Questions tagged [mathematics]
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113
questions
0
votes
1answer
43 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
47 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
36 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 ...
3
votes
1answer
57 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, ...
0
votes
1answer
34 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 & ...
3
votes
2answers
59 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
63 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
46 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.
0
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0answers
93 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
67 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
vote
1answer
48 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
78 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
13 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
81 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
24 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
35 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
109 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
151 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
46 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
votes
0answers
67 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 ...
1
vote
3answers
867 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
votes
0answers
95 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
300 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 ...
2
votes
1answer
260 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
118 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
vote
1answer
62 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
vote
1answer
103 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
votes
1answer
5k 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...
5
votes
1answer
83 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] ...
1
vote
1answer
74 views
How are the three plane equations derived in the NVIDIA's CG Tutorial chapter 8?
I'm reading the chapter 8 of the Cg tutorial and I could not understand 8.4.1 :
Because all these coordinates lie in the plane of the same triangle, it is possible to derive plane equations for x, ...
5
votes
0answers
165 views
Ray tracing implicit surfaces using Sturm's theorem
I am trying to render implicit surfaces given by a polynomial equation $F(x,y,z) = 0$ using Sturm's theorem.
Plugging the parametric ray equation $r(t) = o + td$, where $o\in\mathbb{R}^3$ is the ray ...
1
vote
1answer
114 views
How to simulate elastic material with restoring shape
I'd like to simulate a rubber-like material. This material if deformed would experience a restoring force to its original shape, a bit like a school rubber ereaser.
I tried with a spring-mass system ...
1
vote
1answer
54 views
How different can the number of pixels in a straight line be to its real length?
I'm working on a game with a programmable robot. It uses a laser range finder to get the distance to walls.
I'm using DDA to generate a line from the robot, going in the direction it is pointing, ...
0
votes
1answer
133 views
BRDF ray directions
The BRDF takes two directions, $\omega_{o}$ and $\omega_{i}$. I've heard that both directions should point away from the surface (one towards the camera, one towards the light), but iq's Oren-Nayar ...
0
votes
1answer
44 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} = \...
0
votes
1answer
159 views
How to compute volume of intersection of non-axis-aligned cuboids in 3D?
Given two cuboids in 3D space (8 vertex coordinates each) that are arbitrarily oriented, how can we find the volume of overlap between them in the fastest manner?
1
vote
2answers
559 views
Geometric interpretation of this bilinear interpolation equation?
Bilinear interpolation can be achieved by interpolating two values across the x axis, and then interpolating between the results across the y axis, like in the image below (from https://blog.demofox....
4
votes
1answer
461 views
GLSL shapes signed distance field implementation explanation?
I'm trying to understand all primitives In this article.After hard work I just learn Sphere and Cube , I wrote description here.
I could draw 2D shapes but I have trouble understanding 3D below codes:...
4
votes
1answer
132 views
Can someone explain this formula for parse RGB to HSL?
Im trying to complain the algorithm to calculate the HSL value form a RGB color. I understand the algorithm for the Hue, but im lost with the Lightness and saturation. Someone can explain why?
There ...
3
votes
1answer
501 views
Delta angle of two vectors about positive x axis
How do I calculate angle C?
I can only know what angle between vector and x positive vector {1, 0}
Angle between green and red is 60 degrees.
Angle between blue ...
2
votes
1answer
72 views
How can I draw regular polygons along the horizontal axis?
I drew simple triangle wave (that you can see It on graph toy).
f1(x) = frac(x/(PI+5))*(PI+5)
f2(x) = frac(-x/(PI+5))*(PI+5)
f3(x) = min(f1(x),f2(x))*1.5
...
4
votes
2answers
336 views
What is a Gaussian Lobe concerning BRDF and NDF?
I was reading a paper about voxel cone tracing and came across this term. So, what is a Gaussian Lobe or a Lobe in general?
I am asking in the context of Computer Graphics, BRDF and NDF.
1
vote
1answer
172 views
Changing sin frequency smoothly in shader
In my vertex shader I am using a sin function to offset vertices. But as I change the frequency of my sin function I notice some ...
4
votes
2answers
64 views
Modulo vs Scaling vs Capping when performing filters
I'm currently taking a graphics course and we've recently covered cross-correlation with regards to using a filter matrix that is applied to a region of pixels in a sort of continual raster-type scan ...
1
vote
1answer
97 views
Why are BRDF and the lighting uncorrelated?
In relation to this question, in the accepted answer I have a trivial question probably.
W.r.t. the following integral
$$
L_o(x\rightarrow \Theta) = \int_{\Omega_x} f_r(x,\Psi\rightarrow\Theta)L_i(x\...
3
votes
2answers
99 views
Why is the approximation valid, in the formula provided by Brian Karis?
I'm sorry I'm bringing this topic up again, but I need to expound some of the topics.
With reference to this question, I was wondering if someone can help me out in expanding some of the details.
In ...
6
votes
1answer
798 views
Microfacet shading for diffuse materials
I recently replaced the Lambertian BRDF in my path-tracer with Oren-Nayar, under the assumption that I could adjust it to use the GGX distribution model with appropriate masking/shadowing.
PBR ...
1
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0answers
63 views
Hashing a point on cubic sphere
Let's say I have a point on a potential cubic sphere inflated using this:
...
2
votes
1answer
95 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, ...
2
votes
1answer
79 views
Paper for the approximation formula provided by Brian Karis
In these slides, specifically page 11, the following formula is reported:
$$
\frac{1}{N} \sum_{k=1}^N \frac{L_i(l_k)f(l_k,v)\cos(\theta_{l_k})}{p(l_k,v)} \approx \left( \frac{1}{N} \sum_{k=1}^N L_i(...
