The trend in science and engineering applications has been to produce larger data sets, since computers and imaging technology are getting faster and storage space is increasing. Large amounts of data are diﬃcult to visualize, and it is impossible to directly visualize them on inexpensive computers. Many visualization techniques exist that visualize certain types of large data. However, a general solution does not exist. A hierarchical method provides the foundation for a solution. Linear and quadratic decomposition elements can be used to form an approximation hierarchy representing large data; a user can then visualize this hierarchy on low-end machines. A hierarchical approximation method is described that uses linear, quadratic, and curved-quadratic decompositional elements. Linear element approximation and visualization has been studied extensively in the past. Higher-order element approximation and visualization is not nearly as developed as that for linear elements, thus, more research is needed. Fundamental visualization techniques—such as isosurfacing, ray casting, and cutting planes—for quadratic elements are described.