Homothety {LearnGeom}

Creates an homothety from a given polygon

Description

Homothety creates an homothety from a given polygon

Usage

Homothety(Poly, C, k, lines = F)

Arguments

Poly

Polygon object, previously created with function CreatePolygon

C

Vector containing the xy-coordinates of the center of the homothety

k

Number which represents the expansion or contraction factor for the homothety

lines

Boolean. When lines = TRUE, the plot displays the lines that connect the center of the homothety with the points of the polygons (the original and the transformed one). If missing, it works as with lines = FALSE, so the lines are not displayed

Value

Returns the coordinates of a polygon that has been transformed according to the homothethy with center at C and factor k

References

https://www.encyclopediaofmath.org/index.php/Homothety

Examples

x_min <- -2
x_max <- 6
y_min <- -3
y_max <- 5
CoordinatePlane(x_min, x_max, y_min, y_max)
P1 <- c(0,0)
P2 <- c(1,1)
P3 <- c(2,0) 
Poly <- CreatePolygon(P1, P2, P3)
Draw(Poly, "blue")
C <- c(-1,-2)
k1 <- 0.5
Poly_homothety1 <- Homothety(Poly, C, k1, lines = TRUE)
Draw(Poly_homothety1, "orange")
k2 <- 2
Poly_homothety2 <- Homothety(Poly, C, k2, lines = TRUE)
Draw(Poly_homothety2, "orange")