Mobile Augmented Reality for Learning 3D Transformations in Computer Graphics

Abstract

Learning computer graphics is challenging because it requires a diverse range of skills, such as mathematics, programming, problem-solving, and visual-spatial skills. In this thesis, we rst investigate factors predicting success in computer graphics and we will show that one of the strongest success predictors is visualspatial skills. An important topic in computer graphics is three-dimensional (3D) transformations, which are used for model transformations, view transformations, and other computer graphics topics such as ray tracing. Transformations are also closely related to visual-spatial skills, such as mental rotation and spatial visualisation. We hence investigate what problems students have with 3D transformations by using historical data from eleven years of exam results and by conducting a user study. Our results suggest that most students understand primitive transformations, but often make errors with sequences of transformations, e.g., due to not understanding how transformations a ect each other; or by misunderstanding how the order of execution of transformations is related to the order they are written in the English language, the order of function calls in OpenGL code, or as a matrix product. Other frequent errors are misunderstanding the rotation direction (i.e., clockwise vs. anti-clockwise) and misinterpreting scaling factors. In addition, many students seem to lack spatial reasoning skills to interpret images of 3D transformations and to make mental models of their e ect. Based on our results we motivate, design, and evaluate a simple mobile augmented reality (AR) tool to help the understanding of 3D transformations. The application augments the camera view with 3D objects and their projected shadows on the coordinate planes, animates sequences of primitive transformations, and shows the relationship between graphics API code and textual descriptions of primitive operations. Our results suggest that AR technology can improve motivation, help learners to visualise 3D transformations, and improve understanding and the ability to answer questions about 3D transformations. We conclude our thesis with a discussion of implications for computer graphics teaching and we suggest avenues for future research.