Length13h 13m
About this audiobook
"Principles of Computational Geometry" delves into the intersection of mathematics, algorithms, and computer science to solve geometric problems using computational methods. We cover a wide range of topics, from fundamental geometric concepts to advanced algorithmic techniques. Our book explores geometric data structures and algorithms designed to efficiently tackle issues like geometric modeling, spatial analysis, and geometric optimization.
We introduce readers to key concepts like convex hulls, Voronoi diagrams, and Delaunay triangulations, which serve as building blocks for solving complex geometric problems. Additionally, we discuss techniques for geometric transformation, intersection detection, and geometric search, providing the tools needed to analyze and manipulate geometric data effectively.
Throughout the text, we highlight practical applications of computational geometry, ranging from computer graphics and image processing to robotics and geographic information systems. We also explore the theoretical underpinnings of computational geometry, offering insights into the mathematical foundations of algorithms and their computational complexity.
Overall, "Principles of Computational Geometry" serves as a comprehensive guide for students, researchers, and practitioners interested in leveraging computational methods to solve geometric problems efficiently and effectively. With its blend of theory and practical applications, our book offers a valuable resource for anyone exploring the rich and diverse field of computational geometry.
Audiobook details
GenreScience and Nature, Education and Learning
Length13 hrs 13 mins
Narrated byListen with 1,000+ voices
FormateBook with Audio
Publish dateFeb 20, 2025
LanguageEnglish
Table of contents
1Introduction to Computational Geometry
21.1 Definition and Scope
3Geometric Primitives:
4Geometric Algorithms:
5Data Structures:: Computational Complexity:
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61.2 Historical Overview
71.2.1 Milestones in the Development of Computational Geometry
81.2.2 Influential Figures in the Field
9Early Developments and Foundations
10Key Concepts and Problems
11Influential Figures in Computational Geometry
12Algorithmic Breakthroughs and Advancements
13Applications and Impact
14Future Directions and Challenges
151.2.3 Evolution of Key Algorithms and Techniques
16Early Developments
17Convex Hull Algorithms
18Voronoi Diagrams
19Delaunay Triangulation
20Line Segment Intersection
21Geometric Data Structures
22Computational Geometry in Practice
231.3 Importance and Applications
24Importance of Computational Geometry:
25Applications of Computational Geometry:
261.3.1 Role in Geographic Information Systems (GIS)
271.3.2 Impact on Computer Graphics and Animation
281.3.3 Applications in Robotics and Automation
29Understanding Computational Geometry:: Key Concepts in Computational Geometry:
301.4 Challenges and Current Trends: Applications of Computational Geometry
311.5 Summary
321.6 Exercise
33Foundations of Geometry
34Historical Background:
35Euclidean Geometry:
36Non-Euclidean Geometries:
37Spherical Geometry:
38Hyperbolic Geometry:
39Foundational Issues and Axiomatic Systems:: Hilbert’s axioms for geometry included:
402.1 Euclidean Geometry
412.1.1 Properties of Euclidean Space
422.1.2 Euclidean Transformations
43Foundations of Geometry:
44Euclidean Transformations:
45Properties of Euclidean Transformations:
46Types of Euclidean Transformations:
47Applications of Euclidean Transformations:
48Conclusion:
492.1.3 Euclidean Distance and Metrics
50Euclidean Geometry Fundamentals
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