[Question] How to deal with polar coordinates? about hyperbolic-canvas HOT 2 CLOSED

Hey,

I am not a mathematician, and it's been a few years since I've worked with the underlying mathematics of this library, so the best I can do is answer your questions with code.

I recommend that you reverse engineer the examples below if you want to derive a formula, or ask a question on Mathematics Stack Exchange if you need a more detailed answer.

Answer 1

You can generate a Point object using hyperbolic polar coordinates, then use the instance functions to derive euclidean properties:

// define using hyperbolic polar coordinates
let point = Point.givenHyperbolicPolarCoordinates(r, φ);
// convert to euclidean coordinates using instance methods
let x = point.getX();
let y = point.getY();

Answer 2

let angle = P1.hyperbolicAngleTo(P2);
let distance = P1.hyperbolicDistanceTo(P2);

let P3 = P1.hyperbolicDistantPoint(k * distance, angle);

Answer 3

To get the points P(k) along L2:

let Pk = Q.hyperbolicDistantPoint(k, 0);

It looks like I need to add a function to conveniently generate L2, but for now you can do this:

// k is any nonzero real number (though should be "small" to comply with javascript limitations; ex: k = 1)
let L2 = Line,givenTwoPoints(Q, Q.hyperbolicDistantPoint(k, 0));

from hyperbolic-canvas.

Nice, thank you. I'll give it a try.

from hyperbolic-canvas.