The increasing use of visual diagrams in educational and work environments, and even our daily lives, has created obstacles for individuals who are blind or visually impaired to "independently" access the information they represent. Although physical tactile pictures can be created to convey the visual information, it is typically a slow, cumbersome, and costly process. Refreshable haptic displays, which interact with computers, promise to make this access quicker, easier, and cheaper. One important aspect in converting visual to tactile diagrams is to simplify the diagram as otherwise it can be too difficult to interpret with touch. Enabling this to be under user control in an interactive environment, such as with refreshable displays, could allow users to avoid being overwhelmed by the diagrams at any instant in time while still retaining access to all information in "storage". Through this article the authors investigate whether two types of diagram simplification--boundary simplification and contextual simplification--showed potential utility in an interactive environment. Boundary simplification was found to be significantly helpful in answering general questions about borders on a geographic map, and contextual simplification was helpful in answering relational questions, as compared to using the original map unchanged. (Contains 4 tables and 4 figures.)