## 1 Introduction  
Augmented reality (AR), a modern information technology integrating virtual assets with real objects, is beneficial for education, such as helping students acquire knowledge and explore physical processes [1, 2, 3, 4, 5]. A review of AR in education over the last 25 years is given in [6], which indicates the future trend of the development of authoring tools. Currently, the adoption of AR technology in teaching has been greatly concerned with tackling the challenges of traditional physical education associated with lack of equipment, difficulty in comprehending concepts, and a tendency of diminishing interest in students [7, 8]. Furthermore, as an emerging and potential education technology, there is a huge demand for AR-based learning resources [9] for wide applications in the sustainable development of education. Numerous research works have been carried out to investigate the flow chart and the architecture of AR development, such as in microprocessor courses [10]. During the creation of AR-based physical experiments [11], the projector-camera system is one of the favorite configurations for creating interactive AR applications without wearing ARglasses [12; 13; 14; 15; 16]. Although the compact and lightweight challenges of AR headsets are tackled by innovative ways such as holographic optical elements and lithography-enabled devices [17], the effectiveness of projector-based AR learning activities has been validated by the satisfaction of users [18]. In fact, the projector-based AR system warps the virtual information onto real objects and brings about a keystone deformation rooted in the 3-dof (pan, tilt, screw) misalignment among projectors, cameras, and screens. Therefore, the homography-based calibration of the keystone effect [13] and the generation of projection content [14] have been frequently addressed when using the projector-based AR to achieve an effective teaching outcome. Furthermore, the projector-based AR learning resource depends upon a large space for high-cost, heavy components such as traditional projectors and desktop PCs to take charge of virtual content and user interactions [19], thus making it less popular for low-cost teaching support multimedia. To provide an affordable AR physical experiment, simple geometric shapes have been frequently designed as AR projection content, since the approximation cuts down the calculation cost of real-time assets [20; 21]. For example, indicative circles are utilized as projection content in the interactive AR exploration of thermal leak phenomena [14]. Obviously, the content-approximated AR system hardly supports the accurate understanding of intrinsic physical quantities such as thermal distribution in targeted phenomena, and the calculated image instead of the specific shape is required to render real physical experiments [22]. Recently, there has been another trend to simplify the hardware configuration of AR systems, such as using POLAR systems as portable PC peripherals [23], and, furthermore, numerical simulations are adopted as the augmented information, such as the AR-based magnetic field application with a tablet screen instead of the conventional projector [24]. Unfortunately, the screen-based AR learning design has some limitations in visualizing the top surface of real objects and keeping the thermal and magnetic reliability of the screen. Therefore, a low-cost AR learning design is still pending for education exploring physical phenomena. In this paper, an accurate and interactive AR learning design for creating affordable projector-based AR physical experiments is proposed. In Section 2, an AR-learning design method is presented based on the low-cost hardware setup with a digital light processing (DLP) module. In Section 3, an off/online algorithm for generating assets is proposed by combing the finite element simulation and the poly fitting method to support the simplified hardware configuration.