intersection = CGA3D.inline((extract_detailed) => {
const ei = 1e5 + 1e4; // e_infty
const eo = .5 * (1e5 - 1e4); // e_0
// (and apparently, swapping the +/- in both e0 and ei is OK)
const E = ei^eo;
const eq = (a,b) => a-b == 0; // can't use == for array equality
const pt = (x,y,z) => x*1e1 + y*1e2 + z*1e3 + .5*(x*x+y*y+z*z)*ei + eo;
// var a = pt(4,5,6);
// var b = pt(7,8,9);
// var d = Math.hypot(7-4, 8-5, 9-6);
// return eq(a<<b, -.5*d*d); // true
const extract = pp => {
const r = Math.sqrt(Math.abs((pp << pp)[0]));
const le = pp << (ei^pp) - (pp << pp)*ei;
const ri = r*(ei << pp);
const denom = (ei << pp)**2;
return [
-(le - ri) / denom,
-(le + ri) / denom,
];
};
var sphere1 = pt(3,0,-.5)^pt(-1,0,-.5)^pt(1,2,-.5)^pt(1,0,1.5);
var sphere2 = pt(3,0,1)^pt(-1,0,1)^pt(1,2,1)^pt(1,0,3);
var line = pt(0,0,0)^pt(1,0,0)^ei;
var intersection1 = (sphere1&line);
// return [extract(intersection1), extract_detailed(intersection1)];
return extract(intersection1); // <-- WORKS
var sphere3 = pt(4,1,0)^pt(0,1,0)^pt(2,3,0)^pt(2,1,2);
var intersection2 = (sphere3&sphere2&sphere1);
return extract(intersection2); // <!-- does not work, but in particular, /denom = /bignumber => 0
return [intersection1, intersection2, (sphere1&sphere2)];
})(extract_detailed)
CGA3D.inline((extract_detailed) => {
const ei = 1e5 + 1e4; const _ei = x => .5*(x/1e5 + x/1e4);
const eo = .5 * (1e5 - 1e4); const _eo = x => (x/1e5 - x/1e4);
// (and apparently, swapping the +/- in both e0 and ei is OK)
const E = ei^eo;
const eq = (a,b) => a-b == 0; // can't use == for array equality
const pt = (x,y,z) => x*1e1 + y*1e2 + z*1e3 + .5*(x*x+y*y+z*z)*ei + eo;
const extract = pp => {
const r = Math.sqrt(Math.abs((pp << pp)[0]));
const le = pp << (ei^pp) - (pp << pp)*ei;
const ri = r*(ei << pp);
const denom = (ei << pp)**2;
return [
-(le - ri) / denom,
-(le + ri) / denom,
];
};
const pa = 3e1 + 4e2 + 5e3;
const pb = 7e1 + 8e2 + 9e3;
const a = pt(3,4,5);
const b = pt(7,8,9);
const V = a^b;
/*
const extract_detailed = pp => {
const _b = ((V / 1e12)[0])*1e12 + ((V / 1e13)[0])*1e13 + ((V / 1e23)[0])*1e23; // Euclidean bivector
const _gamma = 2 * (V / 1e45)[0];
var _v = 2*_ei(V); _v = _v[1]*1e1 + _v[2]*1e2 + _v[3]*1e3;
var _u = -_eo(V); _u = _u[1]*1e1 + _u[2]*1e2 + _u[3]*1e3;
// V = _b + .5*_v*ei - _u*eo + .5*_gamma*E
const _sigma = .5*_gamma**2 - (_u << _v)[0];
const _rho = Math.sqrt(_sigma**2 - _u**2 * _v**2);
const _pa_len = Math.sqrt(_sigma + _rho) / _u.Length;
const _pb_len = Math.sqrt(_sigma - _rho) / _u.Length;
const _pa = _pa_len*(_pa_len**2*_u + _v).Normalized;
const _pb = _pb_len*(_pb_len**2*_u + _v).Normalized;
return [_pa,_pb];
}
*/
const myV = pa^pb + .5*(pa**2*pb - pb**2*pa)*ei - (pb-pa)*eo + .5*(pa**2 - pb**2)*E;
// https://arxiv.org/pdf/1306.1007.pdf
return [extract_detailed(V), extract(V)];
})(extract_detailed)
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Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
