LogInGiacomo Balma showcased his algorithm, fully implemented in OpenCL.
This position-based particle orientation dynamics algorithm, developed by FX TD Giacomo Balma over the past month, calculates a particle's orientation by considering only the positions of its neighbors. The process involves comparing the current positions to those from the previous substep and extracting the orientation from that comparison.
The algorithm is fully implemented in OpenCL for Houdini's DOPs and introduces minimal overhead to the simulation, particularly when combined with a fast OpenCL neighbor search algorithm like the one used in Vellum. By computing particle orientation, especially for grains, as demonstrated in this case, it enables the creation of interesting non-spherical shape instances and up-res techniques, with more to come.
The orientation is determined by comparing the positions of the current-frame neighbors with those from the previous simulation frame, identifying the best-fitting rotation, and updating the particle's orientation quaternion. Solving for the optimal rotation falls under the category of the absolute orientation problem.
As Giacomo mentioned, "Efficient Absolute Orientation Revisited" by Lourakis et al. offers a comprehensive overview of various existing solutions. He began by implementing and testing several of these in Houdini. The paper suggests that the Optimal Linear Attitude Estimator algorithm should be the most efficient. However, the version he implemented was only slightly faster, and the small approximation error it introduced quickly accumulated frame by frame. As a result, he switched to the more reliable method outlined in "Least-Squares Fitting of Two 3-D Point Sets". In summary, this involves computing the covariance matrix of the two neighbor point-clouds and using singular value decomposition to extract the rotation matrix.
Right now, Giacomo is focusing on developing a cost-effective method to preserve angular momentum for particles that detach or are in free flight. Find all the papers in the original post here and stay updated on Giacomo Balma's work by following him on LinkedIn.
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