| Type: | Package |
| Title: | Building Mandalas from Parametric Equations of Classical Curves |
| Version: | 0.1.0 |
| Author: | Luciane Ferreira Alcoforado |
| Maintainer: | Luciane Ferreira Alcoforado <lucianea@id.uff.br> |
| Description: | Provides an algorithm for creating mandalas. From the perspective of classic mathematical curves and rigid movements on the plane, the package allows you to select curves and produce mandalas from the curve. The algorithm was developed based on the book by Alcoforado et. al. entitled "Art, Geometry and Mandalas with R" (2022) in press by the USP Open Books Portal. |
| Depends: | R (≥ 3.2) |
| Imports: | ggplot2 |
| License: | GPL-3 |
| URL: | https://lucianealcoforado.shinyapps.io/Mandala/ |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.1 |
| NeedsCompilation: | no |
| Packaged: | 2022-11-02 11:21:42 UTC; TPC02 |
| Repository: | CRAN |
| Date/Publication: | 2022-11-02 19:42:41 UTC |
Mandalar: package for building mandalas from parametric equations of classical curves
Description
Function to reduce points
Usage
f_factor(x, y, k)
Arguments
x |
is a vector length n with coordinate x of point |
y |
is a vector length n with coordinate y of point |
k |
is a vector with factor of decrease or increase points |
Value
Returns a dataframe with the original points plus the respective changed points.
Examples
x=c(1,1)
y=c(0,1)
k=c(0.5)
f_factor(x,y,k)
Mandalar: package for building mandalas from parametric equations of classical curves
Description
Function to rotate points by one or more angles
Usage
f_rotacao(x, y, rotacao)
Arguments
x |
is a vector length n with coordinate x of point |
y |
is a vector length n with coordinate y of point |
rotacao |
is a vector of length k with angles in radians to rotate the point (x,y) |
Details
If x and y dimension is n and rotation dimension is k, then function f_rotacao will return a dataframe with two columns and (n+1)k rows
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Examples
x=c(1,1)
y=c(0,1)
rotacao=c(pi/3, pi/2, pi)
f_rotacao(x,y,rotacao)
creates a dataframe containing the points for the espiral hiperbolica mandala
Description
Function to translation points by shifts on the x-axis or y-axis
Usage
f_trans(x, y, t, d)
Arguments
x |
is a vector length n with coordinate x of point |
y |
is a vector length n with coordinate y of point |
t |
is a vector with shifts on the x or y-axis |
d |
is a direction translation, 1)x or 2)y |
Value
Returns a dataframe with the original points plus the respective translation of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
x=c(1,1)
y=c(0,1)
t=c(-3, 3)
d=1
f_trans(x,y,t,d)
creates a dataframe containing the points for the espiral hiperbolica mandala
Description
Function to translation points by shifts on the x-axis or y-axis or both
Usage
f_transxy(x, y, tx, ty)
Arguments
x |
is a vector length n with coordinate x of point |
y |
is a vector length n with coordinate y of point |
tx |
is a vector with with shifts on the x-axis |
ty |
is a vector with with shifts on the y-axis |
Value
Returns a dataframe with the original points plus the respective translation of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
x=c(1,1)
y=c(0,1)
tx=c(-1,-2)
ty=c(0,0)
f_transxy(x,y,tx,ty)
Create a mandala with algorithm basic
Description
Function to create a mandala with the basic method
Usage
mandalar_basic(curve, theta, k, n, raio, a, b)
Arguments
curve |
Either a character string or a function returning curve equation evaluated at its first argument. Curves "circle","elipse", "cardioide","limacon", "espiral1", "espiral2", "lemniscata", "deltoide" and "astroide" are recognised, case being ignored. |
theta |
is a vector length 2 with start angle and end angle |
k |
is a angle of rotations, k in (0,360) graus |
n |
is a number of points |
raio |
is a positive number for the radius of circle |
a |
is one of the parameters of the curves; for the ellipse is the radius on the x axis |
b |
is one of the parameters of the curves; for the ellipse is the radius on the y axis |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
require(ggplot2)
mandalar_basic("circle", theta = c(0,2*pi), raio=1, k = 45, n=500)
mandalar_basic("cardioide", theta = c(0,2*pi), raio=1, k = 60, n=500)
mandalar_basic("elipse", theta = c(0,2*pi), a=1, b=2, k = 30, n=500)
creates a dataframe containing the points for the astroide mandala
Description
Function to build a astroide
Usage
pastroide(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value. For astroide we do r=3. |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi)
k=45
raio = 1
n=20
pastroide(theta, raio, k, n)
creates a dataframe containing the points for the cardioide mandala
Description
Function to build a cardioide
Usage
pcardioide(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi)
k=45
raio = 1
n=20
pcardioide(theta, raio, k, n)
creates a dataframe containing the points for the circle mandala
Description
Function to build point for the circle base
Usage
pcircle(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi) #half turn angle
raio = 1
k = 45
n=20
pcircle(theta, raio, k, n)
creates a dataframe containing the points for the deltoide mandala
Description
Function to build a deltoide
Usage
pdeltoide(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value. For deltoide we do r=2. |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi)
k=45
raio = 1
n=20
pdeltoide(theta, raio, k, n)
creates a dataframe containing the points for the elipse mandala
Description
Function to build point for the elipse base
Usage
pelipse(theta, a, b, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
a |
is one of the parameters of the curves; for the ellipse is the radius on the x axis |
b |
is one of the parameters of the curves; for the ellipse is the radius on the y axis |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi) #half turn angle
a = 1
b=2
k = 90
n=20
pelipse(theta, a, b, k, n)
creates a dataframe containing the points for the Fermat espiral mandala
Description
Function to build a espiral de Fermat
Usage
pespiral1(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,6*pi)
k=45
raio = 1
n=20
pespiral1(theta, raio, k, n)
creates a dataframe containing the points for the espiral hiperbolica mandala
Description
Function to build a espiral hiperbolica
Usage
pespiral2(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,6*pi)
k=45
raio = 1
n=20
pespiral2(theta, raio, k, n)
creates a dataframe containing the points for the lemniscata mandala
Description
Function to build a lemniscata
Usage
plemniscata(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi)
k=45
raio = 1
n=20
plemniscata(theta, raio, k, n)
creates a dataframe containing the points for the limacon mandala
Description
Function to build a limacon
Usage
plimacon(theta, raio, k, n)
Arguments
theta |
is a vector length 2 with start angle and end angle |
raio |
is a vector length 1 with radius value |
k |
is a vector of length 1 with angles in degree to rotate the point (x,y) |
n |
is a number of points |
Value
Returns a dataframe with the original points plus the respective rotations of these points.
Author(s)
Luciane Ferreira Alcoforado
Examples
theta = c(0,2*pi)
k=45
raio = 1
n=20
plimacon(theta, raio, k, n)
creates a mandala visualization
Description
Function to plot a mandala with points in dataframe
Arguments
dt |
dataframe with points x and y |
Value
Returns a plot
Author(s)
Luciane Ferreira Alcoforado
Examples
require(ggplot2)
n=500; raio=1; t=seq(0,2*pi, length.out = n)
x1=raio*cos(t)
y1=raio*sin(t)
#pontos para os 3 círculos: translação dos pontos iniciais (x1,x=c(x1,x1-raio,x1-2*raio)
x=c(x1,x1-raio,x1-2*raio)
y=c(y1,y1,y1)
dt=data.frame(x,y,z="circulo")
rotacao = (pi/8)*(1:16); n=length(x); xt1=x; yt1=y
dt=f_rotacao(x=dt$x, y=dt$y, rotacao)
plot_mandala(dt)