虛擬實境下創作曼陀羅圖於柏拉圖正立面體之研究

Abstract

曼陀羅源自於佛教儀式，歷經千餘年時空交替，不僅為重要的西藏佛教藝術，其彩繪平面曼陀羅圖具祥和勻稱、典雅安定意象，能讓人平靜與放鬆，誠為當代藝術治療方式選項之一。本研究尋找相關文獻書籍，多以平面為主，在網路影音資料中，發現有立體曼陀羅圖之展示，上視圖是曼陀羅平面圖，側面像一座塔樓，引起本研究探討在虛擬實境（Virtual Reality；VR）下，自由創作立體曼陀羅圖的可行性。評估各種開發工具，選擇使用Gravity Sketch工具，創作浮雕式曼陀羅圖，進而結合平鋪技法在柏拉圖正十二面立面體創建立體曼陀羅。本研究採用對稱、重覆、輻射均衡的美學形式作為曼陀羅特色，以幾何、大自然花草為創作元素，表現結構式及半結構式曼陀羅圖。浮雕式曼陀羅圖分別採用8個、12個、6個對稱點；代表佛教中的八苦、十二因緣、六道輪廻的對應關係，試圖融合佛學意涵到作品，作品系列以新生、繁華、凋零對應到人生的青年、中年、老年階段。因柏拉圖正十二面立面體由12個五邊形構成，接近球體，本研究在進行創作前，探討相關圖學原理，試圖建立平鋪單位形於近似球體之數學模式；於繪製單位形（unit shape）平鋪在每一個五邊形後，使單位形交會在立面體的每一個面或頂點上，進而達到使觀賞者看到曼陀羅圖無縫平鋪於近似球體表面的效果。總計作品共45件，計有浮雕式12件實驗、3件主題作品、柏拉圖立面體27件實驗及3件主題作品。希冀本研究所提出之學理引證與創作作品，能為後續立體曼陀羅圖之研究建立參考基石。Mandala originated from Buddhist ceremonies. It has gradually change thru space-time transition. It is not only an important Tibetan Buddhist art, but its painted flat mandala has auspicious and well-proportioned, elegant and stable images, which can help people calm and relax and is truly one of the options for contemporary art therapy. This study searched for relevant literature and books, and most of them were two-dimensional. In the audio-visual materials on the Internet, we found an exhibition of three-dimensional mandala diagrams. The top view is a plan view of a mandala, and the side is like a tower. This study evaluates various development tools and chooses to use the Gravity Sketch tool to create embossed mandala diagrams, and then combine the tiling technique to create a three-dimensional mandala on the Platonic dodecahedron. This study adopts the aesthetic form of symmetry, repetition, and radiation balance as the characteristics of mandala, and uses geometry and natural flowers and plants as developing elements to explore structural and semi-structural mandala diagrams. The embossed mandala diagrams use 8, 12, and 6 symmetrical points respectively; they represent the corresponding relationship between the eight sufferings, twelve karmas, and the six circles in Buddhism, and try to integrate the connotation of Buddhism into the works. The series of works correspond to the youth, middle age, and old age of life. Because Plato's regular twelve-sided cube is composed of 12 pentagons, it is close to a sphere. Before the creation, this study discusses the relevant graphics principles, trying to establish a mathematical model of flattening the unit shape on an approximate sphere; after drawing the unit shape tiled on each pentagon, the unit shape intersects on each face or vertex of the cube, and then achieves the effect that the viewer sees the mandala map seamlessly tiled on the approximate spherical surface. There area total of 45 works, including 12 experiments in embossed mandala diagrams, 3 themed works, 27 experiments in Plato's cube and 3 themed works. It is hoped that the academic citations and creations proposed by this research institute can establish a reference cornerstone for the subsequent research on three-dimensional mandala diagrams.