Hyperbola: R6 class representing a hyperbola
In PlaneGeometry: Plane Geometry
Hyperbola R Documentation
R6 class representing a hyperbola
Description
A hyperbola is given by two intersecting asymptotes, named
L1 and L2, and a point on this hyperbola, named M.
Active bindings
L1get or set the asymptote L1
L2get or set the asymptote L2
Mget or set the point M
Methods
Public methods
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Method new()
Create a new Hyperbola object.
Usage
Hyperbola$new(L1, L2, M)
Arguments
L1, L2two intersecting lines given as Line objects, the
asymptotes
Ma point on the hyperbola
Returns
A new Hyperbola object.
Method center()
Center of the hyperbola.
Usage
Hyperbola$center()
Returns
The center of the hyperbola, i.e. the point where
the two asymptotes meet each other.
Method OAB()
Parametric equation O \pm cosh(t) A + sinh(t) B
representing the hyperbola.
Usage
Hyperbola$OAB()
Returns
The point O and the two vectors A and B
in a list.
Examples
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
hyperbola$OAB()
Method vertices()
Vertices of the hyperbola.
Usage
Hyperbola$vertices()
Returns
The two vertices V1 and V2 in a list.
Method abce()
The numbers a (semi-major axis, i.e. distance
from center to vertex),
b (semi-minor axis),
c (linear eccentricity)
and e (eccentricity)
associated to the hyperbola.
Usage
Hyperbola$abce()
Returns
The four numbers a, b, c and e
in a list.
Method foci()
Foci of the hyperbola.
Usage
Hyperbola$foci()
Returns
The two foci F1 and F2 in a list.
Method plot()
Plot hyperbola.
Usage
Hyperbola$plot(add = FALSE, ...)
Arguments
addBoolean, whether to add this plot to the current plot
...named arguments passed to lines
Returns
Nothing, called for plotting.
Examples
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
plot(hyperbola, lwd = 2)
points(t(M), pch = 19, col = "blue")
O <- hyperbola$center()
points(t(O), pch = 19)
draw(L1, col = "red")
draw(L2, col = "red")
vertices <- hyperbola$vertices()
points(rbind(vertices$V1, vertices$V2), pch = 19)
majorAxis <- Line$new(vertices$V1, vertices$V2)
draw(majorAxis, lty = "dashed")
foci <- hyperbola$foci()
points(rbind(foci$F1, foci$F2), pch = 19, col = "green")
Method includes()
Whether a point belongs to the hyperbola.
Usage
Hyperbola$includes(P)
Arguments
Pa point
Returns
A Boolean value.
Examples
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
hyperbola$includes(M)
Method equation()
Implicit quadratic equation of the hyperbola
Axxx2 + 2Axyxy + Ayyy2 + 2Bxx + 2Byy + C = 0
Usage
Hyperbola$equation()
Returns
The coefficients of the equation in a named list.
Examples
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
eq <- hyperbola$equation()
x <- M[1]; y <- M[2]
with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
V1 <- hyperbola$vertices()$V1
x <- V1[1]; y <- V1[2]
with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
Method clone()
The objects of this class are cloneable with this method.
Usage
Hyperbola$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
## ------------------------------------------------
## Method `Hyperbola$OAB`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
hyperbola$OAB()
## ------------------------------------------------
## Method `Hyperbola$plot`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
plot(hyperbola, lwd = 2)
points(t(M), pch = 19, col = "blue")
O <- hyperbola$center()
points(t(O), pch = 19)
draw(L1, col = "red")
draw(L2, col = "red")
vertices <- hyperbola$vertices()
points(rbind(vertices$V1, vertices$V2), pch = 19)
majorAxis <- Line$new(vertices$V1, vertices$V2)
draw(majorAxis, lty = "dashed")
foci <- hyperbola$foci()
points(rbind(foci$F1, foci$F2), pch = 19, col = "green")
## ------------------------------------------------
## Method `Hyperbola$includes`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
hyperbola$includes(M)
## ------------------------------------------------
## Method `Hyperbola$equation`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
eq <- hyperbola$equation()
x <- M[1]; y <- M[2]
with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
V1 <- hyperbola$vertices()$V1
x <- V1[1]; y <- V1[2]
with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
PlaneGeometry documentation built on Aug. 10, 2023, 1:09 a.m.
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| Hyperbola | R Documentation |
R6 class representing a hyperbola
Description
A hyperbola is given by two intersecting asymptotes, named
L1 and L2, and a point on this hyperbola, named M.
Active bindings
L1get or set the asymptote
L1L2get or set the asymptote
L2Mget or set the point
M
Methods
Public methods
Method new()
Create a new Hyperbola object.
Usage
Hyperbola$new(L1, L2, M)
Arguments
L1, L2two intersecting lines given as
Lineobjects, the asymptotesMa point on the hyperbola
Returns
A new Hyperbola object.
Method center()
Center of the hyperbola.
Usage
Hyperbola$center()
Returns
The center of the hyperbola, i.e. the point where the two asymptotes meet each other.
Method OAB()
Parametric equation O \pm cosh(t) A + sinh(t) B
representing the hyperbola.
Usage
Hyperbola$OAB()
Returns
The point O and the two vectors A and B
in a list.
Examples
L1 <- LineFromInterceptAndSlope(0, 2) L2 <- LineFromInterceptAndSlope(-2, -0.5) M <- c(4, 3) hyperbola <- Hyperbola$new(L1, L2, M) hyperbola$OAB()
Method vertices()
Vertices of the hyperbola.
Usage
Hyperbola$vertices()
Returns
The two vertices V1 and V2 in a list.
Method abce()
The numbers a (semi-major axis, i.e. distance
from center to vertex),
b (semi-minor axis),
c (linear eccentricity)
and e (eccentricity)
associated to the hyperbola.
Usage
Hyperbola$abce()
Returns
The four numbers a, b, c and e
in a list.
Method foci()
Foci of the hyperbola.
Usage
Hyperbola$foci()
Returns
The two foci F1 and F2 in a list.
Method plot()
Plot hyperbola.
Usage
Hyperbola$plot(add = FALSE, ...)
Arguments
addBoolean, whether to add this plot to the current plot
...named arguments passed to
lines
Returns
Nothing, called for plotting.
Examples
L1 <- LineFromInterceptAndSlope(0, 2) L2 <- LineFromInterceptAndSlope(-2, -0.5) M <- c(4, 3) hyperbola <- Hyperbola$new(L1, L2, M) plot(hyperbola, lwd = 2) points(t(M), pch = 19, col = "blue") O <- hyperbola$center() points(t(O), pch = 19) draw(L1, col = "red") draw(L2, col = "red") vertices <- hyperbola$vertices() points(rbind(vertices$V1, vertices$V2), pch = 19) majorAxis <- Line$new(vertices$V1, vertices$V2) draw(majorAxis, lty = "dashed") foci <- hyperbola$foci() points(rbind(foci$F1, foci$F2), pch = 19, col = "green")
Method includes()
Whether a point belongs to the hyperbola.
Usage
Hyperbola$includes(P)
Arguments
Pa point
Returns
A Boolean value.
Examples
L1 <- LineFromInterceptAndSlope(0, 2) L2 <- LineFromInterceptAndSlope(-2, -0.5) M <- c(4, 3) hyperbola <- Hyperbola$new(L1, L2, M) hyperbola$includes(M)
Method equation()
Implicit quadratic equation of the hyperbola Axxx2 + 2Axyxy + Ayyy2 + 2Bxx + 2Byy + C = 0
Usage
Hyperbola$equation()
Returns
The coefficients of the equation in a named list.
Examples
L1 <- LineFromInterceptAndSlope(0, 2) L2 <- LineFromInterceptAndSlope(-2, -0.5) M <- c(4, 3) hyperbola <- Hyperbola$new(L1, L2, M) eq <- hyperbola$equation() x <- M[1]; y <- M[2] with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C) V1 <- hyperbola$vertices()$V1 x <- V1[1]; y <- V1[2] with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
Method clone()
The objects of this class are cloneable with this method.
Usage
Hyperbola$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
## ------------------------------------------------
## Method `Hyperbola$OAB`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
hyperbola$OAB()
## ------------------------------------------------
## Method `Hyperbola$plot`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
plot(hyperbola, lwd = 2)
points(t(M), pch = 19, col = "blue")
O <- hyperbola$center()
points(t(O), pch = 19)
draw(L1, col = "red")
draw(L2, col = "red")
vertices <- hyperbola$vertices()
points(rbind(vertices$V1, vertices$V2), pch = 19)
majorAxis <- Line$new(vertices$V1, vertices$V2)
draw(majorAxis, lty = "dashed")
foci <- hyperbola$foci()
points(rbind(foci$F1, foci$F2), pch = 19, col = "green")
## ------------------------------------------------
## Method `Hyperbola$includes`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
hyperbola$includes(M)
## ------------------------------------------------
## Method `Hyperbola$equation`
## ------------------------------------------------
L1 <- LineFromInterceptAndSlope(0, 2)
L2 <- LineFromInterceptAndSlope(-2, -0.5)
M <- c(4, 3)
hyperbola <- Hyperbola$new(L1, L2, M)
eq <- hyperbola$equation()
x <- M[1]; y <- M[2]
with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
V1 <- hyperbola$vertices()$V1
x <- V1[1]; y <- V1[2]
with(eq, Axx*x^2 + 2*Axy*x*y + Ayy*y^2 + 2*Bx*x + 2*By*y + C)
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