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Questions tagged [mathematics]

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38 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
50 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
62 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
45 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 ...
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1answer
77 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
12 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
46 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
23 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
33 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
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2answers
84 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
141 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
44 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
66 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
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3answers
490 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
92 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
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1answer
260 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
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1answer
231 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
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1answer
79 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
61 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
94 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
3k 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
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1answer
76 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
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1answer
73 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
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0answers
160 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
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1answer
105 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
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1answer
47 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, ...
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1answer
130 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 ...
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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} = \...
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1answer
131 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?
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2answers
533 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....
3
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1answer
344 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
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1answer
128 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
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1answer
461 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
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1answer
66 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
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2answers
284 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.
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1answer
162 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
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2answers
62 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
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1answer
96 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
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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 ...
5
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1answer
715 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
62 views

Hashing a point on cubic sphere

Let's say I have a point on a potential cubic sphere inflated using this: ...
2
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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
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1answer
77 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(...
1
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2answers
197 views

AABB bounding boxes

Here's a constructor to construct a axis-aligned bounding box given two opposite vertices on the bounding box, from Pharr's Physically Based Rendering, Third Edition. ...
3
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1answer
742 views

Probability density function while using spherical coordinates

I'm following this tutorial where at somepoint the derived PDF for spherical coordinates for a Lambertian surface is \begin{array}{l} p(\theta, \phi) = \dfrac{\sin \theta}{2 \pi}. \end{array} But as ...
4
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1answer
229 views

Where does the cosine factor comes from in the GGX PDF?

The GGX NDF, as it appears on the paper where it is presented is: $$D(m)=\frac{\alpha_g^2\space\chi^+(m\cdot n)}{\pi\cos^4(\theta_m)(\alpha_g^2+\tan^2(\theta_m))^2}$$ It is equivalent, in the range $...
1
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1answer
58 views

Is there any free software to visualize a texture mapped to a sphere? [closed]

I am trying to study the texture deformations caused when mapping a rectangle to a sphere, if I had a software that took an image as an input and displayed how it looks like when texture mapped to a ...
1
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1answer
98 views

Matlab scatter hotmap [closed]

I have two columns of data, x(angle) and y(distance), they are my experiment results(figure 1). How can I use these results to make a ‘hotmap diagram’ by matlab? The z axis is the density value of xy ...
6
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1answer
239 views

Logarithmic spiral with equal vertex spacing, what equations?

I need to draw a logarithmic spiral (or close approximation) whose vertices are equally spaced, such that the lines between any two consecutive vertices are of equal length. (Actually, that spiral is ...
1
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1answer
381 views

Hooke's Law vector form

I'm studying spring model. There is a suggested equation (Hooke's Law vector form) But, I couldn't understand how to derive that equation. I'm reading 'Computer Animation Algorithms and Techniques ...