Spring-mass systems are widely used in computer animation to model soft objects. Although the systems can be numerically solved either by explicit methods or implicit methods, it has been difficult to obtain stable results from explicit methods. This paper describes detailed discussion on stabilizing explicit methods in spring-mass simulation. The simulation procedures are modeled as a linear digital system, and system stability is mathematically defined. This allows us to develop theories of simulation stability. The application of these theories to explicit methods allows them to become as stable as implicit methods. Furthermore, a faster explicit method is proposed. Experiments confirm the theories and demonstrate the efficiency of the proposed methods.

There are many web sites where net users can post and distribute their illustration images. A typical way to draw a digital illustration is first to draw rough lines on a paper and then to trace the lines on a graphics-tablet by hand. The input lines usually contain fluctuation due to hand-drawing, which limits the quality of illustration. Therefore, it is important to remove the fluctuation and to smooth the lines while maintaining sharp features such as corners. Although naive applications of moving average filters can smooth input lines, they may cause over-smoothing artifacts in which sharp features are lost by the filtering. This paper describes an improved line smoothing method using adaptive moving averages, which smoothes input lines while keeping high curvature points. The proposed method evaluates curvatures of input lines and adaptively controls the filter-size to reduce the over-smoothing artifacts. Experiments demonstrated advantages of the proposed method over the previous method in terms of achieving smoothing effect while still preserving sharp feature preservation.