A digital medium environment is described to dynamically modify or extend an existing path in a user interface. An un-parameterized input is received that is originated by user interaction with a user interface to specify a path to be drawn. A parameterized path is fit as a mathematical ordering representation of the path to be drawn as specified by the un-parametrized input. A determination is made as to whether the parameterized path is to extend or modify the existing path in the user interface. The existing path is modified or extended in the user interface using the parameterized path in response to the determining that the parameterized path is to modify or extend the existing path.