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Efficient and informative visualization of surfaces with uncertainties is an important topic with many applications in science and engineering. In these applications, the correct course of action may depend not only on the location of a boundary, but on the precision with which that location is known. Examples include environmental pollution borderline detection, oil basin edge characterization, or discrimination between cancerous and healthy tissue in medicine. We present a method for producing visualizations of surfaces with uncertainties using points as display primitives. Our approach is to render the surface as a collection of points and to displace each point from its original location along the surface normal by an amount proportional to the uncertainty at that point. This approach can be used in combination with other techniques such as pseudocoloring to produce efficient and revealing visualizations. The basic approach is sufficiently flexible to allow natural extensions; we show incorporation of expressive modulation of opacity, change of the stroke primitive, and addition of an underlying polygonal model. The method is used to visualize real and simulated tumor formations with uncertainty of tumor boundaries. The point-based technique is compared to pseudocoloring for a position estimation task in a preliminary user study.