Paul Arc Length Based On The Breakdown Of The Curve Deformation

In fields of geometric modeling and computer animation, deformation is a useful tool to simulate the manipulation and operation and has been extensively studied in recent years. Great progress has been made in this field, however the some problem of deformation with constraints are still not entirely resolved, for example, the volume constraint, the area constraint and arc-length constraintThe arc-length constraint is discussed in this paper. In real world, when an object is deformed, its length usually remains constant The work presented in this paper focuses on arc-length preserving deformation. The curve is firstly simplified into a control polyline by recording the lost arc-length. Implement required deformation on the polyline. The algorithm computes the new node position of the control polyline, while minimizing the kinetic energy subject to joint angle limit. Finally, apply subdivision on control polyline to obtain a smooth curve. The parameters of the subdivision scheme are selected to preserve the arc-length upon each segmentThe results of the experiments indicate that we are able to achieve efficient deformations on high-detailed curves. And the deformed curve has at least C1 continuity. This technique also provides interactive response by progressively refining the solution of the optimization problem, thus it will has good foreground of application in animation for games and films, simulation for cloth, and robots programming.