A user of a modeling application modifies an initial virtual object using a sketch drawn on one or more construction planes. Typically, construction planes are connected by an axis that intersects the virtual object. The user can draw a sketch on each construction plane, and the modeling application interpolates a shape along the axis between the sketches to determine what material in the virtual object is to be removed from it. In this manner, material may be removed to create a recess or hole in the virtual object or otherwise to slice away material from the object. A user can use two or more axes and construction planes to produce complex shapes from the initial virtual object. A user can also select a portion of a virtual object and mirror the selected portion. Modifications that the user makes in the selected portion are made correspondingly in the mirrored portion.