Ellipse: R6 class representing an ellipse
In PlaneGeometry: Plane Geometry
Ellipse R Documentation
R6 class representing an ellipse
Description
An ellipse is given by a center, two radii (rmajor
and rminor), and the angle (alpha) between the major axis and
the horizontal direction.
Active bindings
centerget or set the center
rmajorget or set the major radius of the ellipse
rminorget or set the minor radius of the ellipse
alphaget or set the angle of the ellipse
degreesget or set the degrees field
Methods
Public methods
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Method new()
Create a new Ellipse object.
Usage
Ellipse$new(center, rmajor, rminor, alpha, degrees = TRUE)
Arguments
centera point, the center of the rotation
rmajorpositive number, the major radius
rminorpositive number, the minor radius
alphaa number, the angle between the major axis and the
horizontal direction
degreeslogical, whether alpha is given in degrees
Returns
A new Ellipse object.
Examples
Ellipse$new(c(1,1), 3, 2, 30)
Method print()
Show instance of an Ellipse object.
Usage
Ellipse$print(...)
Arguments
...ignored
Method isEqual()
Check whether the reference ellipse equals an ellipse.
Usage
Ellipse$isEqual(ell)
Arguments
ellAn Ellipse object.
Method equation()
The coefficients of the implicit equation of the ellipse.
Usage
Ellipse$equation()
Details
The implicit equation of the ellipse is
Ax² + Bxy + Cy² + Dx + Ey + F = 0. This method returns
A, B, C, D, E and F.
Returns
A named numeric vector.
Method includes()
Check whether a point lies on the reference ellipse.
Usage
Ellipse$includes(M)
Arguments
Ma point
Method contains()
Check whether a point is contained in the reference ellipse.
Usage
Ellipse$contains(M)
Arguments
Ma point
Method matrix()
Returns the 2x2 matrix S associated to the reference
ellipse. The equation of the ellipse is t(M-O) %*% S %*% (M-O) = 1.
Usage
Ellipse$matrix()
Examples
ell <- Ellipse$new(c(1,1), 5, 1, 30)
S <- ell$matrix()
O <- ell$center
pts <- ell$path(4L) # four points on the ellipse
apply(pts, 1L, function(M) t(M-O) %*% S %*% (M-O))
Method path()
Path that forms the reference ellipse.
Usage
Ellipse$path(npoints = 100L, closed = FALSE, outer = FALSE)
Arguments
npointsnumber of points of the path
closedBoolean, whether to return a closed path; you don't need
a closed path if you want to plot it with
polygon
outerBoolean; if TRUE, the ellipse will be contained
inside the path, otherwise it will contain the path
Returns
A matrix with two columns x and y of
length npoints.
Examples
library(PlaneGeometry)
ell <- Ellipse$new(c(1, -1), rmajor = 3, rminor = 2, alpha = 30)
innerPath <- ell$path(npoints = 10)
outerPath <- ell$path(npoints = 10, outer = TRUE)
bbox <- ell$boundingbox()
plot(NULL, asp = 1, xlim = bbox$x, ylim = bbox$y, xlab = NA, ylab = NA)
draw(ell, border = "red", lty = "dashed")
polygon(innerPath, border = "blue", lwd = 2)
polygon(outerPath, border = "green", lwd = 2)
Method diameter()
Diameter and conjugate diameter of the reference ellipse.
Usage
Ellipse$diameter(t, conjugate = FALSE)
Arguments
ta number, the diameter only depends on t modulo
pi; the axes correspond to t=0 and t=pi/2
conjugatelogical, whether to return the conjugate diameter as well
Returns
A Line object or a list of two Line objects if
conjugate = TRUE.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
diameters <- lapply(c(0, pi/3, 2*pi/3), ell$diameter)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell)
invisible(lapply(diameters, draw))
Method perimeter()
Perimeter of the reference ellipse.
Usage
Ellipse$perimeter()
Method pointFromAngle()
Intersection point of the ellipse with the half-line
starting at the ellipse center and forming angle theta with
the major axis.
Usage
Ellipse$pointFromAngle(theta, degrees = TRUE)
Arguments
thetaa number, the angle, or a numeric vector
degreeslogical, whether theta is given in degrees
Returns
A point of the ellipse if length(theta)==1 or a
two-column matrix of points of the ellipse if
length(theta) > 1 (one point per row).
Method pointFromEccentricAngle()
Point of the ellipse with given eccentric angle.
Usage
Ellipse$pointFromEccentricAngle(t)
Arguments
ta number, the eccentric angle in radians, or a numeric vector
Returns
A point of the ellipse if length(t)==1 or a
two-column matrix of points of the ellipse if
length(t) > 1 (one point per row).
Method semiMajorAxis()
Semi-major axis of the ellipse.
Usage
Ellipse$semiMajorAxis()
Returns
A segment (Line object).
Method semiMinorAxis()
Semi-minor axis of the ellipse.
Usage
Ellipse$semiMinorAxis()
Returns
A segment (Line object).
Method foci()
Foci of the reference ellipse.
Usage
Ellipse$foci()
Returns
A list with the two foci.
Method tangent()
Tangents of the reference ellipse at a point given by
its eccentric angle.
Usage
Ellipse$tangent(t)
Arguments
teccentric angle, there is one tangent for each value of t
modulo 2*pi; for t = 0, pi/2, pi, -pi/2, these are the
tangents at the vertices of the ellipse
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
tangents <- lapply(c(0, pi/3, 2*pi/3, pi, 4*pi/3, 5*pi/3), ell$tangent)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, col = "yellow")
invisible(lapply(tangents, draw, col = "blue"))
Method normal()
Normal unit vector to the ellipse.
Usage
Ellipse$normal(t)
Arguments
ta number, the eccentric angle in radians of the point of the
ellipse at which we want the normal unit vector
Returns
The normal unit vector to the ellipse at the point given by
eccentric angle t.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
t_ <- seq(0, 2*pi, length.out = 13)[-1]
plot(NULL, asp = 1, xlim = c(-5,7), ylim = c(-3,5),
xlab = NA, ylab = NA)
draw(ell, col = "magenta")
for(i in 1:length(t_)){
t <- t_[i]
P <- ell$pointFromEccentricAngle(t)
v <- ell$normal(t)
draw(Line$new(P, P+v, FALSE, FALSE))
}
Method theta2t()
Convert angle to eccentric angle.
Usage
Ellipse$theta2t(theta, degrees = TRUE)
Arguments
thetaangle between the major axis and the half-line starting
at the center of the ellipse and passing through the point of interest
on the ellipse
degreeslogical, whether theta is given in degrees
Returns
The eccentric angle of the point of interest on the ellipse,
in radians.
Examples
O <- c(1, 1)
ell <- Ellipse$new(O, 5, 2, 30)
theta <- 20
P <- ell$pointFromAngle(theta)
t <- ell$theta2t(theta)
tg <- ell$tangent(t)
OP <- Line$new(O, P, FALSE, FALSE)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,5),
xlab = NA, ylab = NA)
draw(ell, col = "antiquewhite")
points(P[1], P[2], pch = 19)
draw(tg, col = "red")
draw(OP)
draw(ell$semiMajorAxis())
text(t(O+c(1,0.9)), expression(theta))
Method regressionLines()
Regression lines. The regression line of y on x intersects
the ellipse at its rightmost point and its leftmost point.
The tangents at these points are vertical.
The regression line of x on y intersects the ellipse at its
topmost point and its bottommost point.
The tangents at these points are horizontal.
Usage
Ellipse$regressionLines()
Returns
A list with two Line objects:
the regression line of y on x and the regression line of x on y.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
reglines <- ell$regressionLines()
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
draw(reglines$YonX, lwd = 2, col = "blue")
draw(reglines$XonY, lwd = 2, col = "green")
Method boundingbox()
Return the smallest rectangle parallel to the axes
which contains the reference ellipse.
Usage
Ellipse$boundingbox()
Returns
A list with two components: the x-limits in x and the
y-limits in y.
Examples
ell <- Ellipse$new(c(2,2), 5, 3, 40)
box <- ell$boundingbox()
plot(NULL, asp = 1, xlim = box$x, ylim = box$y, xlab = NA, ylab = NA)
draw(ell, col = "seaShell", border = "blue")
abline(v = box$x, lty = 2); abline(h = box$y, lty = 2)
Method randomPoints()
Random points on or in the reference ellipse.
Usage
Ellipse$randomPoints(n, where = "in")
Arguments
nan integer, the desired number of points
where"in" to generate inside the ellipse,
"on" to generate on the ellipse
Returns
The generated points in a two columns matrix with n rows.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
pts <- ell$randomPoints(100)
plot(NULL, type="n", asp=1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
points(pts, pch = 19, col = "blue")
Method clone()
The objects of this class are cloneable with this method.
Usage
Ellipse$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
## ------------------------------------------------
## Method `Ellipse$new`
## ------------------------------------------------
Ellipse$new(c(1,1), 3, 2, 30)
## ------------------------------------------------
## Method `Ellipse$matrix`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 1, 30)
S <- ell$matrix()
O <- ell$center
pts <- ell$path(4L) # four points on the ellipse
apply(pts, 1L, function(M) t(M-O) %*% S %*% (M-O))
## ------------------------------------------------
## Method `Ellipse$path`
## ------------------------------------------------
library(PlaneGeometry)
ell <- Ellipse$new(c(1, -1), rmajor = 3, rminor = 2, alpha = 30)
innerPath <- ell$path(npoints = 10)
outerPath <- ell$path(npoints = 10, outer = TRUE)
bbox <- ell$boundingbox()
plot(NULL, asp = 1, xlim = bbox$x, ylim = bbox$y, xlab = NA, ylab = NA)
draw(ell, border = "red", lty = "dashed")
polygon(innerPath, border = "blue", lwd = 2)
polygon(outerPath, border = "green", lwd = 2)
## ------------------------------------------------
## Method `Ellipse$diameter`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
diameters <- lapply(c(0, pi/3, 2*pi/3), ell$diameter)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell)
invisible(lapply(diameters, draw))
## ------------------------------------------------
## Method `Ellipse$tangent`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
tangents <- lapply(c(0, pi/3, 2*pi/3, pi, 4*pi/3, 5*pi/3), ell$tangent)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, col = "yellow")
invisible(lapply(tangents, draw, col = "blue"))
## ------------------------------------------------
## Method `Ellipse$normal`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
t_ <- seq(0, 2*pi, length.out = 13)[-1]
plot(NULL, asp = 1, xlim = c(-5,7), ylim = c(-3,5),
xlab = NA, ylab = NA)
draw(ell, col = "magenta")
for(i in 1:length(t_)){
t <- t_[i]
P <- ell$pointFromEccentricAngle(t)
v <- ell$normal(t)
draw(Line$new(P, P+v, FALSE, FALSE))
}
## ------------------------------------------------
## Method `Ellipse$theta2t`
## ------------------------------------------------
O <- c(1, 1)
ell <- Ellipse$new(O, 5, 2, 30)
theta <- 20
P <- ell$pointFromAngle(theta)
t <- ell$theta2t(theta)
tg <- ell$tangent(t)
OP <- Line$new(O, P, FALSE, FALSE)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,5),
xlab = NA, ylab = NA)
draw(ell, col = "antiquewhite")
points(P[1], P[2], pch = 19)
draw(tg, col = "red")
draw(OP)
draw(ell$semiMajorAxis())
text(t(O+c(1,0.9)), expression(theta))
## ------------------------------------------------
## Method `Ellipse$regressionLines`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
reglines <- ell$regressionLines()
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
draw(reglines$YonX, lwd = 2, col = "blue")
draw(reglines$XonY, lwd = 2, col = "green")
## ------------------------------------------------
## Method `Ellipse$boundingbox`
## ------------------------------------------------
ell <- Ellipse$new(c(2,2), 5, 3, 40)
box <- ell$boundingbox()
plot(NULL, asp = 1, xlim = box$x, ylim = box$y, xlab = NA, ylab = NA)
draw(ell, col = "seaShell", border = "blue")
abline(v = box$x, lty = 2); abline(h = box$y, lty = 2)
## ------------------------------------------------
## Method `Ellipse$randomPoints`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
pts <- ell$randomPoints(100)
plot(NULL, type="n", asp=1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
points(pts, pch = 19, col = "blue")
PlaneGeometry documentation built on Aug. 10, 2023, 1:09 a.m.
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| Ellipse | R Documentation |
R6 class representing an ellipse
Description
An ellipse is given by a center, two radii (rmajor
and rminor), and the angle (alpha) between the major axis and
the horizontal direction.
Active bindings
centerget or set the center
rmajorget or set the major radius of the ellipse
rminorget or set the minor radius of the ellipse
alphaget or set the angle of the ellipse
degreesget or set the
degreesfield
Methods
Public methods
Method new()
Create a new Ellipse object.
Usage
Ellipse$new(center, rmajor, rminor, alpha, degrees = TRUE)
Arguments
centera point, the center of the rotation
rmajorpositive number, the major radius
rminorpositive number, the minor radius
alphaa number, the angle between the major axis and the horizontal direction
degreeslogical, whether
alphais given in degrees
Returns
A new Ellipse object.
Examples
Ellipse$new(c(1,1), 3, 2, 30)
Method print()
Show instance of an Ellipse object.
Usage
Ellipse$print(...)
Arguments
...ignored
Method isEqual()
Check whether the reference ellipse equals an ellipse.
Usage
Ellipse$isEqual(ell)
Arguments
ellAn
Ellipseobject.
Method equation()
The coefficients of the implicit equation of the ellipse.
Usage
Ellipse$equation()
Details
The implicit equation of the ellipse is
Ax² + Bxy + Cy² + Dx + Ey + F = 0. This method returns
A, B, C, D, E and F.
Returns
A named numeric vector.
Method includes()
Check whether a point lies on the reference ellipse.
Usage
Ellipse$includes(M)
Arguments
Ma point
Method contains()
Check whether a point is contained in the reference ellipse.
Usage
Ellipse$contains(M)
Arguments
Ma point
Method matrix()
Returns the 2x2 matrix S associated to the reference
ellipse. The equation of the ellipse is t(M-O) %*% S %*% (M-O) = 1.
Usage
Ellipse$matrix()
Examples
ell <- Ellipse$new(c(1,1), 5, 1, 30) S <- ell$matrix() O <- ell$center pts <- ell$path(4L) # four points on the ellipse apply(pts, 1L, function(M) t(M-O) %*% S %*% (M-O))
Method path()
Path that forms the reference ellipse.
Usage
Ellipse$path(npoints = 100L, closed = FALSE, outer = FALSE)
Arguments
npointsnumber of points of the path
closedBoolean, whether to return a closed path; you don't need a closed path if you want to plot it with
polygonouterBoolean; if
TRUE, the ellipse will be contained inside the path, otherwise it will contain the path
Returns
A matrix with two columns x and y of
length npoints.
Examples
library(PlaneGeometry) ell <- Ellipse$new(c(1, -1), rmajor = 3, rminor = 2, alpha = 30) innerPath <- ell$path(npoints = 10) outerPath <- ell$path(npoints = 10, outer = TRUE) bbox <- ell$boundingbox() plot(NULL, asp = 1, xlim = bbox$x, ylim = bbox$y, xlab = NA, ylab = NA) draw(ell, border = "red", lty = "dashed") polygon(innerPath, border = "blue", lwd = 2) polygon(outerPath, border = "green", lwd = 2)
Method diameter()
Diameter and conjugate diameter of the reference ellipse.
Usage
Ellipse$diameter(t, conjugate = FALSE)
Arguments
ta number, the diameter only depends on
tmodulopi; the axes correspond tot=0andt=pi/2conjugatelogical, whether to return the conjugate diameter as well
Returns
A Line object or a list of two Line objects if
conjugate = TRUE.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
diameters <- lapply(c(0, pi/3, 2*pi/3), ell$diameter)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell)
invisible(lapply(diameters, draw))
Method perimeter()
Perimeter of the reference ellipse.
Usage
Ellipse$perimeter()
Method pointFromAngle()
Intersection point of the ellipse with the half-line
starting at the ellipse center and forming angle theta with
the major axis.
Usage
Ellipse$pointFromAngle(theta, degrees = TRUE)
Arguments
thetaa number, the angle, or a numeric vector
degreeslogical, whether
thetais given in degrees
Returns
A point of the ellipse if length(theta)==1 or a
two-column matrix of points of the ellipse if
length(theta) > 1 (one point per row).
Method pointFromEccentricAngle()
Point of the ellipse with given eccentric angle.
Usage
Ellipse$pointFromEccentricAngle(t)
Arguments
ta number, the eccentric angle in radians, or a numeric vector
Returns
A point of the ellipse if length(t)==1 or a
two-column matrix of points of the ellipse if
length(t) > 1 (one point per row).
Method semiMajorAxis()
Semi-major axis of the ellipse.
Usage
Ellipse$semiMajorAxis()
Returns
A segment (Line object).
Method semiMinorAxis()
Semi-minor axis of the ellipse.
Usage
Ellipse$semiMinorAxis()
Returns
A segment (Line object).
Method foci()
Foci of the reference ellipse.
Usage
Ellipse$foci()
Returns
A list with the two foci.
Method tangent()
Tangents of the reference ellipse at a point given by its eccentric angle.
Usage
Ellipse$tangent(t)
Arguments
teccentric angle, there is one tangent for each value of
tmodulo2*pi; fort = 0, pi/2, pi, -pi/2, these are the tangents at the vertices of the ellipse
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
tangents <- lapply(c(0, pi/3, 2*pi/3, pi, 4*pi/3, 5*pi/3), ell$tangent)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, col = "yellow")
invisible(lapply(tangents, draw, col = "blue"))
Method normal()
Normal unit vector to the ellipse.
Usage
Ellipse$normal(t)
Arguments
ta number, the eccentric angle in radians of the point of the ellipse at which we want the normal unit vector
Returns
The normal unit vector to the ellipse at the point given by
eccentric angle t.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
t_ <- seq(0, 2*pi, length.out = 13)[-1]
plot(NULL, asp = 1, xlim = c(-5,7), ylim = c(-3,5),
xlab = NA, ylab = NA)
draw(ell, col = "magenta")
for(i in 1:length(t_)){
t <- t_[i]
P <- ell$pointFromEccentricAngle(t)
v <- ell$normal(t)
draw(Line$new(P, P+v, FALSE, FALSE))
}
Method theta2t()
Convert angle to eccentric angle.
Usage
Ellipse$theta2t(theta, degrees = TRUE)
Arguments
thetaangle between the major axis and the half-line starting at the center of the ellipse and passing through the point of interest on the ellipse
degreeslogical, whether
thetais given in degrees
Returns
The eccentric angle of the point of interest on the ellipse, in radians.
Examples
O <- c(1, 1)
ell <- Ellipse$new(O, 5, 2, 30)
theta <- 20
P <- ell$pointFromAngle(theta)
t <- ell$theta2t(theta)
tg <- ell$tangent(t)
OP <- Line$new(O, P, FALSE, FALSE)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,5),
xlab = NA, ylab = NA)
draw(ell, col = "antiquewhite")
points(P[1], P[2], pch = 19)
draw(tg, col = "red")
draw(OP)
draw(ell$semiMajorAxis())
text(t(O+c(1,0.9)), expression(theta))
Method regressionLines()
Regression lines. The regression line of y on x intersects the ellipse at its rightmost point and its leftmost point. The tangents at these points are vertical. The regression line of x on y intersects the ellipse at its topmost point and its bottommost point. The tangents at these points are horizontal.
Usage
Ellipse$regressionLines()
Returns
A list with two Line objects:
the regression line of y on x and the regression line of x on y.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
reglines <- ell$regressionLines()
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
draw(reglines$YonX, lwd = 2, col = "blue")
draw(reglines$XonY, lwd = 2, col = "green")
Method boundingbox()
Return the smallest rectangle parallel to the axes which contains the reference ellipse.
Usage
Ellipse$boundingbox()
Returns
A list with two components: the x-limits in x and the
y-limits in y.
Examples
ell <- Ellipse$new(c(2,2), 5, 3, 40) box <- ell$boundingbox() plot(NULL, asp = 1, xlim = box$x, ylim = box$y, xlab = NA, ylab = NA) draw(ell, col = "seaShell", border = "blue") abline(v = box$x, lty = 2); abline(h = box$y, lty = 2)
Method randomPoints()
Random points on or in the reference ellipse.
Usage
Ellipse$randomPoints(n, where = "in")
Arguments
nan integer, the desired number of points
where"in"to generate inside the ellipse,"on"to generate on the ellipse
Returns
The generated points in a two columns matrix with n rows.
Examples
ell <- Ellipse$new(c(1,1), 5, 2, 30)
pts <- ell$randomPoints(100)
plot(NULL, type="n", asp=1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
points(pts, pch = 19, col = "blue")
Method clone()
The objects of this class are cloneable with this method.
Usage
Ellipse$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
## ------------------------------------------------
## Method `Ellipse$new`
## ------------------------------------------------
Ellipse$new(c(1,1), 3, 2, 30)
## ------------------------------------------------
## Method `Ellipse$matrix`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 1, 30)
S <- ell$matrix()
O <- ell$center
pts <- ell$path(4L) # four points on the ellipse
apply(pts, 1L, function(M) t(M-O) %*% S %*% (M-O))
## ------------------------------------------------
## Method `Ellipse$path`
## ------------------------------------------------
library(PlaneGeometry)
ell <- Ellipse$new(c(1, -1), rmajor = 3, rminor = 2, alpha = 30)
innerPath <- ell$path(npoints = 10)
outerPath <- ell$path(npoints = 10, outer = TRUE)
bbox <- ell$boundingbox()
plot(NULL, asp = 1, xlim = bbox$x, ylim = bbox$y, xlab = NA, ylab = NA)
draw(ell, border = "red", lty = "dashed")
polygon(innerPath, border = "blue", lwd = 2)
polygon(outerPath, border = "green", lwd = 2)
## ------------------------------------------------
## Method `Ellipse$diameter`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
diameters <- lapply(c(0, pi/3, 2*pi/3), ell$diameter)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell)
invisible(lapply(diameters, draw))
## ------------------------------------------------
## Method `Ellipse$tangent`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
tangents <- lapply(c(0, pi/3, 2*pi/3, pi, 4*pi/3, 5*pi/3), ell$tangent)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, col = "yellow")
invisible(lapply(tangents, draw, col = "blue"))
## ------------------------------------------------
## Method `Ellipse$normal`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
t_ <- seq(0, 2*pi, length.out = 13)[-1]
plot(NULL, asp = 1, xlim = c(-5,7), ylim = c(-3,5),
xlab = NA, ylab = NA)
draw(ell, col = "magenta")
for(i in 1:length(t_)){
t <- t_[i]
P <- ell$pointFromEccentricAngle(t)
v <- ell$normal(t)
draw(Line$new(P, P+v, FALSE, FALSE))
}
## ------------------------------------------------
## Method `Ellipse$theta2t`
## ------------------------------------------------
O <- c(1, 1)
ell <- Ellipse$new(O, 5, 2, 30)
theta <- 20
P <- ell$pointFromAngle(theta)
t <- ell$theta2t(theta)
tg <- ell$tangent(t)
OP <- Line$new(O, P, FALSE, FALSE)
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,5),
xlab = NA, ylab = NA)
draw(ell, col = "antiquewhite")
points(P[1], P[2], pch = 19)
draw(tg, col = "red")
draw(OP)
draw(ell$semiMajorAxis())
text(t(O+c(1,0.9)), expression(theta))
## ------------------------------------------------
## Method `Ellipse$regressionLines`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
reglines <- ell$regressionLines()
plot(NULL, asp = 1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
draw(reglines$YonX, lwd = 2, col = "blue")
draw(reglines$XonY, lwd = 2, col = "green")
## ------------------------------------------------
## Method `Ellipse$boundingbox`
## ------------------------------------------------
ell <- Ellipse$new(c(2,2), 5, 3, 40)
box <- ell$boundingbox()
plot(NULL, asp = 1, xlim = box$x, ylim = box$y, xlab = NA, ylab = NA)
draw(ell, col = "seaShell", border = "blue")
abline(v = box$x, lty = 2); abline(h = box$y, lty = 2)
## ------------------------------------------------
## Method `Ellipse$randomPoints`
## ------------------------------------------------
ell <- Ellipse$new(c(1,1), 5, 2, 30)
pts <- ell$randomPoints(100)
plot(NULL, type="n", asp=1, xlim = c(-4,6), ylim = c(-2,4),
xlab = NA, ylab = NA)
draw(ell, lwd = 2)
points(pts, pch = 19, col = "blue")
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