Yes, it is possible to use Gnuplot made by Lazarus to plot a 3D surface along with its orthogonal line in Julia. There are multiple ways to achieve this, and in this article, we will explore three different options.

## Option 1: Using the Gadfly Package

The Gadfly package in Julia provides a high-level plotting interface that can be used to create various types of plots, including 3D surfaces. To plot a 3D surface along with its orthogonal line using Gadfly, you can follow these steps:

```
using Gadfly
# Define the function for the surface
f(x, y) = x^2 + y^2
# Define the range of x and y values
x = -10:0.1:10
y = -10:0.1:10
# Create a grid of x and y values
X = repeat(x', length(y), 1)
Y = repeat(y, 1, length(x))
# Evaluate the function at each point in the grid
Z = f.(X, Y)
# Create the 3D surface plot
surface_plot = plot(x=X[:], y=Y[:], z=Z[:], Geom.contour)
# Create the orthogonal line
line_plot = plot(x=[-10, 10], y=[0, 0], Geom.line)
# Combine the surface plot and the line plot
combined_plot = surface_plot + line_plot
# Display the plot
display(combined_plot)
```

This code defines a function `f(x, y)`

that represents the surface equation. It then creates a grid of x and y values, evaluates the function at each point in the grid, and creates a 3D surface plot using the `plot`

function from Gadfly. It also creates a line plot representing the orthogonal line and combines it with the surface plot using the `+`

operator. Finally, it displays the combined plot using the `display`

function.

## Option 2: Using the PyPlot Package

Another option is to use the PyPlot package, which provides a Julia interface to the popular Matplotlib library in Python. To plot a 3D surface along with its orthogonal line using PyPlot, you can follow these steps:

```
using PyPlot
# Define the function for the surface
f(x, y) = x^2 + y^2
# Define the range of x and y values
x = -10:0.1:10
y = -10:0.1:10
# Create a grid of x and y values
X = repeat(x', length(y), 1)
Y = repeat(y, 1, length(x))
# Evaluate the function at each point in the grid
Z = f.(X, Y)
# Create the 3D surface plot
fig = figure()
ax = fig.add_subplot(111, projection="3d")
ax.plot_surface(X, Y, Z)
# Create the orthogonal line
ax.plot([-10, 10], [0, 0], [0, 0], color="red")
# Display the plot
show()
```

This code is similar to the previous option, but it uses the `plot_surface`

function from PyPlot to create the 3D surface plot and the `plot`

function to create the line plot. It also uses the `figure`

and `add_subplot`

functions to create the plot and the `show`

function to display it.

## Option 3: Using the Plots Package

The Plots package in Julia provides a unified interface to various plotting backends, including Gadfly and PyPlot. To plot a 3D surface along with its orthogonal line using Plots, you can follow these steps:

```
using Plots
# Define the function for the surface
f(x, y) = x^2 + y^2
# Define the range of x and y values
x = -10:0.1:10
y = -10:0.1:10
# Create a grid of x and y values
X = repeat(x', length(y), 1)
Y = repeat(y, 1, length(x))
# Evaluate the function at each point in the grid
Z = f.(X, Y)
# Create the 3D surface plot
surface_plot = plot(x=X[:], y=Y[:], z=Z[:], st=:surface)
# Create the orthogonal line
line_plot = plot([-10, 10], [0, 0], st=:line, lc=:red)
# Combine the surface plot and the line plot
combined_plot = surface_plot + line_plot
# Display the plot
display(combined_plot)
```

This code is similar to the first option, but it uses the `plot`

function from Plots to create the 3D surface plot and the line plot. It also uses the `st`

argument to specify the plot type and the `lc`

argument to specify the line color.

After exploring these three options, it is difficult to determine which one is better as it depends on personal preference and specific requirements. However, the Gadfly package provides a high-level interface and is well-suited for creating publication-quality plots, while the PyPlot package offers more flexibility and compatibility with the popular Matplotlib library. The Plots package, on the other hand, provides a unified interface to multiple backends and allows for easy switching between them. Ultimately, the choice of package depends on the user’s familiarity with the interface and the desired level of customization.