hreflection {gyro}

Hyperbolic reflection

Description

Hyperbolic reflection in the Poincaré disk.

Usage

hreflection(A, B, M)

Arguments

A, B

two points in the Poincaré disk defining the reflection line

M

a point in the Poincaré disk to be reflected

Value

A point in the Poincaré disk, the image of M by the hyperbolic reflection with respect to the line passing through A and B.

Examples

library(gyro)
library(plotrix)
A <- c(0.45, 0.78)
B <- c(0.1, -0.5)
M <- c(0.7, 0)
opar <- par(mar = c(0, 0, 0, 0))
plot(NULL, type = "n", xlim = c(-1, 1), ylim = c(-1, 1), asp = 1,
     axes = FALSE, xlab = NA, ylab = NA)
draw.circle(0, 0, radius = 1, lwd = 2)
lines(gyrosegment(A, B, model = "M"))
points(rbind(A, B), pch = 19)
points(rbind(M), pch = 19, col = "blue")
P <- hreflection(A, B, M)
points(rbind(P), pch = 19, col = "red")
par(opar)