Questions tagged [mathematics]

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2answers
57 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 ...
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1answer
378 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 ...
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3answers
102 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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1answer
21 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 ...
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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'...
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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 ...
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0answers
53 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
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1answer
45 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 ...
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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 ...
3
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1answer
338 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 ...
3
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1answer
276 views

Barycentric coordinates for 5-sided polytope of two triangles and three trapezoids

I have a triangle that is extended in space and each edge is refracted differently, creating a 5 sided polytope. The initial and final triangles are the view radii segments of a frustum. We need to ...
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1answer
28 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 ...
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1answer
44 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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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 ...
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0answers
32 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
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1answer
72 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 ...
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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
48 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
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
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1answer
38 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
37 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 ...
1
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1answer
102 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 ...
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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 ...
1
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1answer
68 views

Linear independence of three points

What is the best way to prove if three points are linear dependent? This is my current way to do it: $$\mathbf{v_a} = \mathbf{b}-\mathbf{a} \\ \mathbf{v_b} = \mathbf{c}-\mathbf{a} \\ \mathbf{v_c} = \...
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0answers
623 views

How correct is rendering in XYZ / linear RGB space?

I have a spectral power distribution (SPD, 5 nm steps) for all light sources in the scene and SPDs for the reflectance of all surfaces under any light / viewer angle in question. I'm going to ...
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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 ...
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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)}{...
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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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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")
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1answer
61 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 ...
4
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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, \...
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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 ...
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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 ...
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0answers
91 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 ...
2
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1answer
98 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?
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1answer
78 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 ...
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0answers
110 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
80 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 ...
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 & ...
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1answer
132 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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2answers
1k views

How am I able to perform perspective projection without a near plane?

I'm learning about 3D computer graphics, but I'm having a hard time understanding why the near plane of a viewing frustum can not be placed at z position $0$ (right at the camera). I can understand ...
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0answers
74 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
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
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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, ...
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0answers
100 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: <...
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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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0answers
182 views

SDF collision detection

I was wondering if there are any techniques for calculating the intersection point/s between two or more distance fields.
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1answer
91 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
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 ...
2
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1answer
102 views

How to obtain a parametric equation out of a part designed in Autodesk Inventor?

Whenever you make a part in inventor, the software calculates de properties of the whole body given a constant density. Then, automatically, it shows the inertial tensor. As you can recall from math, ...