Analytical Solid Modeling (ASM):

ASM is closely associated to finite element modelling. This is developed to aid designers in the arduous task of modelling complex geometry generally found in design applications. It may be viewed as more of a representation scheme for design than for manufacturing purposes because of its formulation, which does not involve orient able surfaces as does b-rep or c-rep. ASM has now an extensive range of applications such like mass property calculations, composite material modelling, and computer animation.

The technique for making spline or patch curve segments or surface patches is valid in ASM. As surface representation a general solid is defined by x, y and z coordinates. ASM is an extension of the well established tensor product method, introduced to represent surfaces for surface modelling, to 3D parametric space along with the parameters u, v, and w. the tensor product formulation in 3D parametric space is a mapping of a cubic parametric domain defined by u, v, and w values into a solid defined by x, y and z in the Cartesian (modelling) space, as illustrated in Figure. The resulting solid is called as parametric solid or a hyperpatch.