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interpolation-on-manifolds

Abstract math for interpolating angles, vectors, and quaternions on curved manifolds. USE FOR: implementing Lerp (linear interpolation) for vectors; Nlerp (normalized lerp) for directions; Slerp (spherical linear interpolation) for quaternions and unit vectors; shortest-path sign flip when dot product is negative; choosing between Lerp/Nlerp/Slerp; angular lerp with wrap-around. DO NOT USE FOR: quaternion arithmetic (use quaternion-algebra); rotation representation conversions (use 3d-rotation-theory); angle unit conversions (use angles-and-circular-arithmetic).

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

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

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  • SKILL.md2.3 KB
  • references/formulas.md2.0 KB
  • references/numerical-stability.md1.9 KB

SKILL.md(원문)

설치하기 전에 에이전트에게 전달되는 지시 내용을 확인할 수 있습니다.

Interpolation on Manifolds

Lerp (Linear Interpolation)

lerp(a, b, t) = (1−t)·a + t·b Result NOT on unit sphere; constant Euclidean velocity.

Nlerp (Normalized Lerp)

nlerp(a, b, t) = normalize(lerp(a, b, t)) Cheaper than Slerp; breaks down at antipodal inputs.

Slerp (Spherical Linear Interpolation)

Great-circle arc at constant angular velocity:

Ω = arccos(a · b)
slerp(a, b, t) = sin((1−t)Ω)/sin(Ω) · a  +  sin(tΩ)/sin(Ω) · b

Fall back to Lerp when Ω ≈ 0. Undefined for antipodal inputs (Ω = π).

Shortest-Path Flip

For quaternions, q and −q represent the same rotation. If a · b < 0, interpolation takes the long path (> 180°). Fix:

if (a · b < 0):  b = −b    (before calling slerp/nlerp)

Which to Use

SituationMethodReason
Arbitrary vectors in ℝⁿLerpCorrect; no manifold curvature
Unit vectors (approximate)NlerpFast; adequate for small angles
Unit quaternions (smooth)SlerpConstant angular velocity
Unit vectors (exact)SlerpCorrect geodesic arc
Angles with wrappingAngular lerpHandles 350°↔10° via shortest arc

Angular Lerp (Wrap-Aware)

delta = reduce(b − a, Full)          // shortest signed difference ∈ [−Full/2, Full/2)
result = a + t · delta

This ensures the interpolation takes the short way around.

Reference Files

FileLoad When
references/formulas.mdSlerp derivation, degenerate cases, angle lerp proof
references/numerical-stability.mdNear-identical inputs, antipodal inputs, sin(Ω)→0 handling

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3d-rotation-theory

무료

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

agent-graph-orchestration

무료

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

agent-harness-logs

무료

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

angles-and-circular-arithmetic

무료

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

claude-code-custom-agents

무료

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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