This project introduces lin-alg, a Rust library providing fundamental linear algebra structures and operations with a focus on performance. It offers core types like vectors and quaternions (with 2D, 3D, and 4D variants), alongside common operations such as addition, subtraction, scalar multiplication, dot and cross products, normalization, and quaternion-specific functionalities like rotations and spherical linear interpolation (slerp). The library aims to be simple, efficient, and dependency-free, suitable for graphics, game development, and other domains requiring linear algebra computations.
This post introduces rotors as a practical alternative to quaternions and matrices for 3D rotations. It explains that rotors, like quaternions, represent rotations as a single action around an arbitrary axis, but offer a simpler, more intuitive geometric interpretation based on the concept of "geometric algebra." The author argues that rotors are easier to understand and implement, visually demonstrating their geometric meaning and providing clear code examples in Python. The post covers basic rotor operations like creating rotations from an axis and angle, composing rotations, and applying rotations to vectors, highlighting rotors' computational efficiency and stability.
Hacker News users discussed the practicality and intuitiveness of using rotors for 3D rotations. Some found the rotor approach more elegant and easier to grasp than quaternions, especially appreciating the clear geometric interpretation and connection to bivectors. Others questioned the claimed advantages, arguing that quaternions remain the superior choice for performance and established library support. The potential benefits of rotors in areas like interpolation and avoiding gimbal lock were acknowledged, but some commenters felt the article didn't fully demonstrate these advantages convincingly. A few requested more comparative benchmarks or examples showcasing rotors' practical superiority in specific scenarios. The lack of widespread adoption and existing tooling for rotors was also raised as a barrier to entry.
This post explores the complexities of representing 3D rotations, contrasting quaternions with other methods like rotation matrices and Euler angles. It highlights the issues of gimbal lock and interpolation difficulties inherent in Euler angles, and the computational cost of rotation matrices. Quaternions, while less intuitive, offer a more elegant and efficient solution. The post breaks down the math behind quaternions, explaining how they represent rotations as points on a 4D hypersphere, and demonstrates their advantages for smooth interpolation and avoiding gimbal lock. It emphasizes the practical benefits of quaternions in computer graphics and other applications requiring 3D manipulation.
HN users generally praised the article for its clear explanation of quaternions and their application to 3D rotations. Several commenters appreciated the visual approach and interactive demos, finding them helpful for understanding the concepts. Some discussed alternative representations like rotation matrices and axis-angle, comparing their strengths and weaknesses to quaternions. A few users pointed out the connection to complex numbers and offered additional resources for further exploration. One commenter mentioned the practical uses of quaternions in game development and other fields. Overall, the discussion highlighted the importance of quaternions as a tool for representing and manipulating rotations in 3D space.
Summary of Comments ( 8 )
https://news.ycombinator.com/item?id=43284811
Hacker News users generally praised the Rust vector and quaternion library for its clear documentation, beginner-friendly approach, and focus on 2D and 3D graphics. Some questioned the practical application of quaternions in 2D, while others appreciated the inclusion for completeness and potential future use. The discussion touched on SIMD support (or lack thereof), with some users highlighting its importance for performance in graphical applications. There were also suggestions for additional features like dual quaternions and geometric algebra support, reflecting a desire for expanded functionality. Some compared the library favorably to existing solutions like glam and nalgebra, praising its simplicity and ease of understanding, particularly for learning purposes.
The Hacker News post titled "Show HN: Rust Vector and Quaternion Lib" (https://news.ycombinator.com/item?id=43284811) has a modest number of comments, focusing primarily on practical aspects and alternatives rather than deep dives into the library's design.
One commenter points out the existence of
nalgebra, a popular linear algebra library in Rust, and questions the rationale behind creating a new library instead of contributing to existing ones. They acknowledge the educational value of such projects but emphasize the benefits of a shared, well-maintained library for the broader community. This comment sparks a brief discussion about the potential reasons for starting a new library, including personal learning experiences, specific needs not met by existing libraries, and the inherent desire to build things from scratch.Another comment highlights the use of
f32(32-bit floating-point numbers) and suggests consideringf64(64-bit floating-point numbers) for improved precision in certain applications, particularly those involving physics simulations. This leads to a short exchange about the trade-offs between performance and precision, with the original poster (OP) acknowledging the suggestion and explaining their choice off32as sufficient for their immediate needs.A third comment mentions the inclusion of quaternions, asking about the intended use cases. The OP responds, indicating their interest in 3D graphics and game development, where quaternions are commonly used for rotations.
Further comments briefly touch on related topics such as the learning resources used by the OP, the possibility of SIMD optimizations, and comparisons to other linear algebra libraries in different languages. There is a general consensus that while the project might not be groundbreaking in terms of features or performance, it serves as a valuable learning experience and a potential starting point for a more comprehensive library.
Overall, the comments are constructive and offer practical suggestions, focusing on the context of the library within the existing Rust ecosystem and its potential applications. They don't delve deeply into the specific implementation details or offer extensive code reviews but provide useful feedback from the perspective of experienced Rust developers.