# Questions tagged [mathematics]

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### 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 ...
372 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 ...
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 ...
177 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 ...
72 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 ...
138 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 ...
9k 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...
152 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] ...
77 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, y, ...
176 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 ...
142 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 ...
85 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, ...
145 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 ...
68 views

102 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 ...
1k 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 ...
68 views

### Hashing a point on cubic sphere

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