中文摘要：

在基于物理的流体动画中,准确而高效地跟踪流体运动界面是提高仿真效果的关键.针对传统算法存在耗散大、效率低等问题,提出了一种自适应的粒子水平集算法.通过建立耗散函数估计的重要性采样模型,获取自适应优化规则;然后基于该优化规则,定义窄带上的局部特征尺寸函数和累积变形率,构建采样点分布的随机过程,在此基础上进行流体界面跟踪计算的优化.实验及应用结果表明：该方法能有效利用计算资源,在界面跟踪的精度与效率方面均优于原有方法,能够得到满足需求的仿真效果.

英文摘要：

Fluid animation is one of the most desirable techniques in computer graphics and virtual reality.As these phenomena contain highly complex behaviors and rich visual details,it is difficult to deal with the complex motion of the water-air interfaces.Therefore,capturing the interface accurately and efficiently is a key issue in fluid animation.In order to address the problem of high numerical diffusion and low efficiency in traditional methods such as level set and particle level set algorithms,an adaptive particle level set method is presented.The particle placement in our approach is modeled as a stochastic process.Desirable goals are then achieved by allocating more computational resource to regions of high numerical dissipation during animation heuristically.In order to derive the optimal-rules of computing the stochastic process,we construct an importance sampling model and evaluate the volume loss in computational domain.The probability density function（PDF）of particle placement is obtained by employing a geometrical-based sampling algorithm which adopts a novel local feature size function on narrow band level set.The efficiency of computing this stochastic process is further improved according to the definition of accumulated shape deformation.Experiments show that the proposed approach provides high quality and low cost both in numerical tests and water animation applications.