Methods and systems are provided for generating graphical representations of orifices and vessels. One method comprises generating a representation of the surface (e.g., an endocardial surface) within a coordinate system, and laterally moving the distal end of an elongated probe within an orifice (e.g., a valve or a vessel ostium) associated with the surface. The method further comprises defining line segments within the coordinate system while the probe distal end is moved within the orifice, wherein each of the line segments represents the probe distal end. The method further comprises defining intersection points within the coordinate system, wherein each of the points represents an intersection of one of the line segments and the surface representation. Lastly, the method comprises graphically generating a representation of the orifice based on the intersection points, e.g., by forming the orifice representation around the intersection points. Another method comprises moving the distal end of an elongated probe within the vessel, defining line segments within a coordinate system while the probe distal end is moved within the vessel, wherein each of the line segments represents the probe distal end, and graphically generating a representation of the vessel based on the line segments.