In 2018, Netease "Naishuihan" and AMD jointly developed an algorithm called "Head & Shoulders" , which is based on AMD's TressFX hair simulation technology , which can clearly simulate the movement of human hair in the game, greatly enhancing the game The realism of the scene. A healthy adult has about 100,000 hairs. If you want to simulate hair in the game scene, you need to interactively model the 100,000 hairs themselves and the surrounding environment. Obviously, this is a very expensive graphics card. algorithm.
Recently, NVIDIA, another graphics card giant that is really "making money" in the field of AI, also announced its latest progress in the field of hair simulation. They proposed a discrete elastic simulation solver (Discrete Elastic Rods, DER) based on the ADMM algorithm. , DER is based on neurophysics to train the network to predict the movement of hair in the real world. At the same time, it can also make full use of the large-scale parallel computing power of the GPU, which greatly reduces the iteration time of the algorithm in the high-resolution hair simulation scene. Currently, DER Has been accepted by SIGGRAPH 2023, the top conference on computer graphics.
Paper link:
https://research.nvidia.com/publication/2023-08_interactive-hair-simulation-gpu-using-admm
Judging from the demonstration video released by NVIDIA, DER has truly realized the realistic hair simulation effect. Compared with the previous method, DER has brought amazing interactive effects. It can not only perform separate real-time physical simulation for each hair, It can even retain the real properties of hair such as elasticity and luster, making the overall effect look more realistic. This effect makes people think, will there be a profession like AI hairstylist in the future? The author introduced in the article that this realistic effect benefits from the neurophysical network inside DER, and based on the discrete elastic link design, DER can decompose the simulation target of large-scale hair, which makes the whole task very suitable for GPU parallelism. The calculation structure finally realizes the real-time interactive physical hair simulation effect. Furthermore, DER can even reduce the previous simulation time from days to hours compared to the state-of-the-art CPU-based simulation solvers, while also improving the quality of hair simulations, which is a real dimensionality reduction hit.
1. The method of this paper
It is not difficult to see from the title of the paper that the DER solver proposed in this paper is designed based on the classic ADMM algorithm. Before introducing the method of this paper, let us first review the ADMM algorithm:
ADMM (Alternating Direction Method of Multipliers) is an optimization algorithm for solving convex optimization problems with constraints. Its core idea is to solve the original problem by converting it into equivalent sub-problems. The advantage of the ADMM algorithm is that it can effectively deal with optimization problems with constraints, and in many cases can obtain a faster convergence speed. It has been widely used in machine learning, signal processing, image processing and other fields.
The discrete elastic simulation solver DER proposed in this paper has an implicit time integration process internally designed to decompose the incremental problem. Since the ADMM algorithm is also a divide-and-conquer algorithm in essence, it adopts a decomposition-coordination method To solve the problem, that is, to find the solution of the large global problem by coordinating the solutions of the small local sub-problems. Therefore DER is very suitable to run on parallel GPU with large video memory.
1.1 Hair Motion Modeling
The authors mention that a classic approach to this problem is to perform a global Newton iteration, reducing the above equation to a series of linear systems with frictional contact constraints, and then any one of many dedicated solvers can be chosen for each hair Example to solve. However, for DER, analyzing multiple hair polygon instances simultaneously involves bulky matrix operations, which lead to inefficient GPU memory access and may require double-precision solving. Therefore, the author began to look for a compromise between completely global iterative (such as Newton iteration) and completely local (such as XPBD[1]) methods, that is, an efficient solution that can be efficiently solved on the GPU and propagate the iterative results at the global level. .
1.2 ADMM problem split
1.3 ADMM problem solving
2. Experimental effect
All the experiments in this article are carried out on a consumer-grade workstation equipped with an Intel Core i9-10980XE CPU and two NVIDIA GeForce 3080 Ti GPUs (12GB each), and the video rendering is done using the NVIDIA Omniverse suite.
2.1 Numerical verification experiment
In this paper, the numerical verification experiment of the DER solver is carried out first, and three experiments related to the elastic simulation performance are set up: cantilever, bending and stick-slip. The purpose is to test the DER numerical simulator. Consistency of predictions. The author mentioned that in order to make full use of the large-scale parallel performance of the DER solver proposed in this paper, for the above three experiments, the author solved all the experimental configuration items at one time. The experimental results are shown in the figure below, from left to right are cantilever , bending and stick-slip experiments.
Among them, the cantilever experiment (the leftmost) mainly calculates the natural sagging degree of both ends of the connecting rod when the connecting rod is in a balanced state under gravity, and calculates the aspect ratio caused by the sagging offset, and compares it with the theoretical aspect ratio. It can be seen from the figure that DER can basically fit the results of the theoretical aspect ratio. For the bending experiment, the author set up a variety of connecting rods with different lengths and natural curvatures, and then simulated to calculate whether they can maintain a flat state under the state of gravity balance. Through experiments, the author found that the predicted results of DER can be kept well with the theoretical analysis curve consistency. In the stick-slip experiment, the author gradually pushed an originally vertical natural connecting rod from one direction to another, and recorded the degree of bending of the connecting rod and the real-time magnitude of its overcoming frictional force. Experiments show that the prediction results of DER on the degree of bending and friction basically fit the theoretical values.
2.2 Algorithm calculation performance experiment
The numerical verification experiments carried out in the previous section focused on verifying the algorithmic accuracy and convergence of the DER solver, and in this section, the author also evaluates the computational performance of DER. As shown in the figure below, the author used DER to carry out hair experiments, and simulated experiments on experimental bodies with 16,000 and 128,000 hairs respectively. The simulation targets include continuous-time collisions and discontinuous-time collisions .
Due to exceeding the memory limit of a single GPU, for the "Hairball 128k, CT" scene, the author tested on 2 GPUs, and used the same quality segmentation technique to handle contacts involving vertices on different GPUs. The table below summarizes the simulation calculation timing results, where the 16,000 hair configuration can run at almost real-time interactive frame rate , while the larger 128,000 hair configuration takes about 40 minutes to complete.
2.3 Application scenarios of the method in this paper
The ADMM-based discrete simulation solver for DER proposed in this paper has achieved simulation accuracy and computational efficiency far superior to traditional methods. The author of this paper then looks forward to a very interesting application direction for DER, which is to introduce DER as an AI assistant in human hair styling . For example, the author envisions an original editing tool based on physical simulation, which can be used by users to adjust hairstyles. During the adjustment process, the algorithm will follow the conditions such as the elasticity and self-collision constraints of the hairstyle itself to ensure the real level and volume of the hairstyle. And provide users with real-time hairstyle preview.
In addition, the author also tries to call this AI assistant programmatically. As shown in the figure above, the author provides a series of basic operations (such as external force swing, hair growth or trimming, etc.) for the simulator. Based on these operations, the user can Combining in many different ways to quickly generate a large number of candidate hairstyles, it really feels like Teacher AI Tony.
3. Summary
This paper proposes a hair discrete simulation solver DER based on the ADMM algorithm . Compared with the iterative Newton method, the calculation cost of ADMM is much lower . Adjusting the constraint weights for each hair polygon instance results in a very realistic simulation. In addition, based on Nvidia's professional computing GPU, the author also optimized parallel computing for DER, which greatly reduced the computational load of the algorithm and realized real-time simulation of thousands or even tens of thousands of hairs. In addition to the internal algorithm design, the author also considers some designs of DER on the user experience side. In addition to some existing programmatic editing methods, the author also considers adding some tactile feedback mechanisms and intelligent selection tools to DER in the future . Manipulating, combing and trimming hair from any angle makes the overall experience closer to the real barbershop scene, and then we can design hairstyles for ourselves on the computer.
reference
[1] Miles Macklin, Matthias Müller, and Nuttapong Chentanez. 2016. XPBD: PositionBased Simulation of Compliant Constrained Dynamics. In Proceedings of the 9th International Conference on Motion in Games (Burlingame, California) (MIG ’16). Association for Computing Machinery, New York, NY, USA, 49–54
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