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Bezier Quadratic

bezier_quadratic
Read-onlyIdempotent

Point on a quadratic Bezier at t, as an exact fraction. (0,0), (1,1), (2,0) at one half is (1, 1/2). Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/bezier-quadratic

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "points": "<points>",
      "t": "<t>"
    },
    "name": "bezier_quadratic"
  }
}

Input Schema

NameRequiredDescriptionDefault
tYes
pointsYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A3.7/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare read-only, idempotent, non-destructive behavior, and the description adds meaningful commercial/transport context: the tool costs $0.001 USDC per successful call via x402 on Solana and is also reachable over HTTPS. It does not discuss payment failure behavior, rate limits, or other operational details, but it goes well beyond what the annotations provide.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is three compact sentences: purpose and example first, followed by pricing and the HTTPS endpoint. Every sentence contributes useful information and there is no filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

The description covers the output format through 'as an exact fraction' and the example, and annotations handle safety semantics. However, the missing details about t's accepted string format and valid range matter for correct invocation, and there is no output schema to fall back on.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

With 0% schema description coverage, the description must carry parameter meaning. The example '(0,0), (1,1), (2,0) at one half is (1, 1/2)' clarifies that points are three 2D control points and t is the Bezier parameter, but it does not specify the accepted t format, range, or string syntax despite t being a string in the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific operation: compute a point on a quadratic Bezier at parameter t, returned as an exact fraction, with a concrete example. It implicitly separates itself from bezier_cubic by saying 'quadratic' and from derivative/tangent/split by specifying a point at t, but it does not explicitly name or contrast those siblings.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The intended use is implied by the mathematical description and example, but there is no explicit guidance on when to choose this over bezier_cubic, bezier_derivative, bezier_tangent, or bezier_split. No exclusions or alternative-selection advice are given.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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