Techniques to control shape interaction in a user interface are described. In one or more implementations, a method is described of controlling user interface shape interaction by a computing device. A shape is displayed in a user interface by the computing device, the shape described using a plurality of points, each of the points having an associated radius. An input is detected, by the computing device, involving modification of the associated radius of least one of the plurality of points. A determination is made, by the computing device, whether modification of the associated radius of the at least one point causes an intersection of the associated radius of one or more of the plurality of points neighboring the at least one point. Responsive to the determination that the modification causes the intersection, the associated radius of the one or more points are modified such that the intersection does not occur. The shape is displayed by the computing device as having the modified associated radius of the at least one point.