## 1 Introduction
Moreover, it is suitable for touch interaction in a mobile environment because it uses only a sensor, attached to the nail, as an input device. The user's head movements (especially head rotation) can be tracked from the sensors built in most AR HMDs that can be used in a mobile environment. The head movement is a popular interaction method in commercialized HMDs [3; 4] for selecting a virtual object and is faster and more efficient than the hand interaction (mid-air hand gesture) [15]. We design two interaction methods to manipulate a virtual object, which combine touch interaction and head movements with ray casting [16] and Wireframe Widget [17]. Ray casting is one of the fastest and easiest methods for selecting a virtual object [18]. Here, the user points at objects with a virtual ray emanating from a virtual hand, and then, the objects intersecting with the virtual ray can be selected and manipulated. Wireframe Widget is a widget for manipulating a 3D virtual object in Microsoft Hololens [4], which is a commercial HMD-supporting mobile AR. It can manipulate the position, rotation, and scale of a virtual object separately with widget objects. A user prefers that the  
Figure 1: Conceptual diagram of manipulating a virtual object: An interaction that combines touch interaction and head movements in a mobile augmented reality (AR) environment on a head-mounted display (HMD). (**A**) The user can select the virtual object with ray casting using touch interaction and head motion. (**B**) The user can manipulate the selected virtual object using touch interaction and head motion. (**C**) A picture of the index finger on a nail-mounted internal measurement unit (IMU) sensor. position of the 3D virtual object can be manipulated with 3 DOF, its angle can be rotated with 1 DOF separation, and its scale can be uniformly manipulated (or adjusted) [19; 20]. Wireframe Widget allows user-preferred interaction when manipulating virtual objects. When manipulating the position of a virtual object, separation DOF can be manipulated more precisely than 3 DOF [11], and when a user uses a 2 DOF controller, he/she prefers to manipulate the 3D position of the virtual object by separating the 3D position into the position of a plane (2 DOF) and that of an axis (1 DOF). Given this background, in this study, we design two interactions to manipulate the 3D position: One input modality manipulating the plane position (2 DOF) and the other manipulating the axis position (1 DOF). This paper has the following contributions:  
1. We design two interaction methods that combine touch interaction and head movements, which can conveniently manipulate a virtual object in a mobile AR environment. 2. We confirm that the proposed interaction methods, which are compared with mid-air hand interaction, can conveniently perform the task of repeatedly manipulating a virtual object. 3. Through user evaluation, we confirm that the interaction methods using head movements do not cause serious dizziness. The remainder of this paper is organized as follows. The following section briefly introduces the related work. Section 3 explains the two interactions designed by combining touch interaction and head movements and explains how to manipulate a virtual object with ray casting and the Wireframe Widget by using the designed interactions. To evaluate the proposed interaction methods, in Section 4, we describe user evaluation of manipulating a virtual object. Section 5 discusses the results of the experiment and presents the conclusions.