Hyperpatch Representation:

The variable point of the solid is given by following

p (u, v, w) = [x (u, v, w), y (u, v, w), z (u, v, z)]

u_min ≤ u  ≤ u_max

 v_min ≤  v ≤u_max

 w_min ≤ w ≤ w_max

A general solid is represented by p (u, v, w) =        

i =1  j =1 k =1

0 < u < 1, 0 < v < 1, 0 < w < 1

The creation of an ASM model of an object simply included dividing the object in the proper assembly of non-overlapping hyperpatches. Each hyperpatch may be constructed from curves and/or surface patches. Other construction methods of ASM models may include ruled volumes and sweeping. A ruled volume may be created among two given surface patches by linearly interpolating among them.

ASM is appearing in design and analysis applications that needs information inside in addition to on the boundary of a given object. It is desirable, for instance, in modelling and studying composite materials and fracture mechanics problems. Though, ASM is not sufficient for manufacturing applications such like tool path generation, because face surfaces of hyperpatches are not explicitly stored and are not orient able, that means normals to face surfaces may not mention the interior or exterior of the object.