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* Uncertainty Ellipse Calculation Utilities
*
* Calculate ellipse geometry for uncertainty visualization on maps.
* Supports 1-sigma (68%), 2-sigma (95%), and 3-sigma (99.7%) confidence levels.
*/
export interface EllipseParams {
centerLat: number;
centerLng: number;
sigmaX: number; // Semi-major axis in meters
sigmaY: number; // Semi-minor axis in meters
rotation: number; // Rotation angle in degrees
confidence?: number; // Confidence level multiplier (1, 2, or 3 for sigma levels)
}
export interface GeoJSONFeature {
type: 'Feature';
geometry: {
type: 'Polygon';
coordinates: number[][][];
};
properties: Record<string, unknown>;
}
// Note: EARTH_RADIUS_M reserved for future geographic calculations
// const EARTH_RADIUS_M = 6378137; // Earth radius in meters (WGS84)
/**
* Convert meters to degrees latitude
*/
function metersToDegreesLat(meters: number): number {
return meters / (111320); // 1 degree latitude ≈ 111.32 km
}
/**
* Convert meters to degrees longitude at given latitude
*/
function metersToDegreesLng(meters: number, latitude: number): number {
const latRad = (latitude * Math.PI) / 180;
return meters / (111320 * Math.cos(latRad));
}
/**
* Generate ellipse points as [lng, lat] pairs
*
* @param params - Ellipse parameters
* @param numPoints - Number of points to generate (default: 64 for smooth rendering)
* @returns Array of [lng, lat] coordinates forming the ellipse
*/
export function generateEllipsePoints(
params: EllipseParams,
numPoints: number = 64
): [number, number][] {
const { centerLat, centerLng, sigmaX, sigmaY, rotation, confidence = 1 } = params;
// Scale by confidence level (1σ, 2σ, 3σ)
const scaledSigmaX = sigmaX * confidence;
const scaledSigmaY = sigmaY * confidence;
// Convert rotation to radians
const rotationRad = (rotation * Math.PI) / 180;
const points: [number, number][] = [];
for (let i = 0; i <= numPoints; i++) {
const angle = (i / numPoints) * 2 * Math.PI;
// Parametric ellipse equations
const x = scaledSigmaX * Math.cos(angle);
const y = scaledSigmaY * Math.sin(angle);
// Apply rotation
const xRotated = x * Math.cos(rotationRad) - y * Math.sin(rotationRad);
const yRotated = x * Math.sin(rotationRad) + y * Math.cos(rotationRad);
// Convert to lat/lng offsets
const latOffset = metersToDegreesLat(yRotated);
const lngOffset = metersToDegreesLng(xRotated, centerLat);
// Add to center coordinates
const lng = centerLng + lngOffset;
const lat = centerLat + latOffset;
points.push([lng, lat]);
}
return points;
}
/**
* Create GeoJSON Feature for an uncertainty ellipse
*
* @param params - Ellipse parameters
* @param properties - Additional properties for the feature
* @returns GeoJSON Feature object
*/
export function createEllipseFeature(
params: EllipseParams,
properties: Record<string, unknown> = {}
): GeoJSONFeature {
const coordinates = generateEllipsePoints(params);
return {
type: 'Feature',
geometry: {
type: 'Polygon',
coordinates: [coordinates],
},
properties: {
centerLat: params.centerLat,
centerLng: params.centerLng,
sigmaX: params.sigmaX,
sigmaY: params.sigmaY,
rotation: params.rotation,
confidence: params.confidence || 1,
...properties,
},
};
}
/**
* Create multiple confidence level ellipses (1σ, 2σ, 3σ)
*
* @param params - Base ellipse parameters
* @param levels - Confidence levels to generate (default: [1, 2, 3])
* @returns Array of GeoJSON Features
*/
export function createConfidenceEllipses(
params: Omit<EllipseParams, 'confidence'>,
levels: number[] = [1, 2, 3]
): GeoJSONFeature[] {
return levels.map((level) =>
createEllipseFeature(
{ ...params, confidence: level },
{ confidenceLevel: level }
)
);
}
/**
* Get color for confidence level
*
* @param confidenceLevel - Sigma level (1, 2, or 3)
* @returns Hex color string
*/
export function getConfidenceColor(confidenceLevel: number): string {
switch (confidenceLevel) {
case 1:
return '#10b981'; // Green - 68% confidence
case 2:
return '#f59e0b'; // Yellow/Orange - 95% confidence
case 3:
return '#3b82f6'; // Light Blue - 99.7% confidence
default:
return '#6b7280'; // Gray - fallback
}
}
/**
* Get opacity for confidence level
*
* @param confidenceLevel - Sigma level (1, 2, or 3)
* @returns Opacity value (0-1)
*/
export function getConfidenceOpacity(confidenceLevel: number): number {
switch (confidenceLevel) {
case 1:
return 0.3;
case 2:
return 0.2;
case 3:
return 0.1;
default:
return 0.15;
}
}
/**
* Calculate simple circular uncertainty from single uncertainty value
*
* @param centerLat - Center latitude
* @param centerLng - Center longitude
* @param uncertaintyM - Uncertainty radius in meters
* @returns Ellipse parameters for circular uncertainty
*/
export function createCircularUncertainty(
centerLat: number,
centerLng: number,
uncertaintyM: number
): EllipseParams {
return {
centerLat,
centerLng,
sigmaX: uncertaintyM,
sigmaY: uncertaintyM,
rotation: 0,
confidence: 1,
};
}
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