Physics MCP Server

/** * Type definitions and schemas for plotting tools */ export interface Function2DParams { f: string; // Function expression x_min: number; x_max: number; samples?: number; title?: string; xlabel?: string; ylabel?: string; dpi?: number; width?: number; height?: number; } export interface Parametric2DParams { x_t: string; // x(t) expression y_t: string; // y(t) expression t_min: number; t_max: number; samples?: number; title?: string; xlabel?: string; ylabel?: string; dpi?: number; width?: number; height?: number; } export interface Field2DParams { fx: string; // x-component of field fy: string; // y-component of field x_min: number; x_max: number; y_min: number; y_max: number; grid_points?: number; plot_type?: "quiver" | "stream"; title?: string; xlabel?: string; ylabel?: string; dpi?: number; width?: number; height?: number; } export interface PlotResult { image_png_b64: string; image_svg?: string; csv_data?: string; x_range?: [number, number]; y_range?: [number, number]; samples?: number; } // JSON Schema definitions export const function2DSchema = { type: "object", properties: { f: { type: "string", description: "Function expression f(x)" }, x_min: { type: "number", description: "Minimum x value" }, x_max: { type: "number", description: "Maximum x value" }, samples: { type: "integer", description: "Number of sample points", default: 1000, minimum: 10 }, title: { type: "string", description: "Plot title" }, xlabel: { type: "string", description: "X-axis label", default: "x" }, ylabel: { type: "string", description: "Y-axis label", default: "f(x)" }, dpi: { type: "integer", description: "Image DPI", default: 100, minimum: 50 }, width: { type: "number", description: "Figure width in inches", default: 8 }, height: { type: "number", description: "Figure height in inches", default: 6 } }, required: ["f", "x_min", "x_max"] } as const; export const parametric2DSchema = { type: "object", properties: { x_t: { type: "string", description: "Parametric x(t) expression" }, y_t: { type: "string", description: "Parametric y(t) expression" }, t_min: { type: "number", description: "Minimum parameter value" }, t_max: { type: "number", description: "Maximum parameter value" }, samples: { type: "integer", description: "Number of sample points", default: 1000, minimum: 10 }, title: { type: "string", description: "Plot title" }, xlabel: { type: "string", description: "X-axis label", default: "x" }, ylabel: { type: "string", description: "Y-axis label", default: "y" }, dpi: { type: "integer", description: "Image DPI", default: 100, minimum: 50 }, width: { type: "number", description: "Figure width in inches", default: 8 }, height: { type: "number", description: "Figure height in inches", default: 6 } }, required: ["x_t", "y_t", "t_min", "t_max"] } as const; export const field2DSchema = { type: "object", properties: { fx: { type: "string", description: "X-component of vector field F_x(x,y)" }, fy: { type: "string", description: "Y-component of vector field F_y(x,y)" }, x_min: { type: "number", description: "Minimum x value" }, x_max: { type: "number", description: "Maximum x value" }, y_min: { type: "number", description: "Minimum y value" }, y_max: { type: "number", description: "Maximum y value" }, grid_points: { type: "integer", description: "Grid points per axis", default: 20, minimum: 5 }, plot_type: { type: "string", description: "Type of field plot", enum: ["quiver", "stream"], default: "quiver" }, title: { type: "string", description: "Plot title" }, xlabel: { type: "string", description: "X-axis label", default: "x" }, ylabel: { type: "string", description: "Y-axis label", default: "y" }, dpi: { type: "integer", description: "Image DPI", default: 100, minimum: 50 }, width: { type: "number", description: "Figure width in inches", default: 8 }, height: { type: "number", description: "Figure height in inches", default: 6 } }, required: ["fx", "fy", "x_min", "x_max", "y_min", "y_max"] } as const; export interface PhasePortraitParams { dx: string; // dx/dt expression dy: string; // dy/dt expression x_min: number; x_max: number; y_min: number; y_max: number; grid_points?: number; title?: string; xlabel?: string; ylabel?: string; dpi?: number; width?: number; height?: number; } export interface Surface3DParams { f: string; // z = f(x,y) expression x_min: number; x_max: number; y_min: number; y_max: number; samples?: number; title?: string; xlabel?: string; ylabel?: string; zlabel?: string; dpi?: number; width?: number; height?: number; } export interface Contour2DParams { f: string; // f(x,y) expression x_min: number; x_max: number; y_min: number; y_max: number; levels?: number; samples?: number; title?: string; xlabel?: string; ylabel?: string; dpi?: number; width?: number; height?: number; } export const phasePortraitSchema = { type: "object", properties: { dx: { type: "string", description: "dx/dt expression for the dynamical system" }, dy: { type: "string", description: "dy/dt expression for the dynamical system" }, x_min: { type: "number", description: "Minimum x value" }, x_max: { type: "number", description: "Maximum x value" }, y_min: { type: "number", description: "Minimum y value" }, y_max: { type: "number", description: "Maximum y value" }, grid_points: { type: "integer", description: "Grid points per axis", default: 20, minimum: 5 }, title: { type: "string", description: "Plot title" }, xlabel: { type: "string", description: "X-axis label", default: "x" }, ylabel: { type: "string", description: "Y-axis label", default: "y" }, dpi: { type: "integer", description: "Image DPI", default: 100, minimum: 50 }, width: { type: "number", description: "Figure width in inches", default: 8 }, height: { type: "number", description: "Figure height in inches", default: 6 } }, required: ["dx", "dy", "x_min", "x_max", "y_min", "y_max"] } as const; export const surface3DSchema = { type: "object", properties: { f: { type: "string", description: "3D surface function z = f(x,y)" }, x_min: { type: "number", description: "Minimum x value" }, x_max: { type: "number", description: "Maximum x value" }, y_min: { type: "number", description: "Minimum y value" }, y_max: { type: "number", description: "Maximum y value" }, samples: { type: "integer", description: "Grid samples per axis", default: 50, minimum: 10, maximum: 100 }, title: { type: "string", description: "Plot title" }, xlabel: { type: "string", description: "X-axis label", default: "x" }, ylabel: { type: "string", description: "Y-axis label", default: "y" }, zlabel: { type: "string", description: "Z-axis label", default: "z" }, dpi: { type: "integer", description: "Image DPI", default: 100, minimum: 50 }, width: { type: "number", description: "Figure width in inches", default: 10 }, height: { type: "number", description: "Figure height in inches", default: 8 } }, required: ["f", "x_min", "x_max", "y_min", "y_max"] } as const; export const contour2DSchema = { type: "object", properties: { f: { type: "string", description: "Function f(x,y) for contour plot" }, x_min: { type: "number", description: "Minimum x value" }, x_max: { type: "number", description: "Maximum x value" }, y_min: { type: "number", description: "Minimum y value" }, y_max: { type: "number", description: "Maximum y value" }, levels: { type: "integer", description: "Number of contour levels", default: 15, minimum: 5 }, samples: { type: "integer", description: "Grid samples per axis", default: 100, minimum: 20 }, title: { type: "string", description: "Plot title" }, xlabel: { type: "string", description: "X-axis label", default: "x" }, ylabel: { type: "string", description: "Y-axis label", default: "y" }, dpi: { type: "integer", description: "Image DPI", default: 100, minimum: 50 }, width: { type: "number", description: "Figure width in inches", default: 8 }, height: { type: "number", description: "Figure height in inches", default: 6 } }, required: ["f", "x_min", "x_max", "y_min", "y_max"] } as const; // Phase 5: Advanced Visualization Types export interface Volume3DParams { f: string; // SymPy-like expression in x,y,z x: [number, number] | [number, number, number]; // [min, max, steps?] y: [number, number] | [number, number, number]; z: [number, number] | [number, number, number]; mode?: "slices" | "isosurface"; iso_level?: number; // Used when mode='isosurface' emit_animation?: boolean; animate_axis?: "x" | "y" | "z"; fps?: number; format?: "mp4" | "webm" | "gif"; samples_cap?: number; allow_large?: boolean; } export interface AnimationParams { frame_expr: string; // Expression producing frame array or 2D function value at (x,t) x_range?: [number, number] | [number, number, number]; t_range: [number, number] | [number, number, number]; renderer?: "imshow" | "contour" | "line"; fps?: number; format?: "mp4" | "webm" | "gif"; dpi?: number; emit_frames?: boolean; emit_csv?: boolean; frames_cap?: number; allow_large?: boolean; } export interface InteractiveParams { expr: string; x_range?: [number, number] | [number, number, number]; controls: Array<{ name: string; min: number; max: number; step: number; default: number; }>; renderer?: "line" | "contour" | "surface"; grid_limit?: number; // produce at most N precomputed thumbnails } export interface VRExportParams { geometry: { vertices: number[][]; // Array of [x,y,z] coordinates faces: number[][]; // Array of vertex indices normals?: number[][]; // Optional normals colors?: number[][]; // Optional colors }; format?: "glb" | "ply"; extras?: Record<string, any>; } export const volume3DSchema = { type: "object", properties: { f: { type: "string", description: "SymPy-like expression in x,y,z; numeric eval is vectorized" }, x: { type: "array", items: { type: "number" }, minItems: 2, maxItems: 3, description: "[min,max,steps?]" }, y: { type: "array", items: { type: "number" }, minItems: 2, maxItems: 3 }, z: { type: "array", items: { type: "number" }, minItems: 2, maxItems: 3 }, mode: { type: "string", enum: ["slices", "isosurface"], default: "slices" }, iso_level: { type: "number", description: "Used when mode='isosurface'" }, emit_animation: { type: "boolean", default: false }, animate_axis: { type: "string", enum: ["x", "y", "z"], default: "z" }, fps: { type: "integer", default: 24 }, format: { type: "string", enum: ["mp4", "webm", "gif"], default: "mp4" }, samples_cap: { type: "integer", default: 160 }, allow_large: { type: "boolean", default: false } }, required: ["f", "x", "y", "z"] } as const; export const animationSchema = { type: "object", properties: { frame_expr: { type: "string", description: "Expression producing frame array or 2D function value at (x,t)" }, x_range: { type: "array", items: { type: "number" }, minItems: 2, maxItems: 3 }, t_range: { type: "array", items: { type: "number" }, minItems: 2, maxItems: 3 }, renderer: { type: "string", enum: ["imshow", "contour", "line"], default: "imshow" }, fps: { type: "integer", default: 24 }, format: { type: "string", enum: ["mp4", "webm", "gif"], default: "mp4" }, dpi: { type: "integer", default: 120 }, emit_frames: { type: "boolean", default: false }, emit_csv: { type: "boolean", default: false }, frames_cap: { type: "integer", default: 300 }, allow_large: { type: "boolean", default: false } }, required: ["frame_expr", "t_range"] } as const; export const interactiveSchema = { type: "object", properties: { expr: { type: "string" }, x_range: { type: "array", items: { type: "number" }, minItems: 2, maxItems: 3 }, controls: { type: "array", items: { type: "object", properties: { name: { type: "string" }, min: { type: "number" }, max: { type: "number" }, step: { type: "number" }, default: { type: "number" } }, required: ["name", "min", "max", "step", "default"] } }, renderer: { type: "string", enum: ["line", "contour", "surface"], default: "line" }, grid_limit: { type: "integer", default: 24 } // produce at most N precomputed thumbnails }, required: ["expr", "controls"] } as const; export const vrExportSchema = { type: "object", properties: { geometry: { type: "object", properties: { vertices: { type: "array", items: { type: "array", items: { type: "number" }, minItems: 3, maxItems: 3 } }, faces: { type: "array", items: { type: "array", items: { type: "integer", minimum: 0 } } }, normals: { type: "array", items: { type: "array", items: { type: "number" } }, nullable: true }, colors: { type: "array", items: { type: "array", items: { type: "number" } }, nullable: true } }, required: ["vertices", "faces"] }, format: { type: "string", enum: ["glb", "ply"], default: "glb" }, extras: { type: "object" } }, required: ["geometry"] } as const;