Mastering Computational Geometry Algorithms with C++ from Udemy

Computational Geometry algorithms have tons of applications in the fields like computer games, computer simulation, computer graphic, CAD/CAM software's, Navigation systems and many more day to day applications. But the data structure and algorithms fall under this category is still considered specialized area due to inherit complexities of those. To become fluent in computational geometry you need at least following knowledge.

Through knowledge on linear algebra and geometrical representation of those.
Mathematical representation of geometrical shapes.
Computational steps for primitive test like intersection and distance queries.
Good understanding on algorithms in computational geometry and where to use those.

In this course I will cover all the required knowledge for you to be fluent and confident on Computational Geometry. Following are the topic expected to cover in this course.

Topics

Basics of linear algebra including vector and matrix arithmetic and implementation of those operations.
Mathematical representation of basic geometry primitives and implementation.
Computational approach for finding intersections and distance between basic primitives like rectangles, lines, planes etc.
Orientation test on geometric primitives.
Polygon triangulation.
Monotone polygon partition.
Plane sweep algorithms.
Convex hull calculations and implementation in both 2D and 3D space.
Overview of simple tree data structures like Binary Search Trees (BST) and Red Black Tree (RBT)
KD Tree implementation and range queries using KDTrees.
Range Trees..
Graph Theory

What's inside

Learning objectives

Applications of computational geometry algorithms.
Able to implement computation geometry algorithms with c++
Precision and performance concern and how to solve them when implementing computational geometry algorithms

Solid understanding on mathematics and the interpretation of mathematics behind computational geometry
Solid understanding on vector algebra to be using in computational geometry.

Applications of computational geometry algorithms.
Able to implement computation geometry algorithms with c++
Precision and performance concern and how to solve them when implementing computational geometry algorithms
Solid understanding on mathematics and the interpretation of mathematics behind computational geometry
Solid understanding on vector algebra to be using in computational geometry.

Syllabus

What are computational Geometry algorithms and real world application. Vector algebra, and geometric representation of vector operations. Implementation of Vector class. Basic geometric queries

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Covers computational geometry algorithms, which are heavily used in computer games, computer simulation, computer graphics, and CAD/CAM software

Requires a solid understanding of linear algebra, geometrical representation, and mathematical representation of geometrical shapes

Focuses on C++ implementation, which allows learners to directly apply the algorithms in practical software development projects

Provides a solid understanding of the mathematics and interpretation of mathematics behind computational geometry, which is essential for deeper understanding

Addresses precision and performance concerns when implementing computational geometry algorithms, which is crucial for real-world applications

Includes an overview of simple tree data structures like Binary Search Trees (BST) and Red Black Tree (RBT), which are fundamental in computer science

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mastering Computational Geometry Algorithms with C++ with these activities:

Review Linear Algebra Fundamentals

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Reinforce your understanding of linear algebra concepts, which are crucial for grasping vector and matrix operations used extensively in computational geometry.

Browse courses on Linear Algebra

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Review vector and matrix operations.
Practice solving linear equation systems.
Study eigenvalues and eigenvectors.

Read 'Computational Geometry: Algorithms and Applications'

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Supplement the course material with a comprehensive textbook that provides in-depth explanations and examples of computational geometry algorithms.

View Computational Geometry on Amazon

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Read the chapters relevant to the course syllabus.
Work through the examples and exercises.
Take notes on key concepts and algorithms.

Implement Basic Geometric Primitives

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Solidify your understanding of geometric primitives by implementing them in C++, focusing on precision and performance.

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Implement point, line, and plane classes.
Implement intersection and distance functions.
Test the implementations thoroughly.

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Write a Blog Post on KD-Tree Applications

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Deepen your understanding of KD-Trees by researching and writing a blog post that explores their various applications in computational geometry and related fields.

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Research KD-Tree applications.
Outline the blog post structure.
Write the blog post with clear explanations.
Include diagrams and examples.

Develop a 2D Convex Hull Visualizer

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Apply your knowledge of convex hull algorithms by creating a visualizer that demonstrates the steps involved in constructing a convex hull.

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Choose a convex hull algorithm (e.g., Graham scan).
Implement the algorithm in C++.
Use a graphics library to visualize the process.
Add interactive features to the visualizer.

Study 'Graphics Gems' series

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Consult a collection of practical solutions and code snippets for common computational geometry problems encountered during implementation.

View Quantum Computing on Amazon

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Browse the table of contents for relevant topics.
Read the articles related to your project.
Adapt the code snippets to your C++ implementation.

Contribute to a Computational Geometry Library

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Enhance your skills and contribute to the community by contributing to an open-source computational geometry library, addressing bugs, improving performance, or adding new features.

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Find an open-source library on GitHub.
Study the library's code and documentation.
Identify a bug or feature to work on.
Submit a pull request with your changes.

Career center

Learners who complete Mastering Computational Geometry Algorithms with C++ will develop knowledge and skills that may be useful to these careers:

Algorithm Developer

An Algorithm Developer researches, designs, and implements algorithms for a variety of applications. This course helps build a foundation for this career, with computational geometry forming its core. The course provides a deep dive into fundamental algorithms. Specifically, the course's focus on geometric primitives, intersection algorithms, polygon triangulation, and convex hull calculations are all essential tools for an Algorithm Developer. Furthermore, the emphasis on C++ implementation ensures that graduates can translate theoretical knowledge into practical, efficient code. An Algorithm Developer will be well-equipped to tackle complex geometric problems across various industries.

See salaries and explore the career path for Algorithm Developer

CAD CAM Software Engineer

A CAD CAM Software Engineer develops software for computer aided design and manufacturing. This course is relevant because computational geometry is at the heart of CAD CAM systems. The course's coverage of mathematical representation of geometric shapes, intersection calculations, and convex hull algorithms helps build a foundation for developing robust and efficient CAD CAM software. Furthermore, the course emphasizes C++ implementation which is highly relevant, as many CAD CAM applications are built using C++. The ability to implement and adapt computational geometry algorithms is essential for a CAD CAM Software Engineer, which this course emphasizes.

See salaries and explore the career path for CAD CAM Software Engineer

Computer Graphics Programmer

A Computer Graphics Programmer develops algorithms and software for generating images and animations. This course helps build a foundation for this career by providing a strong understanding of computational geometry, which is essential for tasks such as rendering, modeling, and animation. Specifically, the course's focus on geometric primitives, transformations, and intersection algorithms directly applies to creating realistic and visually appealing graphics. Furthermore, the C++ implementation skills gained from the course are directly transferable, as C++ is a widely used language in computer graphics. Coverage of convex hull calculation, polygon triangulation and plane sweep algorithms are very helpful in the field of Computer Graphics.

See salaries and explore the career path for Computer Graphics Programmer

Simulation Software Developer

A Simulation Software Developer creates software used to model and simulate real-world systems, often for engineering, scientific, or training purposes. This course helps build a foundation for this role. Computational geometry plays a central role in accurate and efficient simulation. The course's coverage of geometric primitives, intersection algorithms, and collision detection is crucial for developing realistic simulations. Furthermore, the emphasis on C++ implementation aligns with the tools and techniques used in simulation software development. The KD Tree implementation may be useful to optimize searching for object interactions.

See salaries and explore the career path for Simulation Software Developer

Robotics Engineer

A Robotics Engineer designs, builds, and programs robots for various applications. This course helps build a foundation for this role by providing knowledge in computational geometry, a critical aspect of robot navigation and path planning. The course's coverage of vector algebra, geometric primitives, and intersection algorithms is particularly relevant. The implementation of algorithms in C++ as covered in this course may be useful, given its extensive use in robotics programming. Furthermore, understanding of KD Trees and graph theory algorithms will contribute to a robotics engineer's ability to design efficient and intelligent robotic systems.

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Virtual Reality Developer

A Virtual Reality Developer creates immersive experiences for entertainment, training, or simulation. A strong understanding of computational geometry is required to create realistic and interactive VR environments. This course is helpful in gaining that knowledge. VR relies heavily on topics that are covered in this course especially the rendering of 3D geometry, collision detection, and spatial tracking. The C++ emphasis aligns directly with the tools used in VR development, and the skills gained can significantly accelerate a Virtual Reality Developer's ability to create compelling and performant VR experiences. The discussion of Convex hull calculations are useful for collision detection.

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Augmented Reality Developer

An Augmented Reality Developer creates applications that overlay digital information onto the real world. This course helps build a foundation for this role, as computational geometry is essential for tasks such as object recognition, pose estimation, and spatial mapping. The coverage of geometric primitives, feature detection algorithms, and 3D transformations in this course may be useful for developing AR applications. The C++ implementation skills taught in the course are highly relevant, as C++ is often used in AR development. The discussion of Plane sweep algorithms can assist in identifying the layout of a space.

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Navigation System Developer

A Navigation System Developer designs and implements software for navigation systems used in cars, drones, and other vehicles. This course helps build a foundation for this role. Computational geometry is crucial for route planning, obstacle avoidance, and map representation. Topics such as vector algebra, distance calculations, and graph theory algorithms may be useful for building efficient and accurate navigation systems. Moreover, the C++ implementation skills taught in the course are readily applicable, as C++ is often used in embedded systems and navigation software. The KD Tree implementation may be useful to optimize searching for nearby locations.

See salaries and explore the career path for Navigation System Developer

Simulation Engineer

A Simulation Engineer creates computer simulations for various purposes, such as predicting the behavior of physical systems or training individuals in virtual environments. This course helps build a foundation for this role given that computational geometry plays a vital role in creating realistic and accurate simulations. The course's coverage of geometric primitives, intersection algorithms, and collision detection may be useful for developing simulation software. Furthermore, the focus on C++ implementation is highly relevant, as C++ is commonly used in simulation programming. The discussion of KD Trees may be useful to optimize collision detection.

See salaries and explore the career path for Simulation Engineer

Computer Aided Engineering Analyst

A Computer Aided Engineering Analyst uses simulation software to analyze engineering designs and predict their performance. While this role primarily focuses on using existing software, understanding the underlying algorithms is highly valuable. This course helps build a foundation by providing in-depth knowledge of computational geometry, which forms the basis of many CAE tools. The course's coverage of polygon triangulation, finite element mesh generation, and collision detection algorithms helps CAE Analysts better interpret simulation results and optimize design parameters. By taking this course, analysts can leverage the capabilities of CAE software to its full potential.

See salaries and explore the career path for Computer Aided Engineering Analyst

Game Developer

A Game Developer creates video games for computers, consoles, and mobile devices. This course may be useful by covering computational geometry, which is fundamental to game development, especially in areas like collision detection, pathfinding, and 3D modeling. The course's exploration of polygon triangulation, convex hull calculations, and plane sweep algorithms may be useful for optimizing game performance and realism. Furthermore, the focus on C++ implementation directly translates to game development, as C++ is a primary language used in the game industry. Topics on graph theory can assist in designing game mechanics involving pathfinding.

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Geographic Information Systems Specialist

A Geographic Information Systems Specialist analyzes and manages geographic data using GIS software. This course may be useful because computational geometry is used in GIS for spatial analysis, such as determining distances, areas, and relationships between geographic features. The course's coverage of vector algebra, geometric primitives, and range queries may be useful for performing these analyses. The implementation of KD Trees may be useful for spatial indexing and search. Although GIS software often has built in functions, understanding the underlying computational geometry allows for more effective use and customization.

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Software Engineer

A Software Engineer designs, develops, and maintains software systems. This course may be useful in specific areas of software engineering. For instance, the course's coverage of computational geometry is relevant for developing applications that involve spatial data, graphics, or simulations. This course provides a deeper understanding of computational geometry algorithms and their implementation in C++. This can be particularly valuable for Software Engineers working on projects that require efficient and accurate handling of geometric data. Furthermore graph theory algorithms will enhance general problem-solving abilities.

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Machine Learning Engineer

A Machine Learning Engineer develops and deploys machine learning models. This course may be useful because computational geometry techniques can be applied to certain machine learning problems, particularly those involving spatial data or geometric structures. The course's coverage of KD Trees and range trees may be useful for nearest neighbor search and clustering algorithms. While a Machine Learning Engineer focuses on statistical models, familiarity with computational geometry may expand the engineer's toolkit, allowing them to tackle more complex problems. The knowledge gained from this course may improve the performance of machine learning algorithms using a geometric approach.

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Data Scientist

A Data Scientist analyzes large datasets to extract insights and build predictive models. This course may be useful given that computational geometry techniques can be applied to various data science problems, such as clustering, anomaly detection, and dimensionality reduction. The course's coverage of KD Trees and range trees may be useful for nearest neighbor searches and spatial data analysis. Specifically, KD Trees are useful for quickly finding the nearest data points to a given query point. While not a core focus, the foundational knowledge acquired in this course can enhance a Data Scientist's toolkit.

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Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Mastering Computational Geometry Algorithms with C++.

Computational Geometry

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Standard textbook for computational geometry, covering a wide range of topics from basic geometric primitives to advanced algorithms like Voronoi diagrams and Delaunay triangulations. It provides a solid theoretical foundation and detailed explanations of algorithms, making it an excellent resource for understanding the core concepts of the field. It is particularly useful for students and professionals seeking a comprehensive understanding of computational geometry.

Computational Geometry

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Computational Geometry

Kindle Edition

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Quantum Computing

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This collection of short articles on practical solutions to graphics programming problems. While not a comprehensive textbook, it contains many useful algorithms and techniques relevant to computational geometry, particularly for tasks like intersection testing and geometric transformations. It good resource for finding specific solutions to common problems.

Quantum Computing

Kindle Edition

Mastering Computational Geometry Algorithms with C++

What's inside

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