itsnickbarry / hyperbolic-canvas Goto Github PK

The polygon is acting strange. No idea why. I would fix it if I knew more about hyperbolic geometry. https://gist.github.com/x13machine/f6964cd6df7dd0ec809b

The Line object currently represents lines, line segments, and rays, in both the Euclidean and hyperbolic sense. This is potentially confusing, and the Line object should be split into multiple objects.

It's suppose to wrap the player around to the other side. Some place it's not working. I'm assuming the math is wrong.
https://gist.github.com/x13machine/5b0f7aba9a91ad351873

https://github.com/ItsNickBarry/hyperbolic-canvas/blob/gh-pages/lib/Point.js#L51
should be:

var point = Point.givenHyperbolicPolarCoordinates(this.distanceFromCenter() - distance,self.distance > distance?thisAngle:angle);

I think that's right.

https://gist.github.com/x13machine/26c4475c01c189150f7a

I was going to convert the polar coordinates to something like x = angle.cos() * raduis, y = angle.sin() * radius. Then run this library on on the converted output: https://github.com/gfx-rs/genmesh Would this be accurate?

This only happens when I change these:

c.ctx.shadowColor = color;
c.ctx.shadowBlur = 40;
c.ctx.strokeStyle = color;
c.ctx.lineWidth = 2;

https://gist.github.com/x13machine/1c8344d87a698255b0f6

Any ideas on how I could fix this? I saw something similar happen like this with bezier curves.

Hello, and thanks for the nice software! It fits best for my school project, so I would like to learn how to use this software, but I'm having troubles understanding it.

Given Poincaree disk, represented as a circle in the Cartesian coordinate system, centered at the origin (0, 0) and having radius 1, I have some questions:

Question 1

Given a point in hyperbolic plane defined using hyperbolic polar coordinates (r, φ) that projects into the point (x, y) (Euclidean non-polar coordinates) on the Poincaree disk, how to express x and y respectively using r and φ? What formula would it be?

Question 2

Given two points in hyperbolic plane P1 and P2 defined using hyperbolic polar coordinates (r1, φ1) and (r2, φ2) respectively. Given polar hyperbolic point P3 (r3, φ3) as the linear interpolation between P1 and P2 parametrized with some variable k (between 0 (gives P1) and 1 (gives P2)). How to express r3 and φ3 using r1, φ1, r2, φ2, k?

Question 3

Given hyperbolic line L1 defined by polar hyperbolic points (1, 0) and (1, π). Given hyperbolic line L2 that is parallel to the L1 (in hyperbolic plane) and that, when projected to the Poincaree disk, has vertical symmetry. Given hyperbolic polar point Q on L2 that is closest to the origin and hyperbolic distance from Q to the origin is n, and Q projects above the origin on the Poincaree disk. The set of all hyperbolic polar points on line L2 is defined as P(k) where parameter k is a real number in range (-∞, +∞), such that for k < 0 points project to the left side of the Poincaree disk and for k > 0 points project to the right side of the Poincaree disk, while P(0) is Q. Question: how to express P(k) using n and k?

Note: I tried to make questions mathematically formal in order to avoid confusion or spoken language imprecision. I was also reading math papers and wikipedia page about hyperbolic geometry, but still can't find answers to these questions.

Regarding question 1: I read source code and if I understand correctly, x = tanh(r / 2) * cos(φ) and y = tanh(r / 2) * sin(φ), is that correct? If yes, where did the formula come from?

Regarding question 2, I tried to define two hyperbolic points and draw a line between them by iterating k from 0 to 1 and drawing small straight line segments between two consecutive interpolated points. However, no matter what I try, the arc curves to the opposite direction and is mislaced on the Poincaree disk. Same happens regarding question 3: the line curves downwards instead of upwards.

Precise formulas for all 3 questions would be preferred over spoken language explanation, since I am trying to finish my project and I can later understand how it works. Thank you in advance for your time.

When I was working on a hyperbolic geometry idea the Point.js script threw an error with a huge call stack, consisting of these three over and over:

isIdealPoint.js:256
getHyperbolicRadiusPoint.js:63
getEuclideanRadiusPoint.js:42

Apparently isIdealPoint calls getHyperbolicRadiusPoint which calls getEuclideanRadiusPoint which calls isIdealPoint... perhaps, change isIdealPoint to not use the other two functions?

NOTE: I'm not sure if this bug even exists or if my version of the library is outdated.

does Line.hyperbolicIntersect work?

I have to radius set to 7 on q polygon to have reach the end of the disk. The maximum x,y is 1. Shouldn't the radius be 1 to reach the end of the screen? why is it 7?

https://gist.github.com/x13machine/7b73802e92efc9380777