Heat3d

A study on 3D-printed heatmaps

Tyler Wiederich

University of Nebraska-Lincoln

April 7, 2025

Study participation

Before we begin, please access https://shiny.srvanderplas.com/heat3d/ to participate in the pilot study!

Methodology

Goal

The goal of this experiment is to see how well participants estimate values across three chart types.

  • 2D-digital (2dd)
  • 3D-digital (3dd)
  • 3D-printed (3dp)

Stimuli Creation

We use the method of constant stimuli for creating our stimuli.

\[ S=\text{Stimuli} \]

  • All values are between 0 and 100
  • The constant is 50
  • The largest value is 90
  • All other values between 50 and 90 are created such that the ratios between 0.556 and 1 are equally spaced
  • Values between 0 and 50 are chosen such that the same ratios as above are used

Generating Heatmap Data

The general shape of the heatmap is a mixture distribution between mathematical formula and uniform random noise.

\[ Z=0.3\cdot U(0,100) + 0.7\cdot f(X,Y) \]

where \(f(X,Y)\) is any given function, scaled between 0 and 100

  • Top half of a sphere centered at 5.5
  • Lower half of a sphere centered at 5.5

Stimuli Placement

  1. Data is simulated from previous function to generate grid \((X=1\dots 10, Y=1\dots 10)\)
  2. Non-50 value is placed onto grid coordinate that minimizes \(|Z-S|\)
  3. 50 is placed similarly, but only on coordinates that have a Manhattan distance of 3 or 4

\[ |X_1-X_2|+|Y_1-Y_2| = 3 \text{ or } 4 \]

  1. Repeat process 20 times for a list of heatmaps
  2. Use Chi-squared tests to find heatmaps where stimuli are somewhat equally spaced

Heatmap selection

With 9 pairs of values, it is expected to see 1.8 stimuli values in each row/column of the heatmap.

Grid Position 1 2 3 4 5 6 7 8 9 10
Expected 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
Observed \(n_1\) \(n_2\) \(n_3\) \(n_4\) \(n_5\) \(n_6\) \(n_7\) \(n_8\) \(n_9\) \(n_{10}\)

\[ \chi^2=\sum\frac{(\text{Observed}-\text{Expected})^2}{\text{Expected}} \]

We use the grid with the smallest average \(\chi^2\) for the \(X\) and \(Y\) axes.

Study Design

Study Design

For a full replicate, there are \(3\times2\times9=54\) treatment combinations:

  • 3 media types (2dd, 3dd, 3dp)
  • 2 datasets
  • 9 pairs of stimuli

Way too many trials for a single participant’s attention span!

Incomplete Block

Our main interest is the difference between media types, measured at a given ratio and dataset. To accomplish this and to reduce the number of trials per participant, we use 4 of the 9 possible stimuli pairs to create blocks.

\[ 2\times3\times4=24 \]

Experiment

  1. Ask participants which value in a stimuli pair is larger
  2. Ask participants to estimate the value of the smaller stimuli
  3. After each dataset and media combination, ask participant to rate their level of confidence

Population

This study will be used in STAT 218 courses at UNL as a required project.

  • Students who are at least 19 years old and consent to data collection

Students will also complete a series of reflections.

  • Pre-experiment
  • Post-experiment
  • Abstract / paper
  • Video presentation

Other considerations

Type of responses

  • Difference between stimuli and participant response
    • Cleveland and McGill (1984) used \(\log_2(\text{Error}+1/8)\)

Construction of Media

  • How to most similarly construct stimuli so that we can accurately estimate the differences between media types?
    • Color scales for 2dd
    • STL colors for 3dd vs. filament colors for 3dp

Thank you!