Ein Podcast von und mit Kedo Rittershofer. Von manipulativer Triangulation spricht man, wenn uns jemand in einen Konflikt oder ein Problem verwickelt, an dem wir nicht direkt beteiligt sind. Dies kann für den dritten im Bunde zu einer starken psychischen Belastung werden. Es ist nicht selten eine Form der passiv-aggressiven Kommunikation, bei der man eine dritte Person einbezieht, um sich einen Vorteil zu verschaffen. Warum man so etwas macht und wie man sich als Dritter im Bunde dagegen abgrenzen kann, erfährst Du in dieser Podcastfolge.
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Urheber-Prinzip Podcast 2023

#217 Der manipulierte Dritte: Triangulation

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delaunay triangulation and voronoi graphs pdf free

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Fun fact: This started in discord with the question "how to solve nearest point fast without point location + voronoi? (not using kd-tree)", the topic shifted to voronoi/delaunay then I realized "Well, you can use fortune's algo with some mutant set probably (to make the implementation easier/shorter). Someone needs to code it tho. Mutant set as something like that CHT set hack".


Overall I trust in the rotation more than I don't trust this and you could theoretically run incremental delaunay (the O(flips + N) algorithm that you can run from a starting triangulation) from the triangulation you get from this because in case of any misbehavior due to precision, as long as it's not in the lower_bound thing, the result should be a few flips away from a delaunay triangulation (aka close enough to delaunay if we don't use int128 or something with absurd precision to check for flips which is, if you ask me, good enough).


A Voronoi diagram can also be constructed without the delaunay triangulation. Given a set of points, we want to partition and assign a portion of the plane to each one of those points, in such a manner that each position in a given region is closer to that point than any other:


I suppose, the voronoi quality of 'each vertex is equidistant from the 3 closest points' means that any matching triangulation is a delaunay triangulation (there is no point closer than the closest points), but I am hoping for something more... in-depth? Is there such a thing?



How is Qhull used?
 
Google Scholar, and CiteSeer references to Qhull 
 Google Qhull, Images, Books, Patents, Newsgroups, and Who is Qhull? 
MATLAB uses Qhull for their n-d computational geometry functions: convhulln delaunayn griddatan voronoin. 
 
The geometry package of R provides Qhull in R. 
GNU Octave includes Qhull for computational geometry. 
Mathematica's Delaunay interface qh-math. 
The scipy.spatial of SciPy is implemented with Qhull. It includes support for Delaunay triangulations.

Introduction

 
Gregorius' talk on implementing Quickhull, Lloyd's QuickHull3D in Java, and Newbold's Waterman polyhedra 
Fukuda's introduction to convex hulls, Delaunay triangulations, Voronoi diagrams, and linear programming
 
LEDA Guide to geometry algorithms 
MathWorld's Computational Geometry from Wolfram Research 
Skiena's Computational Geometry from his 
Algorithm Design Manual
. 
Stony Brook Algorithm Repository, computational geometry


Qhull Documentation and Support

 
Manual for Qhull and rbox 
 
Quick reference to Programs and Options 
When to use Qhull 
Description of Qhull 
Imprecision in Qhull 
qconvex -- convex hull 
qdelaunay -- Delaunay triangulation 
qvoronoi -- Voronoi diagram 
qhalf -- halfspace intersection about a point 
rbox -- generate point distributions 

 
README.txt - installation instructions
 
COPYING.txt - copyright notice
 
REGISTER.txt - registration
 
Geomview for visualizing Qhull 
FAQ - frequently asked questions about Qhull
 
Changes.txt - change history 
 
Qhull code 
Performance of Qhull 
Index to Qhull Functions 
 
Qhull build systems 
Send e-mail to qhull@qhull.org 
 
Report bugs to qhull_bug@qhull.org

Related URLs

 
Amenta's directory of computational geometry software 
 
BGL Boost Graph Library provides C++ classes for graph data structuresand algorithms, 
CGAL and Ledalibraries for writing computationalgeometry programs and other combinatorial algorithms 
Clarkson's hull program with exact arithmetic for convex hulls, Delaunay triangulations, Voronoi volumes, and alpha shapes. 
 
Erickson's Computational Geometry Pages and Software 
Fukuda's cdd program for halfspace intersectio

Delaunay Triangulation And Voronoi Graphs Pdf Free

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🎧 The New Of The Tower
Welcome to a new, underground, dark world...

🎭 Musical Style & Artistic Evolution

🚀 Avant-Garde Dance Music Without Borders
The New Of The Tower is an independent, self-taught project that fearlessly pushes the limits of dance music with a unique fusion of genres. Officially described as a mix of dark techno, tech-house, electro, and experimental pop, it also incorporates elements of trap, punk, and even classical music.

In practice, each track oscillates between club anthems and conceptual sonic experiences. For instance, “Velvet Guillotine” (2025) is a hypnotic techno hymn built on heavy percussion and distorted vocals—a true “surreal sonic ritual” under neon lights.

The sound is always matched by a cinematic, underground aesthetic: strobe lights, cyberpunk visuals, and immersive atmospheres define every release.

🌍 Eclectic Influences & Genre Alchemy

The New Of The Tower draws from a wide range of sonic traditions:

🏴‍☠️ Dark techno and industrial groove infused with gothic textures and anarchic punk (e.g., “BRUTAL!!” — a chaotic journey of distortion and rebellion).

🌍 Afro-Tech House meets rock guitars à la AC/DC in “Love Letters” (124–126 BPM).

👺 “Masquerade of Bass” blends melodic techno, dark psytrance, and retro synth-pop.

💃 Spanish-language tracks like “Marionetas” and “Vidas Rotas” fuse flamenco sorrow with trap beats and deep 808s.

🎷 “2:59 AM” evokes Amy Winehouse-inspired jazzy cloud-rap, while “She Danced Through Storms” travels through deep house and jazz fusion with a cinematic touch.

🧊 “Still Echoing” merges melodic trance with nostalgic 80s synth-pop.

🧬 Each track is a bold cross-genre experiment: from industrial club bangers to dark electronic ballads, always rich in texture and emotion.

🎛️ Sonic Palette: Instruments & Effects

🎹 Synths & Melodies
Analog pads & leads (often vocoder-enhanced) create retrofuturistic atmospheres.
Punk-style distorted guitars and 80s synthwave textures bring cinematic depth.

🥁 Percussion & Rhythms
Hard techno kicks, metallic hi-hats, tribal drums, and trap-style 808s.
Layered acoustic and electronic elements make for dynamic and precise beats.

🌀 FX & Processing
Rich in glitchy clips, VHS noise, deep delays, and reverb-soaked vocals.

Examples: “Love Letters” is drenched in lo-fi and VHS textures; “4 Malos Polvos” features glitchy ambient layers and emotional auto-tune.

🎨 Each sound is carefully crafted to contribute to a vivid, cinematic soundscape.

🎤 Vocal Treatments: A Sonic Chameleon

Vocals range from:
🎙️ Melodic singing (English & Spanish)
🔥 Punk shouting & spoken rap
🤖 Vocoded retro textures (“Still Echoing”)
💔 Melancholic auto-tuned lines (“4 Malos Polvos”)
💣 Confessional, emotionally intense deliveries
🗣️ The voice becomes another instrument of emotion, soaked in effects like reverb, delay, filters—ranging from ghostly whispers to ecstatic screams.

🌑 Emotional Climate & Storytelling

The overall emotional tone is dark, introspective, and visceral.

Themes revolve around:
💘 Passion, heartbreak, rebellion
🧠 Subconscious states & urban alienation
🕯️ Ritualistic, trance-like experiences (e.g., “Velvet Guillotine”)
🌆 Social suffering (“Marionetas”, “Vidas Rotas”)
😈 Raw eroticism & shame (“4 Malos Polvos”: “each drop is a stab disguised as a caress”)
🎞️ Romantic melancholy in cinematic settings (“2:59 AM”, “She Danced Through Storms”)
🎬 Each track unfolds like an emotional chapter, offering catharsis, vulnerability, and mystery.

📽️ Conceptual Artistry & Vision

The New Of The Tower is not just music—it's an immersive audiovisual concept.

💀 Explores themes of dystopia, poverty, guilt, rebellion
🏙️ Brutalist club visuals, cyberpunk aesthetics
🕯️ Emotional depth with non-commercial intent
🎭 “4 Malos Polvos” = a “dark confession for love sinners,” cinematic and raw
🌀 Each release = a journey through shadow and rhythm
🕺💀 Dance meets darkness—a kind of electronic film noir where each beat tells a deeper truth.

📈 Style Evolution: From EDM to Darkness

🟢 2019–2022: EDM & electro-pop beginnings (Feel EP, “You And Me” — catchy and bright)

🟡 2024: Transition into melodic techno (“Not Living Without You”)

🔴 2025–Present: Shift to dark techno, darkwave, flamenco-trap, and experimental storytelling (“Velvet Guillotine”, “Marionetas”)

🎭 From mainstream dance-pop to raw, conceptual electronic music—always evolving, always fearless.

🎼 Comparable Artists & Influences

🧩 The New Of The Tower resonates with:

🧨 Brutalismus 3000 (techno-punk dystopia)
👾 Perturbator (dark synthwave)
🌘 Mind Against / Recondite (melodic techno & melancholia)
🎤 Boy Harsher, Massive Attack (dark vocals, trip-hop moods)
🔥 Anyma (techno emotion), Latin trap/fusion for its flamenco-trap leanings
🌌 But ultimately, it defines its own world—one built from dark techno, darkwave, nu-jazz, and trap-rock fusion.

🔍 Sources
All analysis is based on official content from:
📻 SoundCloud & YouTube, where each track’s genre, BPM, and atmosphere are detailed, along with the project’s self-described tags and narratives.

📎 Verified by direct observation of mixes like:

“Velvet Guillotine”

“Marionetas”

“4 Malos Polvos”

“Still Echoing”

“Love Letters”

“2:59 AM”

and more.

🎧 The New Of The Tower: Not just a sound, but a dark, immersive, and emotional experience.
Let the beats confess what words cannot.

New tracks tagged #triangulation