multivar-work/plots/demo-plot-1

Parametric Surface Plotter

This project provides a simple way to define and plot parametric 3D surfaces (or curves) using Python.

• A surface is defined with two parameters:

  
  x = x(t, u), \quad y = y(t, u), \quad z = z(t, u)
  

• A curve is defined with a single parameter:

  
  x = x(t), \quad y = y(t), \quad z = z(t)
  

The script will:

• Generate a mesh of points (for surfaces) or a set of points (for curves)
• Plot the result in 3D with Matplotlib
• Save the plot as a high-definition .svg file, named after the parent directory of the script

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Requirements

Install dependencies:

pip install -r requirements.txt

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Usage

Run the script:

python plot_surface.py

A window with the 3D plot will open, and an .svg will be saved in the same directory.

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Defining Your Own Geometry

1. Surfaces (two parameters: t, u)

Surfaces require two parameters because they are 2D objects. You define three functions in plot_surface.py:

def x_func(t, u): return ...
def y_func(t, u): return ...
def z_func(t, u): return ...

Examples:

• Cone

  
  x = 4t\cos(u), \quad y = 4t\sin(u), \quad z = 10t
  

  def x_func(t, u): return 4 * t * np.cos(u)
  def y_func(t, u): return 4 * t * np.sin(u)
  def z_func(t, u): return 10 * t
  

• Sphere (radius 1)

  
  x = \cos(u)\sin(t), \quad y = \sin(u)\sin(t), \quad z = \cos(t)
  

  def x_func(t, u): return np.cos(u) * np.sin(t)
  def y_func(t, u): return np.sin(u) * np.sin(t)
  def z_func(t, u): return np.cos(t)
  

You can adjust parameter ranges in generate_mesh():

def generate_mesh(t_range=(0, 5), u_range=(0, 2*np.pi), n_t=50, n_u=100):
    ...

• Sphere → t_range=(0, np.pi), u_range=(0, 2*np.pi)
• Cone → t_range=(0, 5), u_range=(0, 2*np.pi)

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2. Curves (one parameter: t)

If your object is not a surface but a curve, you only need one parameter t.

Example: Helix

x = \cos(t), \quad y = \sin(t), \quad z = t

def x_func(t): return np.cos(t)
def y_func(t): return np.sin(t)
def z_func(t): return t

Here you don’t need u at all. The code can be simplified to generate a 1D array of points and plot them as a line in 3D.

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Which Should I Use?

• Two parameters (t, u): Use this for surfaces (sphere, torus, cone, paraboloid, etc.).
• One parameter (t): Use this for curves (helix, circle, line, parametric trajectory).

👉 A quick rule:

• If your equation is like z = f(x, y), or implicit in 3 variables, you usually need two parameters.
• If your equation is like x = f(t), y = g(t), z = h(t), then one parameter is enough.

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Notes

• Always use numpy functions (np.sin, np.cos, etc.), not Python’s built-ins, since the parameters are arrays.
• Some surfaces (like cones, hyperboloids) have two branches; you can add an additional z_func_neg if needed.
• The SVG is automatically named after the script’s parent directory.

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✅ With this, you can parametrize and visualize both surfaces (2D) and curves (1D) by editing only a few functions.