细分曲面造型技术英文版【正版保证】 阿里云 lit azw3 txt pdf caj 下载 在线

细分曲面造型技术是当前计算机辅助设计和***业数字化领域的一项重要的曲面造型技术，在逆向工程中有着重要的应用，在高端***业、三维（３Ｄ）打印中的复杂形体设计和***起到积极和不可或缺的作用。

《细分曲面造型技术》共11章，详细介绍细分曲面的理论和造型技术。主要内容包括：细分曲面的数学模型、细分曲面分析、细分曲面性质、面向Ｂ样条曲面混合的ｎ边域曲面片构造、ｎ边域曲面片的光顺、细分曲面插值、细分曲面编辑等。

《细分曲面造型技术》对理论内容进行了精简和浓缩，详细介绍了细分曲面的各种造型技术，可以作为计算数学和应用数学、计算机图形学和机械工程等专业高年级本科生选修、研究生学习的教材使用，也可供几何建模领域的开发人员和科学研究人员参考，还可以作为造型技术手册供工程设计人员查询。

1?Introduction

1．1?Surface?Modeling

1．2?Concept?of?Subdivision?Surfaces

1．3?Development?of?Subdivision?Surfaces

1．4?Idea?of?This?Book

Remarks

Exercises

2?Splines?and?Subdivision

2．1?B-Splines

2．2?B-Spline?Curves?and?Surfaces

2．2．1?B-Spline?Curves?and?Their?Properties

2．2．2?B-Spline?Surfaces?and?Their?Properties

2．3?Knot?Insertion?Algorithm?and?Refinement?of?B-Spline?Curves?and?Surfaces

2．3．1?Subdivision?of?B-Spline?Curves

2．3．2?Subdivision?of?B-Spline?Surface

2．4?Uniform?Subdivision?of?B-Spline?Curves?and?Surfaces

2．4．1?Subdivision?of?Uniform?B-Spline?Curves

2．4．2?Subdivision?of?Uniform?B-Spline?Surfaces

2．5?Box?Spline

2．5．1?Vector?Group?and?Support?Mesh

2．5．2?Inductive?Definition?of?Box?Splines

2．5．3?Basic?Properties?of?Box?Splines

2．6?Box?Spline?Surfaces

2．6．1?Definition?and?Properties

2．6．2?Subdivision?of?Box?Spline?Surfaces

2．6．3?Generating?Function?of?Box?Spline

2．7?Subdivision?Mask?of?Box?Spline?Surface

Remarks

Exercises

3?Meshes?and?Subdivision

3．1?Topological?Structure?of?Meshes?for?Subdivision

3．2?Regular?Mesh

3．3?Subdivision?Scheme

3．4?Quadrila***l?Subdivision

3．4．1?Doo-Sabin?Subdivision

3．4．2?Catmull-Clark?Subdivision

3．4．3?Non-uniform?Subdivision

3．5?Triangular?Subdivision

3．5．1?Loop?Subdivision

3．5．2?Butterfly?Subdivision

3．5．3?□?Subdivision

3．6?Hexagonal?Subdivision

3．6．1?Convexity-Preserving?Subdivision?Scheme

3．6．2?Honeycomb?Subdivision?Scheme

3．7?4-8?Subdivision

3．7．1?4-8?Meshes

3．7．2?Subdivision?Rules

3．8?Classification?of?Subdivision?Schemes

Remarks

Exercises

4?Analysis?of?Subdivision?Surface

4．1?Subdivision?Matrix

4．2?Discrete?Fourier?Transform

4．2．1?Fundament?of?DFT

4．2．2?Discrete?Fourier?Transform

4．2．3?Eigenvalues?and?Eigenvectors?from?DFT

4．3?Eigenvalues?Analysis

4．3．1?Calculation?of?Eigenvalues?and?Eigenvectors

4．3．2?Property?of?the?Limit?Surface

4．3．3?Another?Example?for?Eigenvalues?Analysis

4．4?Characteristic?Mapping

4．4．1?Annular?Surface?and?Its?Gradualness

4．4．2?Definition?of?Characteristic?Mapping

4．4．3?Characteristic?Mapping?and?Continuity?of?Subdivision?Surfaces

4．5?Parameter?Evaluation

4．5．1?Notati***?and?Assumpsits

4．5．2?Mathematical?Setting

4．5．3?Eigenstructure?of?Subdivision?Matrix

4．5．4?Eigenbases?and?Evaluation?for?Non-regular?Patches

4．5．5?Subdivision?Matrix?and?Their?Eigenstructures

4．5．6?Eigenbasis?Functi***

4．5．7?Parameter?Evaluation?and?Characteristic?Mapping

Remarks

Exercises

5?n-Sided?Patches?and?Subdivision?Surfaces

5．1?Methods?for?C***tructing?n-Sided?Patches

5．2?C-C?Subdivision?Surfaces?and?G2?Continuity

5．3?n-Sided?Patches?and?Catmull-Clark?Subdivision

5．3．1?Contribution?of?Our?Method

5．3．2?General?Steps?to?C***truct?n-Sided?Patches?with?Manifold?Method

5．3．3?C***truction?of?Control?Meshes?of?Manifold?Patches

5．3．4?Parameter?Region，?Normalization?Mapping，?and?Basic?Function

5．3．5?Related?Vertex?and?Normalized?Basic?Functi***

5．3．6?Properties?of?the?Patch?S

5．3．7?Extracting?Submeshes?from?C-C?Subdivision?Meshes

5．3．8?Examples

5．4?Subdivision?Modeling，?n-Sided?Patches?and?B-Spline?Boundaries

5．5?C***truct?n-Sided?Patches?by?Using?Non-uniform?C-C?Subdivision?Scheme?and?Skirt-Removed?Approach

5．5．1?Skirt-Removed?Approach

5．5．2?C***truct?n-Sided?Patches?by?Using?Non-uniform?C-C?Subdivision?Scheme?and?Skirt-Removed?Approach

5．6?Non-uniform?C-C?Subdivision?Surface?Interpolating?Corner?Vertices?of?Control?Meshes

5．7?Some?Examples?to?C***truct?Patches?by?Using?the?Non-uniform?C-C?Subdivision?Scheme

Remarks

Exercises

6?Energy?Optimization?Method?and?Subdivision?Surfaces

6．1?Blending?Uniform?Bi-Cubic?B-Spline?Surfaces

6．1．1?Subdivision?Surface?Blending?of?B-Spline?Patches

6．1．2?Optimization?Model?Based?on?Physical?Energy

6．1．3?Compute?Control?Vertices?of?Subdivision?Patches

6．1．4?Preliminary?Discussion?on?Selecting?New?Vertices?by?Energy?Optimization?Method

6．1．5?Select?New?Vertices?by?Energy?Optimization?Method

6．1．6?Determine?Some?New?Vertices

6．1．7?Simplify?Optimization?Model

6．1．8?Examples

6．2?Interpolati***?Using?Subdivision?Surfaces

6．2．1?Subdivision?Surface?and?Interpolation

6．2．2?Direct?Interpolation?Method

6．2．3?Interpolation?Method?with?Fairness

6．2．4?SOR?I***tion?Method?to?Solve?Linear?Systems

6．2．5?Compute?Boundary?Vertices

6．2．6?Evaluating?Energy?Norms?for?Meshes

6．2．7?Examples

Remarks

Exercises

7?In***ctive?Shape?Editing?for?Subdivision?Surfaces

7．1?Adjustment?of?Subdivision?Meshes?Under?Simple?Geometrical?C***traints

7．1．1?Deformation?under?Simple?Geometrical?C***trains

7．1．2?Mapping?the?Relati***hip?of?C***traint?Points?Between?Successive?Subdivision?Levels

7．1．3?The?Deformation?Algorithm

7．2?Editing?of?Subdivision?Level?Meshes?Using?Potential?Functi***

7．2．1?Mesh-C***trained?Deformati***?Under?Potential?Functi***

7．2．2?Updating?of?the?Potential?Function

7．3?Modification?of?the?Limit?Surface?Shape?Under?Geometrical?C***traints

7．3．1?Definition?of?Local?Geometrical?Information?for?Subdivision?Surfaces

7．3．2?Subdivision?Surface?Shape?Modification?Based?on?the?Least-Squares?Method

7．3．3?Subdivision?Surface?Shape?Modification?with?an?Energy?Optimization?Method

7．3．4?Examples?and?Analysis

Remarks

Exercises

8?Intersection?and?Trimming?of?Subdivision?Surfaces

8．1?Related?Work

8．2?Initial?Discrete?Intersection?of?Subdivision?Surfaces

8．2．1?Basic?Idea?of?Discrete?Intersection

8．2．2?Intersection?Test?Between?Quad?Meshes

8．2．3?Subdivision?of?the?Intersected?Mesh?Belt

8．2．4?Error?Control?for?Approximate?Intersection

8．2．5?C***truction?of?Intersection?Lines

8．3?Calculating?High?Precision?Soluti***?with?an?I***tive?Method

8．4?Trimming?Algorithm?for?Subdivision?Surfaces

8．4．1?Determination?of?a?Valid?Parameter?Domain?for?Trimmed?Subdivision?Surfaces

8．4．2?Display?of?Trimmed?Subdivision?Surfaces

8．5?Examples

Remarks

Exercises

9?Subdivision?Surfaces?and?Curve?Networks

9．1?C***truction?of?a?Curve?Network

9．1．1?Basic?Concepts

9．1．2?C***truction?of?a?Curve?Network

9．2?A?Combined?Subdivision?Scheme?and?Its?Improvement

9．2．1?Basic?Principles

9．2．2?Control?Meshes?of?Combined?Subdivision?Surfaces

9．2．3?Basic?***s

9．2．4?Non-uniform?Combined?Subdivision?Schemes

9．3?The?C***truction?of?a?Curve?Network?Interpolation?Surface

9．3．1?Steps?for?C***tructing?an?Interpolated?Surface

9．3．2?Extension?of?the?Combined?Subdivision

9．3．3?Generation?of?the?Initial?Mesh

9．4?Shape?Modification?Based?on?Curve?Network?Editing

9．4．1?Overlapping?Subdivision?Method?for?a?Catmull-Clark?Subdivision?Surface

9．4．2?Overlapping?Subdivision?Method?for?Combined?Subdivision?Surfaces

9．4．3?Local?Updating?of?the?Combined?Subdivision?Surface

9．5?Shape?Fairing?of?a?Combined?Subdivision?Surface?Based?On?Discrete?PDE

9．5．1?Basic?Principle

9．5．2?A?Discrete?PDE?Fairing?Method

9．5．3?Basic?Steps

9．5．4?Example

Remarks

Exercises

10?Fitting?Unstructured?Triangle?Meshes?Using?Subdivision?Surfaces

10．1?A?Simplified?Shrink-Wrapping?Approach?for?Remeshing

10．1．1?Introduction?to?the?Shrink-Wrapping?Approach

10．1．2?C***truction?of?Base?Meshes

10．1．3?Converting?a?Triangle?Mesh?to?a?Quadrila***l?Mesh

10．1．4?Adjusting?the?Positi***?of?the?Vertices?of?Subdivided?Meshes

10．1．5?Choosing?Subdivision?Schemes

10．1．6?Error?Estimation

10．2?Surface?Fitting?by?SLP?（Subdivision?Limit?Position）

10．2．1?The?Error?Function?and?Its?Minimization

10．2．2?The?Base?Mesh?and?Subdivision

10．3?Subdivision?Surface?Fitting?with?a?Squared?Distance?Minimization?Method

10．3．1?C***truction?of?the?Initial?Control?Mesh

10．3．2?Parameterization?of?Mesh?Vertices

10．3．3?Subdivision?Surface?Fitting?Using?a?Squared?Distance?Method

Remarks

Exercises

11?Poisson?Mesh?Editing?Guided?by?Subdivision?Surface

11．1?Traditional?Mesh?Editing?Method

11．2?Poisson?Mesh?Editing

11．3?Poisson?Mesh?Editing?Based?on?Subdivision?Surfaces

11．3．1?C***truction?of?the?Model?Bounding?Mesh

11．3．2?Relati***hip?Between?the?Mesh?Model?and?Subdivision?Surfaces

11．3．3?Boundary?Conditi***?of?Poisson?Equati***?and?Mesh?Local?Transformation

11．3．4?Realization?of?Poisson?Rec***truction?Deformation

11．3．5?Multiresolution?Deformation

11．3．6?Deformation?Instance?Analysis

11．4?Mesh?Deformation?Based?on?Surface?Control

11．4．1?Determination?of?the?Deformation?Region

11．4．2?Refinement?of?the?Deformation?Region

11．4．3?Design?of?Subdivision?Control?Surfaces

11．4．4?The?C***truction?of?Relati***hip?Between?The?Deformation?Mesh?and?the?Subdivision?Control?Surface

11．4．5?Design?of?the?Control?Curve

11．4．6?Local?Transformation?of?the?Triangle?in?The?Deformation?Region

11．4．7?Realization?of?the?Poisson?Rec***truction?Deformation

11．4．8?Deformation?Instances

Remarks

Exercises

References

Wenhe?Liao?is?Professor?in?Nanjing?University?of?Aeronautics?and?Astronautics,?also?the?Vice?President?of?Nanjing?University?of?Science?and?Technology.?He?is?the?director?of?the?Research?Centre?for?Digital?Design?and?Manufacturing?Technology,?Member?of?Geometric?Design?&?Computing?Committee,?China?Society?for?In-dustrial?and?Applied?Mathematics.?His?research?fields?include?air?three-dimensional?（3D）?digi-tal?design,?virtual?assembly,?and?digital?medical?equipment?technology?and?micro-satellite?design.?He?has?published?2?books?and?dozens?of?papers?on?CAD/CAM.

　　Hao?Liu?is?Associate?Professor?in?Nanjing?Uni-versity?of?Aeronautics?and?Astronautics.?He?is?Member?of?Geometric?Design?&?Computing?Committee,?China?Society?for?Industrial?and?Applied?Mathematics.?His?research?fields?include?surface?modeling,?CAD/CAM,?3D?printing?and?CT?image?processing.?He?has?published?a?text-book?and?more?than?ten?papers?on?geometry?modeling?and?CT?image?processing.

　　Tao?Li?is?Lecturer?in?Suzhou?University?of?Sci-ence?and?Technology.?His?research?fields?include?surface?modeling,?reverse?engineering?and?digi-tal?geometry?processing.?He?has?published?more?than?ten?papers?on?geometry?modeling?and?pro-cessing.

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