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Show CHAPTER 7 B-SPLINES AND REFINEMENT Eplastics models the motion of points in space. There can be any number of points and these points can be at any location. The constraints that act upon these points do not have any restrictions with respect to the location or the number of points they can affect. The only restriction is that they are able to look at the state of the system and determine the forces to be applied to some set of points. The points of a B-spline mesh come in rectilinear grids and form a subspace of the allowable sets of points in eplastics. The standard configuration of the constraints (usually springs) of the mesh is to connect every point to its neighbor. Because eplastics is intended to work with B-splines, special control was developed to handle this subspace of point masses and constraints. Control comes in the form of methods to map the mesh of B-spline points to a set of points and constraints in the eplastics modeling space. When eplastics is finished with its modeling, the point masses are mapped back in to a B-spline surface. During the modeling of the motion of the points, it is not forgotten that the points originally came from a B-spline. When the set of points and constraints is refined during a. modeling session, it is essential to retain the connection to the B-spline definition. This ensures the B-spline surface as well as the physical properties of the mesh are consistent, after refinement, with their original definitions. This chapter will describe the mapping mechanism and how it is controlled. It will also define refinement, what problems are associated with refinement of the data, and how those problems are solved. |
