3D Isosurface Plots with Plotly in Python

Data visualization is one of the highlights of data analysis as it involves a graphical representation of data to help extract insights and patterns simply from raw data. We can enhance our ability to interpret data-driven findings greatly!

Utilizing Plotly's dynamic capabilities, we can now transform raw data into highly interactive plots which are seamless in rendering.

In this answer, we will cover a highly interesting type of data visualization plot, an isosurface plot, using this library.

Plotly

Plotly is a data visualization library that allows us to create rich and dynamic visualizations in Python, R, and JavaScript. We can create plots ranging from line graphs and bar charts to maps and 3D visualizations. Some interesting features of Plotly include the following:

1. zooming

2. panning

3. tooltips

4. rotating

5. downloading plots

Let's first understand what isosurface plots are and then implement them.

Isosurface plots

The word isosurface is a combination of iso and surface. Iso refers to "same." An isosurface plot is a type of three-dimensional visualization that represents any surface within a three-dimensional space with the condition that all points on the surface should have the same value. It is used to represent constant value points like temperature or pressure.

We can call it to be the 3D equivalent of contour line plots.

Syntax

The go.Isosurface function creates a 3D isosurface plot by connecting points with the same value within a given range, creating wonderful isosurface plots!

We have to call it within the go.Figure function to render the interactive figure on the screen.

Parameters

A few common parameters for the go.Isosurface function have been mentioned in the table below.

Code implementation

To understand 3D isosurface plots, we will implement various such plots with different customizations and understand how they work.

Basic 3D isosurface plots

The following code is the basic foundation of isosurface plots.

Code explanation

• Line 1: First, we import the necessary modules for our code. We use plotly.graph_objects with the alias name go for our interactive plotting.

• Lines 3–11: Next up, we create a new Figure object fig and add an Isosurface plot to it using the go.Isosurface() function. Let's go through its parameters:

  • x, y, and z: These lists represent the coordinates of vertices in 3D.

  • value: This list represents the scalar values of each vertex of the isosurface.

  • isomin and isomax: These parameters represent the minimum and maximum scalar values for the isosurface, respectively.

  • colorscale: This parameter determines the color scale for our diagram. For instance, 'magma' here.

• Lines 13–17: Having configured the figure, we now update the layout of the figure's scene using fig.update_layout(). In the scene parameter, we customize the axis titles.

• Line 19: Finally, we use fig.show() to display our isosurface plot with our given data. We can see a browser open in which the interactive plot is rendered.

Note: To save the output in an HTML file, fig.write_html("output.html", auto_open=True) can be used.

Demonstration

This is what our basic plot looks like.

Advanced 3D isosurface plots

We will now be implementing isosurface plots with greater customization. Different equations can be modeled using such plots as well.

Code explanation

• Line 1–2: We import our necessary modules, plotly.graph_objects as go, and numpy as np.

• Line 4: We create our 3D coordinate grids X, Y, and Z using np.mgrid. Each grid spans from -5 to 5 i.e., along the axis, and contains 40 points.

• Line 6: We can create our own values to display different kinds of plots. Here, values are calculated as a combination of $X^2 + Y^2 + Z^2$ multiplied by the exponential decay of $((X - 2)^2 + (Y + 2)^2 + (Z - 2)^2)$ with a decay factor of -0.2.

• Lines 8–19: We create a Figure object named fig and add an Isosurface plot to it using go.Isosurface(). To correctly display our plot, we specify flattened x, y, and z coordinates from the grids and the flattened ‘values’ array. Our parameters are:

  • isomin and isomax define the range of displayed values.

  • caps hides the caps of the isosurfaces.

  • slices_z and slices_y define slices along the Z and Y axes.

  • colorscale determines the color mapping. For instance, 'electric'.

• Lines 21–30: Next, we update the figure's layout through fig.update_layout(). Within the scene parameter, we customize the axis titles, set the background color to black, and set the font color to white.

• Line 32: Finally, we display our plot using fig.show().

Demonstration

This is how an isosurface plot with more customizations can look like.

Multiple surfaces

We can simply add more surfaces using the parameter surface_count and defining the number of surfaces we want in the plot.

Demonstration

This is how an isosurface with multiple surfaces looks like.

Opacity

We can change the opacity of the plot to display the layers within vividly. This can be done using the opacity keyword.

Demonstration

This is how an isosurface with multiple surfaces and lesser opacity looks like.

Adding slices to the plot

Here, we add two more parameters. slices_z and slices_y parameters add cross-sectional slices to the isosurface plot along the Z and Y axes, respectively. This allows the visualization of the isosurface's internal structure at specific axis positions.

Demonstration

This is how an isosurface with multiple slices looks like.

Use cases of isosurface plots

There are various ways isosurface plots can be aligned with real-life data. Let's explore a few use cases.

Medical Imaging

Isosurface plots can show detailed anatomical structures from MRI and CT scans.

Geophysics

Isosurface plots can assist in mapping subsurface formations by using seismic or gravity data.

Fluid Dynamics

Isosurface plots are great for visualizing fluid flow around objects and understanding hydrodynamic processes.

Simulations

Isosurface plots can be used in climate modeling and particle physics.