A “Charting Animator” enhances computer-based charting / graphing systems by rendering dynamic animations of chart displays. In general, when a user changes from one chart type to another, adds new data to a chart, or changes, sorts or deletes data, a new chart is generated to replace the old chart. Conventional charting systems simply replace the existing chart with the new chart. In contrast to conventional systems, the Charting Animator renders animated transitions that dynamically morph the original chart into the new chart. Consequently, these animations avoid abrupt changes that can disorient users. Examples of these animations include animating changes from one chart family to another (e.g., changing from a “Bar Chart” to a “Pie Chart”), animating changes from one chart type within a chart family to another chart type (e.g., changing 2D Bar Charts to 3D Bar Charts or Stacked Bar Charts), animating data changes, animating sorts, etc.