feat: add convertStereoToHorizontal() to projection module in @observerly/astrometry

feat: add convertStereoToHorizontal() to projection module in @observerly/astrometry

Author: michealroberts

src/projection.ts

@@ -8,7 +8,7 @@
 
 import { type CartesianCoordinate, type HorizontalCoordinate } from './common'
 
-import { convertDegreesToRadians as radians } from './utilities'
+import { convertRadiansToDegrees as degrees, convertDegreesToRadians as radians } from './utilities'
 
 /*****************************************************************************************************************/
 
@@ -60,3 +60,48 @@ export const convertHorizontalToStereo = (
 }
 
 /*****************************************************************************************************************/
+
+/**
+ *
+ * convertStereoToHorizontal()
+ *
+ * @param cartesianCoordinate representing the { x, y } position of a particular point to transform.
+ * @param width (of type number) representing the width of the projected "canvas"
+ * @param height (of type number) representing the height of the projected "canvas"
+ * @returns the Horizontal Coordinate { alt, az } conversion from the stereographic projection
+ */
+export const convertStereoToHorizontal = (
+  cartesianCoordinate: CartesianCoordinate,
+  extent: { width: number; height: number },
+  focus: number = 0.2
+): HorizontalCoordinate => {
+  const { x, y } = cartesianCoordinate
+
+  const sinalt1 = 0
+
+  const cosalt1 = 1
+
+  const h = extent.height
+
+  const w = extent.width
+
+  const X = (x - w / 2) / h
+
+  const Y = (h - y) / h
+
+  const P = Math.sqrt(Math.pow(X, 2) + Math.pow(Y, 2))
+
+  const c = 2 * Math.atan2(P, 2 * focus)
+
+  const alt = Math.asin(Math.cos(c) * sinalt1 + (Y * Math.sin(c) * cosalt1) / P)
+
+  const az =
+    Math.PI + Math.atan2(X * Math.sin(c), P * cosalt1 * Math.cos(c) - Y * sinalt1 * Math.sin(c))
+
+  return {
+    az: degrees(az),
+    alt: degrees(alt)
+  }
+}
+
+/*****************************************************************************************************************/

tests/projection.spec.ts

@@ -10,14 +10,56 @@ import { describe, expect, it } from 'vitest'
 
 /*****************************************************************************************************************/
 
-import { convertHorizontalToStereo } from '../src'
+import { convertHorizontalToStereo, convertStereoToHorizontal } from '../src'
 
 /*****************************************************************************************************************/
 
 describe('convertHorizontalToStereo', () => {
   it('should be defined', () => {
     expect(convertHorizontalToStereo).toBeDefined()
   })
+
+  it('should return the correct Cartesian Coordinate { x, y } conversion to the stereographic projection', () => {
+    const { x, y } = convertHorizontalToStereo(
+      {
+        az: 180,
+        alt: 61.52543906847783
+      },
+      {
+        width: 2000,
+        height: 2000
+      },
+      0.42
+    )
+
+    expect(x).toBeCloseTo(1000)
+    expect(y).toBeCloseTo(1000)
+  })
+})
+
+/*****************************************************************************************************************/
+
+describe('convertStereoToHorizontal', () => {
+  it('should be defined', () => {
+    expect(convertStereoToHorizontal).toBeDefined()
+  })
+
+  it('should return the correct Horizontal Coordinate { az, alt } conversion from the stereographic projection', () => {
+    const { az, alt } = convertStereoToHorizontal(
+      {
+        x: 1000,
+        y: 1000
+      },
+      {
+        width: 2000,
+        height: 2000
+      },
+      0.42
+    )
+
+    expect(az).toBeCloseTo(180)
+    expect(alt).toBeCloseTo(61.525439)
+  })
 })
 
 /*****************************************************************************************************************/