http://redman.xyz/ 2026-04-22T03:15:55+00:00 http://redman.xyz/ http://redman.xyz/lib/tpl/dokuwiki/images/favicon.ico text/html 2020-04-17T11:01:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/angle_between_two_vectors?rev=1587121260&do=diff Angle between two vectors [[Which one to choose?]] In $\mathbb{R}^n$ there are two angles between any two vectors. The smallest one I'll call $\theta$. The other one, its 360° complement, I'll call $\phi$. The smallest angle between two vectors $\mathbf{u}$ and $\mathbf{v}$ is given by: text/html 2018-05-13T19:51:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/atan2?rev=1526241060&do=diff atan2 $$\mathrm{atan2}: \mathbb{R}^2 \setminus (0, 0) \mapsto (-\pi, \pi]$$ $$\mathrm{atan2}(y, x) = \begin{cases} +\frac{\pi}{2} &: (x = 0) \land (y > 0) -\frac{\pi}{2} &: (x = 0) \land (y < 0) \tan^{-1}\frac{y}{x} &: x > 0 \tan^{-1}\frac{y}{x} + \pi &: (x < 0) \land (y \geq 0) text/html 2020-08-15T19:01:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/cem?rev=1597518060&do=diff cem [[Diffraction on a periodic grating]] Cem is a simple C implementation of the finite-difference time-domain method for solving Maxwell's equations. It can simulate and visualize a number of wave phenomena like diffraction or refraction. Background [[Me presenting at the contest. The text on the slide is a short description of FDTD. [[http://www.lo10.wroc.pl/pl/gala-finalowa-xii-edycji-otwartego-miedzyszkolnego-konkursu-fizycznego-im-bozeny-koronkiewicz.html|Source]]]] Written two years … text/html 2019-04-16T20:36:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/colorimetry?rev=1555446960&do=diff Colorimetry text/html 2020-08-15T18:59:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/engineers_thesis?rev=1597517940&do=diff A comparison of methods of assessing the quality of color rendering of consumer light sources The full text in Polish is available [here]. The LaTeX and Python source code is available at praca_inzynierska. Abstract In science and the industry, many methods of assessing quality of color rendering are in use, from the oldest, created in the middle of the 20th century, to completely new ones. The goal of this work is an overview and comparison of the most widely used of these, with a specific f… text/html 2020-09-09T14:57:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/gsoc2020?rev=1599663420&do=diff Google Summer of Code 2020 [[The kind of stuff I worked on. Picture from [[gsoc:otsu2018_3|this blog entry]].]] I participated as a student in Google Summer of Code in 2020. I worked on New Spectral Upsampling Methods for Colour, an affiliated project of NumFOCUS. I've published my project proposal. Maybe it'll help you if you're planning to participate yourself. The summary of my work, the text/html 2020-08-31T07:59:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/gsoc2020_work_product_submission?rev=1598860740&do=diff Work Product Submission Name: Paweł Redman Organization: NumFOCUS Sub-Organization: Colour Science Mentors: Thomas Mansencal, Michael Mauderer, Hao Xie Overview My work during this year's Google Summer of Code was focused on improving Colour. I have added support for three new spectral upsampling methods and two new color quality metrics text/html 2020-08-30T19:55:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/gsoc_final_report_draft?rev=1598817300&do=diff Work Product Submission (DRAFT) Name: Paweł Redman Organization: NumFOCUS Sub-Organization: Colour Science Mentors: Thomas Mansencal, Michael Mauderer, Hao Xie Overview My work during this year's Google Summer of Code was focused on improving Colour. I have added support for three new spectral upsampling methods and two new color quality metrics text/html 2018-05-01T09:35:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/integrating_cos2x?rev=1525167300&do=diff Integrating cos² x $$ \int \cos^2{x}\,dx = \frac{x + \sin{x}\cos{x}}{2} + C $$ Using the Pythagorean identity Integrate by parts using $u = \cos{x}, du = -\sin{x}$ and $v = \sin{x}, dv = \cos{x}$: $$ \begin{align} & \int \cos{x}\cos{x}\,dx = \sin{x}\cos{x} - \int -\sin{x}\sin{x}\,dx text/html 2018-05-01T09:34:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/integrating_sin2x?rev=1525167240&do=diff Integrating sin² x $$ \int \sin^2{x}\,dx = \frac{x - \sin{x}\cos{x}}{2} + C $$ Using the Pythagorean identity Integrate by parts using $u = \sin{x}, du = \cos{x}$ and $v = -\cos{x}, dv = \sin{x}$: $$ \begin{align} & \int \sin{x}\sin{x}\,dx = -\sin{x}\cos{x} - \int -\cos{x}\cos{x}\,dx text/html 2022-04-15T17:36:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/minitrem?rev=1650044160&do=diff Minitrem [[A screenshot of the game, [[https://www.youtube.com/watch?v=Hkt2JXWH4sw|watch the video]].]] Minitrem is a 2D real-time strategy game with an infinite, procedurally-generated world. The overall theme is loosely based on Tremulous. The game is written in C++, using SFML for graphics and sound. Most of the assets were also made by me. Background text/html 2018-05-06T12:56:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/notation_conventions?rev=1525611360&do=diff Notation and conventions used on this site Every textbook, website, professor, etc. uses their own notation and conventions. To avoid confusion I thought I'd write down mine and try to use them consistently throughout the site. Vectors {| ! Notation ! Meaning text/html 2018-05-06T09:42:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/orthogonal_matrix?rev=1525599720&do=diff Orthogonal matrix An orthogonal matrix is a matrix $\hat{M}$ that satisfies: $$ \hat{M}\hat{M}^\top = \hat{M}^\top\hat{M} = \hat{\mathbb{I}} $$ It has the following properties: * $\hat{M}^{-1} = \hat{M}^\top$ * $\mathrm{det}\hat{R} = \pm 1$ * text/html 2020-03-23T14:32:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/polarization?rev=1584973920&do=diff Polarization [[A screenshot.]] This is a Python program I've written for myself to understand how light polarization works. The source code is available at polarization. It needs a lot of polishing. I'll do that when I find the time then write a proper article. text/html 2020-08-15T19:01:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/ray?rev=1597518060&do=diff ray [[A render of the bundled scene (gamma corrected).]] Ray is a multi-threaded, real-time path tracer, written in C. Paths are traced through an octree, which can be edited at run-time, giving it sort of a “early Minecraft prototype” feel. Being my first “serious” program, it's rather primitive and can't work with complicated geometry or surface models. text/html 2018-05-09T15:30:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/ray_vs_sphere?rev=1525879800&do=diff Ray vs. sphere [[A drawing of a ray intersecting a sphere in two dimensions.]] In $\mathbb{R}^N$, a ray of origin $\mathbf{x_r}$ and direction $\mathbf{v}$ and an N-sphere of origin $\mathbf{x_s}$ and radius $r$ intersect at $\mathbf{x}_I$ given by: $ \mathbf{x}_I = \mathbf{x_r} + t_\pm\mathbf{v} $ where: $$ \begin{align} t_\pm &= \frac{\mathbf{v} \cdot \mathbf{u} \pm \sqrt{(\mathbf{v} \cdot \mathbf{u})^2 - v^2(u^2 - r^2)}}{v^2} text/html 2019-04-16T21:17:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/rotational_symmetries_bravais_lattice?rev=1555449420&do=diff Possible rotational symmetries in a Bravais lattice Any 2- or 3-dimensional Bravais lattice will have at most the following rotational symmetries or their compositions: {| ! Symmetry ! colspan=“2” | Angle of rotation Every other rotational symmetry (e.g. 5-fold) is impossible in such a Bravais lattice, regardless of the lattice basis or the chosen rotation axis. This is also known as the text/html 2020-08-15T19:00:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/schachtmeister2?rev=1597518000&do=diff schachtmeister2 schachtmeister2 is a daemon for white- and blacklisting specified ISPs, hosting providers and so on. It was created for the Der Bunker Tremulous server to combat malicious players evading bans. The source code is available here. The daemon works by looking up a given IP address in WHOIS databases and reverse text/html 2021-08-01T19:19:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://redman.xyz/doku.php/start?rev=1627845540&do=diff Welcome! Welcome to my personal website. I'm Paweł Redman, known online as “enneract,” a programmer and a former Optics student. This wiki serves both as my personal blog and a library for interesting things, relating to science and programming, that I've bothered to write down.