thematic-earth/joe/spherical-earth/spherical-trigonometry.js

HTML-based, whole-Earth thematic maps using locally hosted data layers

/* Copyright (c) 2023 Read Write Tools. Legal use subject to the Thematic Earth Software License Agreement. */
import*as ct from'./coordinate-translations.js';const π=Math.PI,degreesToRadians=π/180,radiansToDegrees=180/π,EARTH_RADIUS=6371;export function interiorAngle(t,a,e,n){const i=t*degreesToRadians,s=e*degreesToRadians,r=(n-a)*degreesToRadians,o=Math.sin(r)*Math.cos(s),d=Math.cos(i)*Math.sin(s)-Math.sin(i)*Math.cos(s)*Math.cos(r);return Math.atan2(o,d)}export function lengthOfArc(t,a,e,n){const i=t*degreesToRadians,s=e*degreesToRadians,r=(e-t)*degreesToRadians,o=(n-a)*degreesToRadians,d=Math.sin(r/2)*Math.sin(r/2)+Math.cos(i)*Math.cos(s)*Math.sin(o/2)*Math.sin(o/2);return 2*Math.asin(Math.sqrt(d))}export function sphericalExcess(t,a,e,n,i,s){var r=lengthOfArc(e,n,i,s),o=lengthOfArc(i,s,t,a),d=lengthOfArc(t,a,e,n),l=(r+o+d)/2;return Math.sqrt(l*(l-r)*(l-o)*(l-d))}export function triangularArea(t,a,e,n,i,s){return sphericalExcess(t,a,e,n,i,s)*6371**2}export function centroidOfEquilateralTriangle(t,a,e,n,i,s){const{x:r,y:o,z:d}=ct.ll2xyz(t,a),{x:l,y:h,z:c}=ct.ll2xyz(e,n),{x:u,y:M,z:g}=ct.ll2xyz(i,s),T=(r+l+u)/3,p=(o+h+M)/3,x=(d+c+g)/3,R=Math.sqrt(T**2+p**2+x**2),f=T/R,A=p/R,y=x/R,{latitude:z,longitude:q}=ct.xyz2ll(f,A,y);return{latitude:z,longitude:q}}export function sphericalMidpoint(t,a,e,n){const{x:i,y:s,z:r}=ct.ll2xyz(t,a),{x:o,y:d,z:l}=ct.ll2xyz(e,n),h=(i+o)/2,c=(s+d)/2,u=(r+l)/2,M=Math.sqrt(h**2+c**2+u**2),g=h/M,T=c/M,p=u/M,x=ct.xyz2ll(g,T,p),R=sphericalMidpointAlt(t,a,e,n),f=JSON.stringify(x.latitude.toFixed(6)+','+x.longitude.toFixed(6)),A=JSON.stringify(R.latitude.toFixed(6)+','+R.longitude.toFixed(6));return f!=A&&console.log(`sphericalMidpoint mismatch ${f} ${A}`),{latitude:x.latitude,longitude:x.longitude}}export function haversine(t,a,e,n){const i=t*degreesToRadians,s=e*degreesToRadians,r=(e-t)*degreesToRadians,o=(n-a)*degreesToRadians,d=Math.sin(r/2)*Math.sin(r/2)+Math.cos(i)*Math.cos(s)*Math.sin(o/2)*Math.sin(o/2);return 6371*(2*Math.atan2(Math.sqrt(d),Math.sqrt(1-d)))}export function bearing(t,a,e,n){const i=t*degreesToRadians,s=e*degreesToRadians,r=a*degreesToRadians,o=n*degreesToRadians,d=(n-a)*degreesToRadians,l=Math.sin(o-r)*Math.cos(s),h=Math.cos(i)*Math.sin(s)-Math.sin(i)*Math.cos(s)*Math.cos(d);return(Math.atan2(l,h)*radiansToDegrees+360)%360}export function sphericalMidpointAlt(t,a,e,n){const i=t*degreesToRadians,s=e*degreesToRadians,r=a*degreesToRadians,o=n*degreesToRadians,d=Math.cos(s)*Math.cos(o-r),l=Math.cos(s)*Math.sin(o-r),h=Math.atan2(Math.sin(i)+Math.sin(s),Math.sqrt((Math.cos(i)+d)*(Math.cos(i)+d)+l*l));var c=(r+Math.atan2(l,Math.cos(i)+d))*radiansToDegrees;return-180==(c=(c+540)%360-180)&&(c=180),{latitude:h*radiansToDegrees,longitude:c}}export function sphericalIntermediatePoint(t,a,e,n,i){if(t+e==0)return null;if(Math.abs(n-a)==Math.PI)return null;if(i<0||i>1)return null;const s=t*degreesToRadians,r=e*degreesToRadians,o=a*degreesToRadians,d=n*degreesToRadians,l=lengthOfArc(t,a,e,n),h=Math.sin((1-i)*l)/Math.sin(l),c=Math.sin(i*l)/Math.sin(l),u=h*Math.cos(s)*Math.cos(o)+c*Math.cos(r)*Math.cos(d),M=h*Math.cos(s)*Math.sin(o)+c*Math.cos(r)*Math.sin(d),g=h*Math.sin(s)+c*Math.sin(r),T=Math.atan2(g,Math.sqrt(u**2+M**2));var p=Math.atan2(M,u)*radiansToDegrees;return{latitude:T*radiansToDegrees,longitude:p=(p+540)%360-180}}export function sphericalFinalPoint(t,a,e,n){const i=t*degreesToRadians,s=a*degreesToRadians,r=e,o=n/6371,d=Math.asin(Math.sin(i)*Math.cos(o)+Math.cos(i)*Math.sin(o)*Math.cos(r));var l=(s+Math.atan2(Math.sin(r)*Math.sin(o)*Math.cos(i),Math.cos(o)-Math.sin(i)*Math.sin(d)))*radiansToDegrees;return{latitude:d*radiansToDegrees,longitude:l=(l+540)%360-180}}export function antipode(t,a){return{latitude:-t,longitude:a>0?a-180:a+180}}export function greatCircleArc(t,a,e,n,i,s){var r=[];for(let d=0;d<i;d++){var o=sphericalIntermediatePoint(t,a,e,n,1==s?d/(i-1):d/i);null!=o&&r.push(o)}return r}export function greatCirclePoints(t,a,e,n,i){const s={latitude:t,longitude:a},r={latitude:e,longitude:n};var o=antipode(s.latitude,s.longitude),d=antipode(r.latitude,r.longitude),l=i/2,h=lengthOfArc(s.latitude,s.longitude,r.latitude,r.longitude)/Math.PI,c=Math.round(l*h),u=l-c,M=greatCircleArc(s.latitude,s.longitude,r.latitude,r.longitude,c,!1),g=greatCircleArc(r.latitude,r.longitude,o.latitude,o.longitude,u,!1),T=greatCircleArc(o.latitude,o.longitude,d.latitude,d.longitude,c,!1),p=greatCircleArc(d.latitude,d.longitude,s.latitude,s.longitude,u,!1);return M.concat(g,T,p,[s])}