gyroreflection {gyro}

Gyroreflection

Description

Gyroreflection of a point with respect to a gyroline in a 2D gyrospace.

Usage

gyroreflection(A, B, M, s, model = "U")

Arguments

A, B, M

three 2D points

s

the gyroparameter (radius of the Poincaré disk if model="M")

model

the hyperbolic model, either "M" (Möbius model, i.e. Poincaré model) or "U" (Ungar model, i.e. Minkowski model)

Value

A 2D point, the image of M by the reflection with respect to the gyroline passing through A and B.

Examples

library(gyro)
A <- c(1.5, 2); B <- c(2, 1)
opar <- par(mar = c(2, 2, 2, 0.5))
plot(rbind(A, B), type = "p", pch = 19, xlab = NA, ylab = NA,
     xlim = c(0.3, 2), ylim = c(0, 2.5), main = "s = 0.3")
s <- 0.3
seg <- gyrosegment(A, B, s = s, model = "U")
lines(seg, col = "blue", lwd = 2)
text(t(A), expression(italic(A)), pos = 3)
text(t(B), expression(italic(B)), pos = 3)
M <- c(1.3, 1.1)
rM <- gyroreflection(A, B, M, s = s, model = "U")
points(rbind(M, rM), type = "p", pch = 19)
text(t(M), expression(italic(M)), pos = 3)
text(t(rM), expression(italic(r(M))), pos = 3)
par(opar)