This paper presents a hybrid method for creating three-dimensional shapes by
sketching silhouette curves. Given a silhouette curve, we approximate its
medial axis as a set of line segments, and convolve a linearly weighted kernel
along each segment. By summing the fields of all segments, an analytical
convolution surface is obtained. The resulting generic shape has circular
cross-section, but can be conveniently modified via sketched profile or shape
parameters of a spatial transform. New components can be similarly designed by
sketching on different projection planes. The convolution surface model lends
itself to smooth merging between the overlapping components. Our method
overcomes several limitations of previous sketched-based systems, including
designing objects of arbitrary genus, objects with semi-sharp features, and the
ability to easily generate variants of shapes.
