Interactive Animation of Shoals Based on Mathematical Ecology

在这项研究中，我们开发了一个生态系统的交互式视觉模拟，其中鱼类种群随着种群的变化而可视化。在计算机图形学中，协调动物运动的计算机模型，称为boid算法，是一种众所周知的技术，用于许多程序，如电脑游戏。虽然使用boid算法可以实现对群集生物的逼真可视化，但没有考虑生物的出生、生长和死亡。数学生态学研究的是种群动态，即不同物种个体数量的波动。我们开发了一个交互式视觉模拟系统，其中鱼群由boid算法组成，鱼的数量根据Lotka-Volterra方程随着时间的推移而变化，通过它们的出生，生长和死亡。研究了两类Lotka-Volterra方程：(1)竞争两种模型和(2)捕食者-猎物模型。为了增加用户的互动，用户可以通过在现场放置圆形网来捕获它们，从而减少个体的数量来改变个体的数量。改变人口后，用户可以直观地看到它的效果。

In this research, we have developed an interactive visual simulation of ecosystems, in which fish schools are visualized with changing the population. In computer graphics, a computer model of coordinated animal motion, which is called the boid algorithm, is a well-known technique and is used in many programs, such as computer games. Although the realistic visualization of flocking creatures is possible using the boid algorithm, the birth, growth, and death of creatures are not taken into consideration. Mathematical ecology deals with population dynamics, the fluctuations of the number of individuals of different species. We developed a interactive visual simulation system in which the schools of fish are formed by the boid algorithm and the numbers of fish are changed with time through their birth, growth, and death based on the Lotka-Volterra's equations. Two kinds of Lotka-Volterra's equations are dealt with: (1) competing two species model and (2) predator-prey model. To add the interaction by the user, the user can change the number of individuals by placing a circular net in the field to capture them and henceforth decreasing the number of individuals. After changing the population, the user can visually see its effect.