# Questions tagged [mathematics]

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### 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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### 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: <...
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.
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### 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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### 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 ...
46 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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### 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, ...
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 ...
64 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 ...
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.
34 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 ...
103 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 ...
150 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): ...
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-...
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 ...
709 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 ...
93 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 ...
289 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 ...
250 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 ...
107 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 ...
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 ...
102 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 ...
4k 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...
79 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] ...
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, ...
163 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 ...
111 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 ...
53 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, ...
132 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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### 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 ...
766 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 ...
63 views

### Hashing a point on cubic sphere

Let's say I have a point on a potential cubic sphere inflated using this: ...
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### 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, ...
78 views