## 1 Introduction  
[PERSON] and [PERSON] [1] introduced the concept of TUIs more than 20 years ago, and later systematised and defined it as:  
...tangible interfaces give physical form to digital information, employing physical artifacts both as representations and controls for computational media [2].  
For VR, tangible interaction represents a huge potential because physical objects can naturally provide rich haptic cues which are often missing in VR experiences. Users often manipulate virtual objects that have clear physical counterparts, through generic controllers in VR, experiencing the exact same sense of weight, temperature, texture, etc., no matter the virtual object. TUIs can provide more natural interactions [3] and would correspond to a better VR solution according to [PERSON] and [PERSON] [4]. TUIs can also result in higher immersiveness [5, 6] because they provide richer sensory feedback than standard controllers. They can also contribute to higher feeling of presence, particularly physical presence as defined by [PERSON] [7]. At the very least, TUIs can be more fun and engaging [8].  
Implementing tangible interaction within a Virtual Environment (VE) requires the system to be able to detect physical objects, ideally with positional and orientation tracking--six Degrees of Freedom (DOF). Over the years, various alternatives have been tried, from active (instrumented with sensors) to passive objects.  
In our work, we leverage the mature marker recognition algorithms for smartphones as a means to detect physical objects while the user is immersed in a VE. This approach has the advantage of being applicable to smartphone-based VR and making use of already existing hardware on the smartphone: the camera. In addition, visual markers are easy to print and fit to various kinds of physical objects, making this approach very cheap and accessible. These characteristics make this approach suitable for Do It Yourself (DIY)scenarios where users receive a template or a kit to assemble but also to in-class situations where a large number of tangibles and VR systems are needed. Because TUIs are also generally equated with ease of use, our approach is also suitable for walk-up-and-use scenarios where users do not have much time to learn how to use the system such as museums and other cultural heritage exploration situations.  
Although there have been some applications to VR, e.g., [9], the design space for marker-based TUIs for VR has not been sufficiently well studied.  
Our primary contribution is the definition and exploration of a design space of marker-based TUI for VR. We first adopted a research-through-design inspired process and produced several prototypes to help us gain insight about the possibilities of marker-based TUIs. Then, similarly to [PERSON] et al. [10], we performed a formative study where we asked participants to envision possible uses and expectations for marker-based TUIs for VR. Based on the proposed ideas and on our own exploration we mapped out a design space with eight dimensions that can help designers understand alternatives for designing marker-based TUIs. We instantiated the design space in a Tangible VR Book for architectural explorations that we then evaluated.