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quaternion-algebra

Abstract math for quaternion algebra (hypercomplex numbers ℍ). USE FOR: implementing quaternion multiplication (Hamilton product, non-commutative); conjugate, norm, and inverse; unit quaternions on S³ as double cover of SO(3); rotating 3D vectors with quaternions; understanding why q and −q represent the same rotation; normalizing after operations; constructing rotation quaternions from axis-angle. DO NOT USE FOR: converting between rotation representations (use 3d-rotation-theory); slerp/lerp interpolation (use interpolation-on-manifolds); basic vector cross/dot products (use vector-algebra).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

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

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  • SKILL.md2.4 KB
  • references/formulas.md2.6 KB
  • references/numerical-stability.md2.0 KB

SKILL.md(원문)

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Quaternion Algebra

Structure

A quaternion q = (x, y, z, w) = xi + yj + zk + w where i, j, k are imaginary units.

Also written as q = (v, w) with vector part v = (x, y, z) and scalar part w.

i² = j² = k² = ijk = −1
ij = k,  jk = i,  ki = j
ji = −k, kj = −i, ik = −j

Core Operations

OperationFormula
Addition(x₁+x₂, y₁+y₂, z₁+z₂, w₁+w₂) — component-wise
Conjugateq* = (−x, −y, −z, w)
Norm‖q‖ = √(x²+y²+z²+w²)
Norm squared‖q‖² = x²+y²+z²+w²
Scalar multiplykq = (kx, ky, kz, kw)

Hamilton Product (Non-Commutative)

q₁ · q₂ = (w₁w₂ − x₁x₂ − y₁y₂ − z₁z₂,
            w₁x₂ + x₁w₂ + y₁z₂ − z₁y₂,
            w₁y₂ − x₁z₂ + y₁w₂ + z₁x₂,
            w₁z₂ + x₁y₂ − y₁x₂ + z₁w₂)

q₁q₂ ≠ q₂q₁ in general. Order matters for composed rotations.

Inverse & Division

q⁻¹ = q* / ‖q‖²

For unit quaternions: q⁻¹ = q* (conjugate = inverse).

Unit Quaternions

‖q‖ = 1. Lives on S³ ⊂ ℝ⁴. Every unit quaternion represents a 3D rotation. Map S³ → SO(3) is 2-to-1: q and −q encode the same rotation.

Rotating a Vector

p' = q · (0, p) · q⨉ (pure quaternion sandwich; extract x,y,z from result)

Reference Files

FileLoad When
references/formulas.mdFull Hamilton product derivation, double-cover proof, rotation construction
references/numerical-stability.mdNormalization drift, dot product sign, re-normalization strategies

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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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