3dgraphics-and-curvesb, R - rextester

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3dgraphics-and-curvesb

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# Gráfico em 3 dimensões

# Curva
t=seq(0,2.5,by=0.05)
u<-function(s){s*cos(s)}
v<-function(s){(-s^2)*sin(s)/4}

curve(u,-1,1)
plot(u(t),v(t),'l',col="red")

# Superfície
c=1
x <- seq(-1.2,1.2, by=0.1)
y <- seq(-1,1,by=0.1)
mf<-function(s,r){z=(s+r*1i)^5+ s+r*1i + c# |f(x,y)|^2; auxiliar para gráfico
abs(z)
}
require(grDevices) # for trans3d
z <- outer(x, y, mf)
z[is.na(z)] <- 4
op <- par(bg = "white")
persp(x, y, z, theta = 20, phi = 30, expand = 0.5)->res
lines(trans3d(u(t),v(t),mf(u(t),v(t)), res), col = "red", lwd = 2) # Inclui curvas

contour(x, y, z,nlevels = 400)
c=1
f<-function(U){U^5+U+c} 
f(1)

h=0.05; p=20/h; Z=0*(0:p)
Z[1]=1.15 -1i               # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); plot(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=1.15+1i               # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-1+1i               # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-1-1i               # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-0.8               # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-0.75             # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-0.75+0.05*1i             # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-0.75-0.05*1i             # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-0.8+0.05*1i             # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

Z[1]=-0.8-0.05*1i             # Condição inicial
for (i in 1:p){ 
Z[i+1]=Z[i]+h*f(Z[i]) # Método de Euler
}
Z[p+1]                # Aproximação para z(20)
f(Z[p+1])

x=Re(Z); y=Im(Z); points(x,y,xlim=c(-1.2,1.2),ylim=c(-1.2,1.2))
s <- seq(length(x)-1); arrows(x[s], y[s], x[s+1], y[s+1], col = "blue",
length = 0.1, angle = 30)

# Campo de direções
library(pracma)
ff <- function(u){ u^5-u+1}

x <- seq(-2,2, by=0.1)
y <- seq(-2,2,by=0.1)

temp <- meshgrid(x,y)
u <-  Re((temp$Y*1i+temp$X)^5-(temp$Y*1i+temp$X)+1)
v <-  Im((temp$Y*1i+temp$X)^5-(temp$Y*1i+temp$X)+1)

plot(range(x),range(y),type="n",xlab=expression(frac(d*Phi,dx)),ylab=expression(d*Phi/dy))
quiver(temp$X,temp$Y,u,v,scale=0.005,length=0.1,angle=1)

[ + ] Show input
Absolute running time: 2.33 sec, cpu time: 1.3 sec, memory peak: 52 Mb, absolute service time: 2,79 sec

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Error(s), warning(s):

There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
There were 50 or more warnings (use warnings() to see the first 50)
Error in library(pracma) : there is no package called ‘pracma’
Execution halted

[1] 3
[1] 0.8774388-0.7448618i
[1] -2.220446e-16-1.110223e-16i
[1] 0.8774388+0.7448618i
[1] -2.220446e-16+1.110223e-16i
[1] -0.5+0.8660254i
[1] -5.56384e-10+1.000929e-09i
[1] -0.5-0.8660254i
[1] -5.56384e-10-1.000929e-09i
[1] -Inf+NaNi
[1] -Inf+NaNi
[1] Inf+NaNi
[1] Inf+NaNi
[1] 0.8774388+0.7448618i
[1] -2.220446e-16+1.110223e-16i
[1] 0.8774388-0.7448618i
[1] -2.220446e-16-1.110223e-16i
[1] -0.5+0.8660254i
[1] 1.982892e-09-6.391743e-09i
[1] -0.5-0.8660254i
[1] 1.982892e-09+6.391743e-09i