gyroABt

Point of coordinate <code>t</code> on the gyroline passing through
 two given points <code>A</code> and <code>B</code>. This is <code>A</code> for <code>t=0</code>
 and this is <code>B</code> for <code>t=1</code>. For <code>t=1/2</code> this is the
 gyromidpoint of the gyrosegment joining <code>A</code> and <code>B</code>.

Hyperbolic geometry in the Minkowski model and the Poincaré
model. The methods are based on the gyrovector space theory developed
by A. A. Ungar that can be found in the book 'Analytic Hyperbolic
Geometry: Mathematical Foundations And Applications'
<doi:10.1142/5914>. The package provides functions to plot
three-dimensional hyperbolic polyhedra and to plot hyperbolic tilings
of the Poincaré disk.

Stc3<a9>phane Laurent

gyro

Hyperbolic Geometry

gyroABt function

<dl><dt>A, B</dt>
<dd>two distinct points</dd>
<dt>t</dt>
<dd>a number</dd>
<dt>s</dt>
<dd>positive number, the radius of the Poincaré ball if
<code>model="M"</code>, otherwise, if <code>model="U"</code>, this number
defines the hyperbolic curvature</dd>
<dt>model</dt>
<dd>the hyperbolic model, either <code>"M"</code> (Möbius model, i.e.
Poincaré model) or <code>"U"</code> (Ungar model, i.e. hyperboloid model)</dd></dl>

Arguments

Point on a gyroline — gyroABt

<dl>

<dt>A, B</dt>
<dd>two distinct points</dd>


<dt>t</dt>
<dd>a number</dd>


<dt>s</dt>
<dd>positive number, the radius of the Poincaré ball if
<code>model="M"</code>, otherwise, if <code>model="U"</code>, this number
defines the hyperbolic curvature</dd>


<dt>model</dt>
<dd>the hyperbolic model, either <code>"M"</code> (Möbius model, i.e.
Poincaré model) or <code>"U"</code> (Ungar model, i.e. hyperboloid model)</dd>

</dl>

gyroABt: Point on a gyroline

Description

Usage

Value

Arguments