# GRAPH 3D

> Plot a formula in three dimensions, then sell the same render to agents. Surfaces, parametric surfaces, 3D curves, solids of revolution, point clouds. Sliders appear for any parameter you name. 8 colour maps, contour bands, animation, 28-graph gallery. WebGL preview plus vector SVG export from the engine the priced render app-tool runs server-side (1 morsel, on EXCHANGE with ODPS v4.1). EN/FI, light/dark, no sign-in needed. This document tells an agent how to call it.

## Installation

Nothing to install. This app runs on an AIMEAT node and is reachable two ways.

Over MCP — attach any MCP-capable client to `https://aimeat.io/v1/mcp` (OAuth 2.1), then:

```
    owner:  happydude500001
    app_id: graph.html        (not "graph")

aimeat_app_tools_get   { owner: "happydude500001", app_id: "graph.html" }
```

Over HTTP — get an identity through the RFC 8628 device flow described at `https://aimeat.io/auth.md`, then
call the endpoints in `https://aimeat.io/v1/spec`.

## Configuration

- **Scopes.** The owner approves a scope set when they approve your agent. A call outside it
  answers 403 naming the scope, never an empty result.
- **Payment.** Priced tools answer 402 with the terms attached until a checkout for them completes;
  completing the checkout IS the invocation.
- **Schemas.** Every tool carries a full input and output schema in the manifest, so nothing has to
  be inferred from the app source: `https://aimeat.io/v1/apps/happydude500001/graph.html/webmcp`

## Usage

```
aimeat_app_tool_invoke {
  owner: "happydude500001",
  app:   "graph.html",
  tool:  "render",
  input: { ... }
}
```

Available tools: `render`, `evaluate`, `presets`.

## What this app does

# GRAPH 3D

## What this is

A 3D plotter. Give it a formula and a domain and it returns a finished 3D graph as a self-contained SVG: surfaces z=f(x,y), parametric surfaces in (u,v), 3D curves in t, solids of revolution and point clouds. Rendering is deterministic and offline — no external calls, and nothing about a request is stored.

## Buy a render

app-tool `render` on happydude500001/graph.html — 1 morsel per call.
MCP: aimeat_app_tool_invoke { "app": "happydude500001/graph.html", "tool": "render", "input": { "kind": "surface", "formula": "sin(x)*cos(y)", "domain": { "x": [-6,6], "y": [-6,6] }, "colormap": "viridis" } }
The result carries `svg` (the complete image), `stats` (min/max/mean of the plotted value) and the resolved `spec`.

## Free companions

- `POST /v1/ext/graph3d/presets` — the 28-graph gallery plus the full formula grammar render accepts (kinds, variables, constants, 38 functions, styles, colour maps, limits). Read this before composing a request by hand.
- `POST /v1/ext/graph3d/evaluate` — the same formula sampled to numbers instead of pixels: the grid, min, max, mean and where the extremes sit.

## Formula grammar

Variables x y z u v t per kind, plus any name you pass in `params`, plus `time` for animation frames. Constants pi, e, tau, phi. Operators + - * / % ^ with implicit multiplication (2x, 3(x+1), sin(x)cos(y)). Functions: sin cos tan asin acos atan atan2 sinh cosh tanh exp log ln log2 log10 sqrt cbrt abs sign floor ceil round trunc min max pow hypot mod clamp step smoothstep mix sinc gauss saw tri square fract.

## Options

kind: surface | curve | parametric | revolution | points. style: solid | solid-wire | wireframe | contour | points. colormap: viridis | plasma | magma | coral | ice | terrain | fire | mono. theme: light | dark | transparent. view: { azimuth, elevation } in degrees. resolution up to 72 for surfaces, 4000 samples for curves. width/height 200-2400. format: svg (default) | dataUri | both.

## Gallery

- `ripple` (classic, surface) — Radial ripple
- `saddle` (classic, surface) — Saddle
- `egg-crate` (classic, surface) — Egg crate
- `monkey-saddle` (classic, surface) — Monkey saddle
- `paraboloid` (classic, surface) — Paraboloid
- `gaussian` (classic, surface) — Gaussian bell
- `mexican-hat` (waves, surface) — Mexican hat
- `interference` (waves, surface) — Two-source interference
- `standing-wave` (waves, surface) — Standing wave (animate t)
- `ripple-decay` (waves, surface) — Decaying ripple (animate t)
- `sinc2d` (waves, surface) — Two-dimensional sinc
- `checker-wave` (waves, surface) — Beat pattern
- `torus` (shapes, parametric) — Torus
- `sphere` (shapes, parametric) — Sphere
- `mobius` (shapes, parametric) — Möbius strip
- `klein` (shapes, parametric) — Klein bottle (figure-8)
- `shell` (shapes, parametric) — Sea shell
- `trefoil` (shapes, curve) — Trefoil knot
- `helix` (shapes, curve) — Helix
- `lissajous` (shapes, curve) — Lissajous 3D
- `vase` (shapes, revolution) — Vase of revolution
- `horn` (shapes, revolution) — Gabriel horn
- `ackley` (analysis, surface) — Ackley function
- `rosenbrock` (analysis, surface) — Rosenbrock valley
- `himmelblau` (analysis, surface) — Himmelblau
- `rastrigin` (analysis, surface) — Rastrigin
- `complex-mod` (analysis, surface) — Modulus of z² − 1
- `normal-mix` (analysis, surface) — Two-cluster density

Pass `{ "preset": "<id>" }` to render one; any other field you send overrides that preset.


## Agent affordances

- Act — WebMCP tool listing for this app: https://aimeat.io/v1/apps/happydude500001/graph.html/webmcp
- Learn — skills bound to this app: https://aimeat.io/v1/apps/happydude500001/graph.html/skills
- App catalog on this node (this app: happydude500001/graph.html): https://aimeat.io/app-catalog.html
- Register an agent on this node (RFC 8628 device flow): https://aimeat.io/auth.md


## Where the rest is

- [llms.txt](https://graph.apps.aimeat.io/llms.txt) · [Site map](https://graph.apps.aimeat.io/sitemap.md)
- [Node manual](https://aimeat.io/llms-full.txt) · [Node glossary](https://aimeat.io/v1/glossary.md) · [OpenAPI](https://aimeat.io/v1/spec)