechanical, please forgive me for asking questions that may seem trivial to you.
First, I'm reading the following paper:
Dam, Erik B., Martin Koch, and Martin Lillholm. Quaternions, ...
1
vote
0answers
107 views
Why does the reflected component in Lambertian path tracing get multiplied by a factor of 2?
I would like to intuitively understand the Path Tracing equation/formula/pseudocode, but I'm not fully getting the last return statement.
As per Wikipedia page:
<...
0
votes
0answers
194 views
SDF collision detection
I was wondering if there are any techniques for calculating the intersection point/s between two or more distance fields.
1
vote
1answer
125 views
Camera Implementation without Limitations
I've developed a simple (Third-Person) Perspective Camera with Orbit controls.
However, my implementation doesn't handle the case where if the pitch goes over 90º it flips upside down. From what I've ...
2
votes
1answer
77 views
Estimating the position of vertexes in a 3D model
Introduction to my project:
We are machine learning scientists and working on a biomedical system for tracking tongue for speech pathology using a technology called EMA (Electromagnetic ...
0
votes
1answer
92 views
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, ...
1
vote
0answers
18 views
How can I detect if an edge has flipped during the UV unfold process?
I'm writing my own UV Unfold operation (similar to Maya's Optimize UV tool or 3DS Max's Relax Tool). My code works great 90% of the time but in some instances, I'm getting faces and edges that flip ...
1
vote
0answers
170 views
Help with understanding the look-at function (the view matrix)
I've been reading this article about the look-at function. I don't understand the part when they're trying to inverse the matrix N.
They say that R is orthogonal because all its row and column ...
0
votes
0answers
29 views
How can I create multivariable function plotting software
I have finished Dennis Ritchie's C book, and I would like to create my own plotting software for enhancing my programming skill,I want sources,books or anything to reach this goal.Thanks for answers.
1
vote
0answers
37 views
Algorithm for randomly generating polyhedrons?
I want to randomly generate polyhedrons which need not be convex. What is the most efficient way for doing so?
I can think of an algorithm for generating random convex polyhedrons, but am unable to ...
1
vote
2answers
160 views
How to calculate interpolation between multiple skeleton poses?
I found out that I should use spherical linear interpolation to blend two poses of a joint. I cannot find what to do if I have hundreds of poses to blend except applying the SLERP iteratively.
What ...
4
votes
0answers
166 views
Pre-filtered environment map, deriving the equation
I'm reading through this article, and more specifically I'm trying to derive the equation that would explain the implementation the following shader (still in the same article):
...
3
votes
0answers
49 views
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-...
