*Examples*

In Figures 16 and 17, two artworks of the artist called Mark Rothko can be seen. The temperatures were chosen by following the chromostereopsis-temperature algorithm presented above. For calculating the saturation and luminance level of each color, an app called "Visual Color Picker 2.6", created by NOVOSIB software co., was used. The saturation (S), lumination (L), and the hexadecimal color code are shown in both Tables 16 and 17, where the final depth temperatures of each color is also given. The temperature range selected was the 14 ◦C and 38 ◦C. As commented before, this is the temperature range to select when the simplest temperature-depth mapping is desired, one in which the extreme depth levels are always mapped to the extreme temperatures, which users can feel without pain. Similarly, the number of depth layers in each image are three, since those are the number of clearly di fferentiated colors which contribute to the chromostereoptic e ffect.

**Figure 16.** *No 1 (Royal Red and Blue)* by Mark Rothko, 1954 [25]. © Mark Rothko.

**Figure 17.** *No5*/*No22* by Mark Rothko, 1950 [26]. © 1998 Kate Rothko Prizel & Christopher Rothko/Artists Rights Society (ARS), New York.


**Table 16.** Temperature-depth mapping of Figure 14.


**Table 17.** Temperature-depth mapping of Figure 15.

### *2.3. Thermal Display System Prototype*

We designed and developed a thermal display system prototype where the artworks can be installed to feel the different temperatures while exploring them. The system consists of an array of petliers, each one with its own heat-sink and fan, which are driven by a dual H-bridge board controlled through an Arduino Mega microcontroller. The peltier element is a device that releases heat through one side while absorbing heat through the other side when an electric current goes through it. The direction of the current determines which side heats up and which one cools down.

Each petlier from the setup was able to adjust their temperature from as low as 13 ◦C to as high as 40 ◦C. The array of petliers can be seen in Figure 18. The artwork is placed on top of the petlier array. The artwork is printed on Thermal Foamed Capsule Paper by means of a braille printer called TactPlus by Kanematsu USA Inc. Tactplus is a printer that uses thermal technology. By heating the paper, braille and graphics can be easily made. As a result, the user can explore the artwork with the hands while feeling the different temperatures. However, for the different temperatures to be felt more clearly, a thin copper layer was placed between the petliers and the artwork. The schematic of this set up can be seen in Figure 19.

**Figure 18.** Peltier temperature sensor and controller.

**Figure 19.** Squematic set up of the prototype, with the relief paper on top of the copper layer and the array of petliers below it.

Each petlier is set to the desired temperature that the visually impaired user feels with the fingers while exploring that zone of the thermal interactive relief artwork. Mark Rothko's work was used as the artwork model due to the strong chromostereoptic e ffect present there and the simplicity of the shapes. However, under the limitation of the array of twelve petliers, any artwork could be installed and the petliers used both for representing either real depth or chromostereoptic depth. An image of the final prototype can be seen in Figure 20.

**Figure 20.** Completed thermal display prototype with the artwork installed on top of the petlier array.

### *2.4. Mark Rothko's Artwork Experiment*

To verify the accuracy of the proposed algorithm, a final test was performed. The test was announced through the university bulletin board and, in total, eight college students agreed to form part of the experiment. All of them claimed to be interested in arts and technology. The average age was 26.6 years.

The purpose of this experiment was to test whether visual color depth appearing in Rothko's work could be transmitted through tactile sense by means of temperature cues, which resulted from the designed temperature-depth mapping algorithm. For this, the relative distance between two objects or colors was defined in a scale from 0 to 5, with 0 meaning no relative distancing at all, and 5 meaning a really strong distance variation between objects. Negative numbers meant the second object was felt farther away than the first. The intention of this test was not notified to the participants until the test was over since the goal was to capture natural feelings through their vision and touch. Therefore, the only information given to the users was the context in which the test was placed (improving art exploration experience for the visually impaired people) and the scale system for defining relative distances that was going to be used during the test.

The test sessions included an explanation of the test and its procedure, visual exploration of the artwork with depth degree scale questionnaire, and tactile exploration of the artwork with temperature conveyed depth degree scale questionnaire. Test duration was about 20 min per person. The testing procedure was the following: (1) Introducing the context of the research, explaining about visually impaired people, art exploration, and thermal cues as a way of presenting di fferent features such as color and depth; (2) Introduction of the petlier display prototype and the artwork installed on it. Also, explanation about depth, color-depth and temperature as a way of conveying nearness

and farness; (3) The tester was asked to assess and give a scale degree of the relative distance between color 1 and 2, and color 3 and 2 of the Rothko artwork that can be seen in Figure 21. This assessment was done both visually and though tactile exploration with temperature feedback. The order was reverted for each person, so if one user started exploring the artwork and giving a scale to the relative depth visually, then the next user would start assessing the depth by touching the artwork. While touching the artwork, the petliers under it controlled the temperature of each color.

**Figure 21.** Rothko's artwork (*No 1 (Royal Red and Blue)*) used during the experiment and temperatures associated to each color (as calculated through the color-based temperature-depth mapping in Section 2).
