Questions tagged [mathematics]
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134
questions
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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 ...
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0answers
29 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 ...
2
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1answer
70 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 ...
1
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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 ...
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1answer
47 views
Finding geodesics on a mesh?
What are some state of the art methods/algorithms to find geodesics on arbitrary manifold meshes?
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0answers
76 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 ...
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1answer
36 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
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1answer
33 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 ...
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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 ...
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0answers
33 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
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1answer
99 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 ...
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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")
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1answer
37 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?
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1answer
60 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
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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
86 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
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1answer
64 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
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1answer
95 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
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1answer
54 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, \...
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0answers
96 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 ...
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1answer
74 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
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1answer
129 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):
...
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0answers
71 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
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0answers
46 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
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1answer
75 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
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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
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3answers
92 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, ...
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0answers
90 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
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0answers
48 views
What library or tool was used to plot these graphs?
I've been wanting to plot graphs that look like these (Taken from this blog post), but I can't figure out what tool, language, or library was used to pull this off.
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164 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
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1answer
101 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 ...
1
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1answer
64 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
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1answer
90 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, ...
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0answers
17 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 ...
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0answers
146 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 ...
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0answers
27 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.
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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 ...
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2answers
149 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
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0answers
163 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
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0answers
48 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-...
2
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0answers
71 views
Constraining a Polyline to Look Smooth
What are the mathematical constraints required for a polyline, i.e., a piecewise linear curve, to appear as a smooth curve to human vision? I've discovered one document that specifies only that the ...
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3answers
2k 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 ...
3
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0answers
103 views
How can you avoid thin triangles in a parametric shape in a smart way?
I have created a closed 3D mesh using a parametric function. The shape is constructed by taking an arbitrary closed b-spline and scaling it based on one of the parameters (similar idea to a parametric ...
1
vote
1answer
365 views
Translate an arcball camera upwards or left-right
This problem is giving me a really hard time.
I'm always looking at the origin and have a camera that moves around it in an arcball mode.
That part works beautifully:
I'm calculating the camera ...
3
votes
1answer
319 views
How to match Blenders polynomial lens distortion model with GLSL?
I'm trying to re-implement Blenders (libmv) polynomial lens distortion model using shadertoy, in order to apply the lens distortion in another application ideally by generating a STMap for that. I ...
2
votes
1answer
171 views
What is the equivalent of rotation matrix in Euler angle space for Quaternions?
I have to load a mesh in Blender (which uses Z and Y as up and forward axes), modify it and export it (with setting up and ...
1
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1answer
71 views
How to rotate a shape in another 3D software so that the rotation matches with the rotation in Blender?
I import a mesh in Blender, export it with setting axis_forward='-Z', axis_up='Y', import in NVIDIA's FleX, rotate it and store it on disk; I call this mesh ...
1
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1answer
137 views
Wrong tangential directions for cubic bezier curve
I am well aware that there are several ways to find the tangents to a Bezier curve. However, I choose to just substitute the result of differentiating the Bezier curve equation.
So, given four ...
4
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1answer
8k views
How to convert Euler angles to Quaternions and get the same Euler angles back from Quaternions?
I am rotating n 3D shape using Euler angles in the order of XYZ meaning that the object is first rotated along the X axis, then Y...
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1answer
137 views
How to randomly draw Quaternions within a specific range of Euler angles for rotation?
I am pretty new to Quaternions so please bear with me. I want to draw random Quaternion samples so that their Euler angle equivalent would range within [-30, +30] ...
