Analytical Solid Modeling (ASM)
ASM is closely related to finite element modeling. It is developed to aid designers in the arduous task of modeling complex geometry commonly found in design applications. It can be viewed as more of a representation scheme for design than for manufacturing purposes due to its formulation, which does not involve orientable surfaces as does b-rep or c-rep. ASM has now a wide range of applications such as mass property calculations, composite material modeling, and computer animation.
The technique for creating spline or patch curve segments or surface patches are valid in ASM. As surface representation a general solid is described by x, y and z coordinates. ASM is an extension of the well established tensor product method, introduced to represent surfaces for surface modeling, to 3D parametric space with the parameters u, v, and w. the tensor product formulation in 3D parametric space is a mapping of a cubic parametric domain described by u, v, and w values into a solid described by x, y and z in the Cartesian (modeling) space, as shown in Figure 6.28. The resulting solid is called a parametric solid or a hyperpatch.