#computational geometry
124 related articles
·3 min
The Longest Straight-Line Path on Earth: How the 32,089 km Route Without Touching Land Was Calculated
How long is the longest straight-line path on Earth? The 32,089 km sea route from Pakistan to Kamchatka and the 11,241 km land route from Lianyungang to Lisbon were found using great circle paths and branch and bound algorithms.
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·4 min
DeepSeek V4 Pro Hands-On Review: The Precision King That Tops Both CFD and FPV Benchmarks
Bilibili creator benchmarks DeepSeek V4 Pro against top LLMs across 6 physics simulation tasks. DeepSeek scores 9 in both CFD and FPV, earning the title of precision king.
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·2 min
Autonomous Mathematical Discovery by AI: How Multi-Agent Open Worlds Are Reshaping the Research Paradigm
Exploring a new paradigm of autonomous mathematical discovery by AI in multi-agent open-world environments—from conjecture generation and collaboration to formal verification.
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·3 min
WorldClaw: An AI Framework That Generates Explorable 3D Open Worlds from a Single Sentence
WorldClaw is Tencent's 3D world generation framework that transforms a single sentence into explorable, editable open worlds using planning agents and self-inspection mechanisms.
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·4 min
GreenTech ML Project Selection: An In-Depth Comparison of Energy Forecasting, Optimization, and Anomaly Detection
In-depth comparison of three end-to-end ML projects in GreenTech: smart energy forecasting, building energy optimization, and energy prediction with anomaly detection—analyzed by technical difficulty, business value, and MLOps completeness.
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·4 min
AI-Assisted Proof of Crouzeix's Conjecture: A Doctor Uses GPT to Crack a 20-Year-Old Math Problem
A Beijing neurosurgeon used GPT to unexpectedly provide a proof approach for the 20-year-old Crouzeix conjecture. Explore this cross-disciplinary breakthrough and AI's role in math.
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·4 min
WorldCloud: An Agentic Framework for Generating Explorable 3D Open Worlds from a Single Sentence
Deep dive into WorldCloud's technical architecture: how multi-agent collaboration generates large-scale, editable, explorable 3D open worlds from a single natural language description.
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·3 min
Ornith 1.5 35B Hands-On: Q4 vs Q8 Quantization Comparison — Which One Is Worth Running?
In-depth comparison of Ornith 1.5 35B-A3B Q4KM vs Q8 quantization across browser OS, FPS games, 3D modeling and more, helping consumer hardware users choose the right version.
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·3 min
AI Can Understand but Struggles to Innovate: The Gap Between Deep Comprehension and Creativity
Prime Intellect research reveals LLMs' core paradox: models deeply understand concepts yet rarely produce new ideas. Exploring the gap between AI comprehension and creativity.
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·1 min
Training DMC Detection with Purely Synthetic Data: Achieving 100 FPS Real-Time Inference on CPU
How to train a YOLOX model for Data Matrix Code detection using only synthetic data, achieving 100 FPS inference on an Intel i5 CPU via ONNX Runtime + OpenVINO — a GPU-free industrial edge solution.
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·3 min
The Ham Sandwich Theorem: The Mathematical Mystery of Perfectly Bisecting Any Shape with a Single Cut
The Ham Sandwich Theorem proves any shape can be precisely bisected with a single cut. Learn how the Intermediate Value Theorem and topology guarantee a perfect dividing line always exists.
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·3 min
Entropic Scree: Reconstructing PCA Dimensionality Reduction by Replacing Variance with Information Entropy
Entropic Scree is a new information-theory-based dimensionality reduction method that replaces linear variance with entropy to estimate intrinsic data dimensions, with applications in neural network bottleneck design.
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·2 min
Mathematics in the Age of AI: How Proof Assistants and Machine Intelligence Are Reshaping Mathematical Research
Exploring how AI is transforming mathematics: from formal verification with Lean proof assistants to ML-driven conjecture generation, analyzing the evolving role of mathematicians and the future of math education.
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·3 min
Is the CLIP Vision Encoder Becoming a Bottleneck for VLMs? The Multimodal Architecture Debate
Analyzing CLIP vision encoder limitations in modern VLMs, exploring shortcomings in counting and spatial reasoning, plus alternatives like hybrid encoders and high-resolution processing.
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·3 min
Spherical Fourier Transform: How to Build 3D Rotation-Equivariant AI Models
Deep dive into how Spherical Fourier Transform and Spherical Harmonics enable 3D rotation-equivariant AI. From Spherical CNN architecture to applications in panoramic imaging, weather prediction, and protein structure prediction.
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·3 min
DeepSeek V4 Pro Hands-On: 5 Complex Coding Projects for Just $0.73
Hands-on test of DeepSeek V4 Pro 0813: completed 5 complex projects including SVG animation, 3D games, spaceship modeling, and SwiftUI native development via Claude Code API for just $0.73 total.
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·3 min
Galileo's Square-Cube Law: Why Giants Are Physically Impossible
Galileo's 1638 Square-Cube Law reveals why giants can't exist: volume grows as the cube while area grows as the square, creating fundamental limits on scaling in engineering, biology, and AI.
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·4 min
Pole of Inaccessibility: How to Find the Most Remote Coordinate in the San Gabriel Mountains Using GIS Algorithms
What is a Pole of Inaccessibility? Learn how to use GIS tools and spatial algorithms to calculate the most remote coordinate in the San Gabriel Mountains, covering OpenStreetMap data, R-tree indexing, and grid sampling optimization.
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·3 min
Visualizing MLPs with VRML: A 3D Neural Network Demo of the XOR Problem
Explore how VRML 3D visualization demonstrates a multi-layer perceptron (MLP) solving the classic XOR problem, showing weight changes, activation propagation, and gradient descent in neural networks.
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·3 min
Mighty Camera Board: Real-Time SLAM and Obstacle Avoidance with a Single Camera + IMU
How Mighty Camera Board achieves real-time SLAM and obstacle avoidance using only a single global shutter camera and IMU, enabling collision avoidance and autonomous navigation for robots and drones.
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