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coordinate-system-conversions

Abstract math for converting between 2D and 3D coordinate systems. USE FOR: Cartesian to/from polar (r, θ); Cartesian to/from spherical (r, azimuth, polar/colatitude); azimuth vs. elevation vs. colatitude conventions; canonical range enforcement after conversion; precision near the origin and poles; choosing azimuth reference direction. DO NOT USE FOR: angle unit conversions (use angles-and-circular-arithmetic); geodetic (lat/lon) coordinates (use geodetic-coordinate-bounds); rotation representations (use 3d-rotation-theory).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

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

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포함된 파일(3)

  • SKILL.md2.5 KB
  • references/formulas.md2.1 KB
  • references/numerical-stability.md1.9 KB

SKILL.md(원문)

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Coordinate System Conversions

2D: Cartesian ↔ Polar

DirectionFormulas
Cartesian → Polarr = √(x²+y²); θ = atan2(y, x)
Polar → Cartesianx = r cos θ; y = r sin θ
  • r ≥ 0 always; r = 0 at origin (θ undefined)
  • θ ∈ (−π, π] from atan2; reduce to [0, 2π) for canonical polar form
  • Azimuth measured CCW from positive x-axis

3D: Cartesian ↔ Spherical

Physics convention (ISO 80000-2): r, polar angle θ from z-axis (colatitude), azimuth φ from x-axis

DirectionFormulas
Cartesian → Sphericalr = √(x²+y²+z²); θ = arccos(z/r); φ = atan2(y, x)
Spherical → Cartesianx = r sin θ cos φ; y = r sin θ sin φ; z = r cos θ

Canonical ranges: r ≥ 0, θ ∈ [0, π], φ ∈ [0, 2π) or (−π, π]

Convention Table (3D)

Name1st angle2nd angleUsed in
Physics (ISO)θ = colatitude from zφ = azimuth from xMath, physics
Geographylat = elevation from equatorlon = azimuth from meridianMaps, geodesy
This codebasepolar = colatitude from zazimuth = CCW from xSpherical coords

⚠ Azimuth and polar are always named explicitly — never assume which is which.

Singular Points

PointConditionIssue
Originr = 0θ and φ undefined
North/South poleθ = 0 or θ = πφ undefined (infinite azimuths map to same point)

3D: Cartesian ↔ Cylindrical (reference)

ρ = √(x²+y²);   φ = atan2(y, x);   z = z
x = ρ cos φ;    y = ρ sin φ;        z = z

Reference Files

FileLoad When
references/formulas.mdDerivations, Jacobians, differential area/volume elements
references/numerical-stability.mdNear-origin, near-pole precision, atan2 edge cases, r near zero

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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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