## 1 Introduction  
Various industries continuously seek to optimize their processes and to enhance user experiences. The persistent pursuit of efficiency, accuracy, and creativity has been a significant driver for technological innovations. Among these innovations, virtual reality (VR), a technology capable of creating a three-dimensional (3D) virtual world that provides users with multiple sensory simulations, has been recognized for its vast potential.  
In a VR environment, users feel as if they are actually at a real scene and can observe the scene in real time [1, 2]. With the increase in demand for VR, coupled with the advances in computer calculation and the popularity of technology, VR has been applied in various industries and scenarios [3]. VR is widely used in various fields, such as games, medical care, training, and design. Among these fields, VR technology is highly applicable to industrial design.  
The 3D computer-aided design (CAD) method enables designers to present their ideas visually. Conventional 3D CAD modeling is performed using a fixed parametric model, that is, using predefined parameters and constraints to create a model. This technique increases the productivity, efficiency, and accuracy in the design process [4, 5] but it is sometimes limited by complexity and hinders creativity.  
Free-form 3D modeling is another 3D CAD technique that is under development. This technique enables designers to create models by using aspects such as gestures and voice and to produce complex and organic shapes in an easy and flexible manner. Free-form 3D modeling can be incorporated with VR technology to achieve higher modeling creativity and operational freedom. Compared with conventional 3D CAD modeling, VR modeling enables designers to view and operate a 3D model in real time, enabling the visualization of more comprehensible spatial relationships and design proportions. In brief, VR adds a more immersive and deeply interactive experience to CAD modeling.  
In CAD modeling, designers' emotional responses, concentration, and sense of control are key factors that affect the design quality and overall design team productivity. Studies have explored the effect of CAD modeling on its users. However, scant research has compared the effects of free-form modeling and parametric CAD modeling on users' emotional responses, flow experiences, and operational performances, particularly, with the incorporation of VR technology.  
Although the incorporation of VR brings a sense of novelty and enjoyment, no clarity exists regarding whether it enhances the concentration and sense of control of designers or whether it is advantageous for achieving the precision required for products designed through CAD, free-form modeling, and parametric modeling.  
In this study, we compared the effects of VR free-form modeling and parametric CAD modeling on designers' emotional responses, flow experiences, and operational performances to clarify the strengths and weaknesses of the two techniques in terms of designers' states of mind. The objectives of this study are described as follows:  
1. To explore the different operational characteristics of CAD modeling and to compare the effects of parametric CAD modeling and VR free-form modeling on designers.
2. To measure emotional response and flow experience and compare the emotional valence, emotional arousal, and flow experience resulting from the use of parametric CAD modeling and VR free-form modeling.
3. To provide recommendations for the CAD process in industrial design and to determine the potential strengths and weaknesses of parametric CAD modeling and VR free-form modeling.