形状モデリング
担当教員
授業の到達目標及びテーマ
The objective of the lectures is to study basic methods related to shape modeling, in particular we will consider: parametric representations, spline approximation and interpolation, differential geometry, and topology of curves and surfaces.
授業の概要と方法
Curves and surfaces arise in many applications such as art, industrial design, mathematics, architecture, and engineering, and numerous computer drawing packages and computer-aided design packages have been developed to facilitate the creation of geometric shapes. The objective of the lectures is to study basic geometric methods, in particular we will consider: ・Differential Geometry of Curves and Surfaces ・Elements of computational geometry ・Preliminary mathematics and methods of parametric representation of curves and shapes ・Representational schemes in geometric modeling for Solids- CSG, Boundary representation, sweeps
授業計画
| 回 | テーマ | 内容 |
|---|---|---|
| 1 | Introduction to Shape modeling and geometry modeling | What is shape modeling? |
| 2 | Basic graphics: Curves | Curve representations are introduced and the simplest types of curve, namely lines and conics, are described. |
| 3 | Differential Geometry of Curves and Surfaces (I) | Curves and their tangents. Parmetric and implicit surfaces. Monge form. |
| 4 | Differential Geometry of Curves and Surfaces (II) | Fundamental forms for surfaces. |
| 5 | Elements of Computational Geometry | Finding Dealunay Triangulations. Finding Convex Hulls: Insertion Hull. A connection between Delaunay triangulation and convex hulls. Point Enclosure: The Ray-Shooting Method. |
| 6 | Parametric representation for curves (I) | The Bezier Curves. Properties of the Bernstein Polynomials. |
| 7 | Parametric representation for curves (II | The Bezier Curves. Properties of the Bézier Curves. The de Casteljau algorithm |
| 8 | Parametric representation for curves (III | The B-spline curves. |
| 9 | Parametric representation for surfaces ( IV) | Quadric Surfaces, Bézier and B-spline Surfaces |
| 10 | Basics of Topology | “Homeomorphism”definition. Euler Formulas. Simplices, Complexes and Cell.s |
| 11 | Representational Schemes in Geometric Modeling For Solids. | Problems of Solid Modeling. Basic Concepts. CSG Representation. Opeartions. |
| 12 | Boundary representation | Manifold Versus Nonmanifold Representation. Winged-Edge Representation. Euler-Operators. |
| 13 | Sweep representation | Notions of sweeping. Classification of sweeps. Point membership classification for sweeps. |
| 14 | Fractals and their Applications, Gramma-Based models, L-systems | Deterministic fractals and random. Fractal dimension. |
| 15 | Introduction to Genetic Algorithms | Principles of Genetic Algorithms and their applications to shape design. |
授業外に行うべき学習活動
Read lectures and solve problems
テキスト
Lecture notes
参考書
Given in lecture notes
成績評価基準
According to exam
情報機器使用
PC