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reference-ellipsoids

Abstract math for reference ellipsoids used in geodesy. USE FOR: computing semi-minor axis from flattening; eccentricity and eccentricity squared; first and second eccentricity; arithmetic mean radius; radii of curvature in the meridian and prime vertical; ellipsoid surface area; ellipsoid volume; understanding WGS84/GRS80 parameters; implementing Ellipsoid<T> types. DO NOT USE FOR: geodetic coordinate bounds (use geodetic-coordinate-bounds); datum transformations (use helmert-datum-transformation); map projections.

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NetFabric/NetFabric.Numerics스타 36(GitHub 36 + cccskills 0)

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  • SKILL.md2.5 KB
  • references/formulas.md1.9 KB
  • references/numerical-stability.md1.6 KB

SKILL.md(원문)

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Reference Ellipsoids

Definition

An ellipsoid of revolution is generated by rotating an ellipse around its polar axis. Defined by two independent parameters (choose any two of a, b, f, e):

ParameterSymbolDefinition
Semi-major (equatorial) radiusaRadius at equator
Semi-minor (polar) radiusbRadius at poles
Flatteningff = (a−b)/a
Eccentricityee = √(f(2−f)) = √(1−b²/a²)
Eccentricity squarede²e² = f(2−f) = 1−b²/a²

Derived Parameters

b   = a(1−f)
e²  = f(2−f)
e   = √(e²)
e'² = e²/(1−e²)             (second eccentricity squared)
n   = (a−b)/(a+b) = f/(2−f) (third flattening, used in Helmert series)

Radii of Curvature

NameSymbolFormulaAt
Meridian radius of curvatureMa(1−e²) / (1−e²sin²φ)^(3/2)Latitude φ
Prime vertical radiusNa / √(1−e²sin²φ)Latitude φ
At equator (M)—a(1−e²)φ = 0
At pole (M)—a/√(1−e²)φ = 90°
At equator (N)—aφ = 0
At pole (N)—a/√(1−e²)φ = 90°

Global Metrics

Arithmetic mean radius R₁ = (2a + b) / 3
Surface area S = 2πa² (1 + (1−e²)/e · atanh(e))
Volume V = (4/3)π a² b

Standard Ellipsoids

Namea (m)1/f
WGS 846 378 137.0298.257 223 563
GRS 806 378 137.0298.257 222 101
Airy 18306 377 563.396299.324 964 6
Clarke 18666 378 206.4294.978 698 2
International 19246 378 388.0297.0
Bessel 18416 377 397.155299.152 812 8

Reference Files

FileLoad When
references/formulas.mdSurface area derivation, curvature proof, series expansions
references/numerical-stability.mdEccentricity near zero, curvature at poles, overflow for large a

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Abstract math for 3D rotation representations and conversions. USE FOR: understanding axis-angle representation; Euler angles (yaw/pitch/roll, convention choices); rotation matrices (SO(3)); quaternion-based rotation; converting between representations; identifying and avoiding gimbal lock; composing rotations; half-angle formula; right-hand rule. DO NOT USE FOR: quaternion arithmetic details (use quaternion-algebra); slerp/lerp interpolation (use interpolation-on-manifolds); coordinate system definitions (use coordinate-system-conversions).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

NetFabric/NetFabric.Numerics362026년 8월 10일 업데이트

Design and scaffold multi-agent squads/swarms using the graph orchestration pattern (nodes = agents, edges = dependencies/data flow). USE FOR: designing a coordination topology for a multi-agent squad (sequential pipeline, parallel fan-out/aggregation, branching, feedback loop, cyclic); building an orchestrator agent that delegates to specialist agents; setting up an adversarial/tribunal code or document review with independent reviewers; scaffolding a squad's agent files for a target coding-agent harness (e.g. Copilot CLI or Claude Code custom agents). DO NOT USE FOR: authoring a single agent's frontmatter/prompt body (use copilot-cli-custom-agents, claude-code-custom-agents, or the target harness's own skill); SKILL.md authoring (use create-skill); ad-hoc multi-agent chat with no explicit topology.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

NetFabric/NetFabric.Numerics362026년 8월 10일 업데이트

Find, inspect, query, redact, and troubleshoot logs, transcripts, sessions, and OpenTelemetry data from coding-agent harnesses on Windows, macOS, Linux, and WSL. USE FOR: GitHub Copilot in VS Code; Copilot CLI; Claude Code; OpenAI Codex; Gemini CLI; OpenCode; Cursor, Windsurf, Kiro, or other VS Code-family editors; locating log files; diagnosing tool or model failures; correlating turns, subagents, and tool calls; querying JSONL, plaintext, or SQLite without spending model tokens; preparing sanitized diagnostics. DO NOT USE FOR: application logs unrelated to coding agents; uploading raw logs; treating unstable transcript schemas as public APIs.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

NetFabric/NetFabric.Numerics362026년 8월 10일 업데이트

agents-md

무료

Author and maintain AGENTS.md files — the open, tool-agnostic format for giving coding agents project context. Use when: creating AGENTS.md; writing an agent instructions file; root or nested AGENTS.md for monorepos; migrating CLAUDE.md, AGENT.md, .cursor/rules, or copilot-instructions.md to AGENTS.md; greenfield project setup before code exists; brownfield onboarding for an existing codebase; documenting build/test/lint commands, code style, PR/commit conventions, and security considerations for agents; AGENTS.md discovery and precedence rules. Works for any language, framework, or project size. DO NOT USE FOR: authoring SKILL.md skill files (use create-skill); APM package/plugin authoring (use apm-producer); language-specific style rules (use language skills e.g. csharp-best-practices).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

NetFabric/NetFabric.Numerics362026년 8월 10일 업데이트

Abstract math for angle measurement, unit systems, and circular arithmetic. USE FOR: implementing angle types; converting between degrees/radians/gradians/revolutions; reducing angles to canonical range [0, Full); computing reference angles and quadrants; implementing safe modular arithmetic with negative inputs; angle addition and subtraction; classifying angles by sign and size. DO NOT USE FOR: trigonometric functions (use trigonometric-functions); coordinate conversions (use coordinate-system-conversions); interpolation (use interpolation-on-manifolds).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

NetFabric/NetFabric.Numerics362026년 8월 10일 업데이트

Create and maintain Claude Code custom subagents (.claude/agents/*.md files). USE FOR: authoring project (.claude/agents/) or user (~/.claude/agents/) subagent files; frontmatter fields (name, description, tools, disallowedTools, model, permissionMode, maxTurns, skills, mcpServers, hooks, memory, background, effort, isolation, color, initialPrompt); writing descriptions that drive automatic delegation and 'use proactively' phrasing; invoking subagents via natural language, @-mention, session-wide --agent, or the Agent tool; restricting which subagent types a coordinator can spawn with Agent(name1, name2); nested subagents and depth limits; built-in subagents (Explore, Plan, general-purpose, claude); troubleshooting a subagent that won't load or isn't invoked. DO NOT USE FOR: GitHub Copilot CLI custom agents (use copilot-cli-custom-agents); agent teams/teammates (a different, session-spanning feature); MCP server authoring; SKILL.md authoring (use create-skill).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

NetFabric/NetFabric.Numerics362026년 8월 10일 업데이트

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