@uor-foundation/geometry/dist/geodesics.d.ts

Layer 5: Geometric manifolds - the shape of mathematical space

import type { FieldSubstrate } from '@uor-foundation/field-substrate';
import type { ResonanceDynamics } from '@uor-foundation/resonance';
import type { PageTopology } from '@uor-foundation/topology';
export interface GeodesicPath {
    start: bigint;
    end: bigint;
    path: bigint[];
    length: number;
    curvature: number[];
}
export interface GeodesicFlow {
    position: bigint;
    velocity: number;
    acceleration: number;
}
export declare class GeodesicCalculator {
    private fieldSubstrate;
    private resonance;
    private topology;
    private metric;
    constructor(fieldSubstrate: FieldSubstrate, resonance: ResonanceDynamics, topology: PageTopology);
    findGeodesic(start: bigint, end: bigint): GeodesicPath;
    dijkstraGeodesic(start: bigint, end: bigint): bigint[];
    straightLineGeodesic(start: bigint, end: bigint): bigint[];
    private getGeodesicNeighbors;
    computePathLength(path: bigint[]): number;
    computePathCurvature(path: bigint[]): number[];
    geodesicFlow(start: bigint, velocity: number, time: number): GeodesicFlow;
    exponentialMap(basePoint: bigint, tangentVector: number[], t: number): bigint;
    parallelTransport(vector: number[], path: bigint[]): number[];
    isGeodesic(path: bigint[]): boolean;
    geodesicDeviation(path1: bigint[], path2: bigint[]): number[];
    conjugatePoints(start: bigint, direction: number[]): bigint[];
    private computeJacobian;
}
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