| Title: | Building Mandalas from Parametric Equations of Classical Curves |
|---|---|
| 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. |
| Authors: | Luciane Ferreira Alcoforado |
| Maintainer: | Luciane Ferreira Alcoforado <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-11-06 03:25:55 UTC |
| Source: | https://github.com/lucianea/mandalar |
Function to reduce points
f_factor(x, y, k)f_factor(x, y, k)
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 |
Returns a dataframe with the original points plus the respective changed points.
x=c(1,1) y=c(0,1) k=c(0.5) f_factor(x,y,k)x=c(1,1) y=c(0,1) k=c(0.5) f_factor(x,y,k)
Function to rotate points by one or more angles
f_rotacao(x, y, rotacao)f_rotacao(x, y, rotacao)
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) |
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
Returns a dataframe with the original points plus the respective rotations of these points.
x=c(1,1) y=c(0,1) rotacao=c(pi/3, pi/2, pi) f_rotacao(x,y,rotacao)x=c(1,1) y=c(0,1) rotacao=c(pi/3, pi/2, pi) f_rotacao(x,y,rotacao)
Function to translation points by shifts on the x-axis or y-axis
f_trans(x, y, t, d)f_trans(x, y, t, d)
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 |
Returns a dataframe with the original points plus the respective translation of these points.
Luciane Ferreira Alcoforado
x=c(1,1) y=c(0,1) t=c(-3, 3) d=1 f_trans(x,y,t,d)x=c(1,1) y=c(0,1) t=c(-3, 3) d=1 f_trans(x,y,t,d)
Function to translation points by shifts on the x-axis or y-axis or both
f_transxy(x, y, tx, ty)f_transxy(x, y, tx, ty)
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 |
Returns a dataframe with the original points plus the respective translation of these points.
Luciane Ferreira Alcoforado
x=c(1,1) y=c(0,1) tx=c(-1,-2) ty=c(0,0) f_transxy(x,y,tx,ty)x=c(1,1) y=c(0,1) tx=c(-1,-2) ty=c(0,0) f_transxy(x,y,tx,ty)
Function to create a mandala with the basic method
mandalar_basic(curve, theta, k, n, raio, a, b)mandalar_basic(curve, theta, k, n, raio, a, b)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
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)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)
Function to build a astroide
pastroide(theta, raio, k, n)pastroide(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,2*pi) k=45 raio = 1 n=20 pastroide(theta, raio, k, n)theta = c(0,2*pi) k=45 raio = 1 n=20 pastroide(theta, raio, k, n)
Function to build a cardioide
pcardioide(theta, raio, k, n)pcardioide(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,2*pi) k=45 raio = 1 n=20 pcardioide(theta, raio, k, n)theta = c(0,2*pi) k=45 raio = 1 n=20 pcardioide(theta, raio, k, n)
Function to build point for the circle base
pcircle(theta, raio, k, n)pcircle(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,2*pi) #half turn angle raio = 1 k = 45 n=20 pcircle(theta, raio, k, n)theta = c(0,2*pi) #half turn angle raio = 1 k = 45 n=20 pcircle(theta, raio, k, n)
Function to build a deltoide
pdeltoide(theta, raio, k, n)pdeltoide(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,2*pi) k=45 raio = 1 n=20 pdeltoide(theta, raio, k, n)theta = c(0,2*pi) k=45 raio = 1 n=20 pdeltoide(theta, raio, k, n)
Function to build point for the elipse base
pelipse(theta, a, b, k, n)pelipse(theta, a, b, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,2*pi) #half turn angle a = 1 b=2 k = 90 n=20 pelipse(theta, a, b, k, n)theta = c(0,2*pi) #half turn angle a = 1 b=2 k = 90 n=20 pelipse(theta, a, b, k, n)
Function to build a espiral de Fermat
pespiral1(theta, raio, k, n)pespiral1(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,6*pi) k=45 raio = 1 n=20 pespiral1(theta, raio, k, n)theta = c(0,6*pi) k=45 raio = 1 n=20 pespiral1(theta, raio, k, n)
Function to build a espiral hiperbolica
pespiral2(theta, raio, k, n)pespiral2(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,6*pi) k=45 raio = 1 n=20 pespiral2(theta, raio, k, n)theta = c(0,6*pi) k=45 raio = 1 n=20 pespiral2(theta, raio, k, n)
Function to build a lemniscata
plemniscata(theta, raio, k, n)plemniscata(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado
theta = c(0,2*pi) k=45 raio = 1 n=20 plemniscata(theta, raio, k, n)theta = c(0,2*pi) k=45 raio = 1 n=20 plemniscata(theta, raio, k, n)
Function to build a limacon
plimacon(theta, raio, k, n)plimacon(theta, raio, k, n)
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 |
Returns a dataframe with the original points plus the respective rotations of these points.
Luciane Ferreira Alcoforado, João Paulo
theta = c(0,2*pi) k=45 raio = 1 n=20 plimacon(theta, raio, k, n)theta = c(0,2*pi) k=45 raio = 1 n=20 plimacon(theta, raio, k, n)
Function to plot a mandala with points in dataframe
dt |
dataframe with points x and y |
Returns a plot
Luciane Ferreira Alcoforado
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)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)