A performance-based representation is developed utilizing multi-dimensional clipping and transformation algorithms. Given analytic performance functions, three types of supporting information is presented to the decision maker: 1) a function matrix that describes the performance attributes varying with the decision variables; 2) a decision space that illustrates the feasible decision set that meets performance requirements, and; 3) a performance space that provides the feasible performance region and the Pareto Optimal set. The performance-based representation is compatible with other influential design methodologies. A case study is presented for aircraft beam design utilizing constraint based reasoning and decision based design. The results demonstrate not only the benefit of the representation on interactive parametric design, but also an intriguing comparison between constraint based reasoning and decision based design approaches incorporated with the described representation. While a linearized parametric design problem is implemented, the approach shows a potential extension to non-linear systems.