風格融合與變形三維模型

Abstract

早期幾何處理的技術多著重於多邊形(polygon)的編輯，然而，若只能編輯多邊形，則對於幾何模型的細節都須一一手工調整，設計師將會花費很多時間於瑣碎的工作上。為了減少設計師的負擔，使設計師更能專注於創作設計，學者們提出各類電腦輔助設計建模的方法，例如基於草圖建模法(sketch-based modeling)和基於實例建模法(example-based modeling)等等。這類的方法可用於產生任何的模型，但對於特殊目的的模型，如拼圖與傢具，設計師卻較難利用這類方法產生他們，因為設計師在設計這類物品時，尚需注意其他性質。舉例來說，設計傢具模型時，除外觀外，也需考慮物理特性、功能性等性質。因此，對於這類物品，學者們也提出了各類建模方法，除外觀外，也同時輔助計算其他性質。本論文研究亦屬於此範疇。我們提出了兩個輔助建模系統，用於輔助產生風格化模型與可變形模型。可應用於啟發設計師靈感，並幫助新手用戶簡單的產生模型。兩系統分別描述如下。

我們提出的第一個方法是三維模型風格化。在日常生活中，我們常會看到各種造型商品，例如乳牛造型馬克杯。這類商品的核心概念，是將一個特定的造型風格賦予到一個功能性的物品上。然而，用傳統的建模工具製作造型商品的模型是很耗時的，設計師必須手工的調整幾何的形狀與顏色。在本篇文章的第一部分，我們提出了一個風格化的方法，給兩個輸入模型，我們的方法可將其中一模型的風格賦予給另一模型上。我們的方法分為兩個階段。第一階段模型被表示成拓樸關係，並使用成長樹演算法算出可能的拓樸組合。對於每一個可能的拓樸組合，於第二階段利用變形(morphing)技巧將兩模型的色彩與形狀融合。結果顯示我們的方法可產生多樣的風格商品。此外，更和一個近期的研究結果(Zoomorphic)比較，使用者認為我們的合成結果更合理、更好看、且更能保留輸入模型特徵。

我們提出的第二個方法為三維模型可變形化。由電影《 變形金剛》所獲得的靈感，該電影裡機器人可自由切換成車子和機器人的型態。我們稱這種藉由關節的旋轉與伸縮來改變形狀的模型為可變形模型。在日常生活中，也常看到可變形模型的應用，例如摺疊家具，變形玩具等等。然而，設計與製作可變形模型是個困難的任務。設計師必須考慮如何切割與擺放子元件，也需考慮變形的順序，使得產生的可變形模型可順利的切換於兩個形狀之間。在本研究中，我們做了一個初步的嘗試，目標是輔助設計師產生可變形模型與其變形動畫。我們根據使用者給定的來源模型、目標模型和目標骨架，採用模擬退火最佳化演算法來分割來源模型。之後再利用兩階段的路徑搜尋演算法計算變形動畫。第一階段我們決定了骨頭移動的順序，而第二階段採用快速探索隨機樹(rapidly-exploring Random Tree, RRT)計算關節伸縮旋轉的角度。雖然我們沒有完全地避開碰撞，實驗結果顯示我們的系統可產生可變形模型與其變形動畫。

Earlier work on geometry processing usually focused the editing of polygons. However, designers will spend much time on tedious work if they can only edit polygons. They have to manually adjust every triangles. To reduce the burden on designers, researchers proposed various modeling techniques, such as sketch-based modeling and example-based modeling. Those methods can be applied to create every types of models, but for specific purpose models, like puzzles and furniture, designers are difficult to design by using those tools. Designers should consider more attributes, such as functionality and physical properties, when creating those products. Some modeling methods for those specific 3D models were proposed as well. In addition to the shape of 3D models, those methods also calculated other attribute to assist designers. The research of this thesis belongs to this category. We propose approaches to assist designers in generating two specific models: stylized or transformable models. They can be used to assist designers in seeking ideas and exploring the design space as well as help novice users create their own designs easily. The two approaches described as follow:

First, an approach for stylizing 3D models is proposed. Products in the cartoon or animal style are very common in our daily life, e.g., Hello Kitty fan, cow mug, etc. However, using conventional modeling tools to create a style product is time consuming. It is tedious to manually modify geometrical details and set texture coordinates. We propose a system to help designers on creating style products. The core concept of such products is to add a particular style to a functional product. Given two input models with one providing style and the other providing function (usage), our approach will extract the style of one 3D model and transfer the style to another 3D model. In implementation, the two models are first mixed at the topological level. A tree-growing algorithm is utilized to search for all possible combinations of the two models. Then, a morphing technique is employed to combined the models at textural and geometric levels. Results show that the proposed approach generates various appealing models. We further compare the results of this work with those of the work of Zoomorphic design. The comparison indicates that our results are more appealing, feature-preserving, and reasonable.

Second, an approach for making transformable 3D models is proposed. The motivation is inspired from the movie ``Transformer'' that the robots in the movie can freely transform between cars and robots. We define a transformable model as a 3D model whose shape can be changed by only rotating or translating it component parts. There are also many other applications of transformable models in our daily life, such as folding furnitures and folding toys. Nevertheless, creating a transformable model is not an easy task. Designers should consider how to shape and arrange each component part so that the model can transform between two very different shapes. They also need to plan a transformation process carefully to ensure that the parts do not collide with each other. In the thesis, we propose a prototype trying to assist designers in designing and animating transformable models, in which a source model is optimally segmented based on a target model and skeleton provided by users, and the motion of transformation is mapped from the source to target models. Although we do not completely avoid collisions, our experimental results indicate that our system can transform a 3D model plausibly.