Questions tagged [mathematics]

The knowledge of the numbers, formulas, shapes and quantities. In the computer graphics, almost exclusively linear algebra is being used.

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Draw angles lines in raster graphics using bresenham line algorithm

I at the moment trying to draw some angled lines using bresenham line algorithm which can circulate a 2d array of size 21x21, as a line angled from 0 - 2pi. So the idea is that the program has to ...
Bob Burt's user avatar
  • 183
14 votes
3 answers
5k views

Correct Specular Term of the Cook-Torrance / Torrance-Sparrow Model

For a while I have been doing some research on the topic of Physically Based Rendering. One reflection model that is mentioned over and over is the Cook-Torrance / Torrance-Sparrow model. It seems ...
Thordal's user avatar
  • 141
9 votes
1 answer
5k views

Understanding Jump Flooding Algorithm (JFA) for Voronoi Diagrams

I'm having trouble understanding the JFA. As far as I understood the algorithm, it walks log(n) times through every pixel (no matter if it is a seed or not) and looks at that pixel's neighbors in $(x+...
Muad's user avatar
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9 votes
2 answers
10k views

How to achieve gimbal lock with Euler angles?

I was studying about Euler angles and I came across the problem gimbal lock which can occur by using Euler angles. In gimbal lock we lose one axis of rotation. But how? And when does it happen? On ...
videogamechef's user avatar
7 votes
1 answer
195 views

2D sampling with multidimensional transformations

I'm currently learning mathemetical concepts of distribution and the way to use them in a ray tracer with the book "Physically Based Rendering". Let's start by uniformly sampling an hemisphere: As ...
Qzaac's user avatar
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4 votes
1 answer
13k 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...
Amir's user avatar
  • 241
4 votes
2 answers
188 views

intersection between line segments - narrowed precondition

I believe that the issue may already have been discussed here. I want to find if two line segments does intersect and if they do then find and store and intesection points. Now it is already confirmed ...
sajis997's user avatar
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3 votes
1 answer
199 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(...
user8469759's user avatar
2 votes
1 answer
2k 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 ...
Row Rebel's user avatar
2 votes
0 answers
1k views

Line segment intersection test and find the point of intersection

Thanks for the suggestions. Now I am doing it as follows: First off it is identified if two line segments intersect or not. And I am using the algorithm described in the book - "Introduction to ...
sajis997's user avatar
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2 votes
2 answers
136 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 ...
user8469759's user avatar
1 vote
1 answer
73 views

Finding geodesics on a mesh?

What are some state of the art methods/algorithms to find geodesics on arbitrary manifold meshes?
Makogan's user avatar
  • 1,706
0 votes
1 answer
130 views

How compute new camera parameters given a velocity vector?

My goal is to update camera parameters given a velocity vector so that the camera points in the direction of the velocity vector. How should one compute the update matrix for the camera parameters?
Amir's user avatar
  • 241