Techniques for nonlinear representations for vector objects are described that support construction of a nonlinear vector graph to represent a vector object. In an implementation, a user input is received including a plurality of points and at least one primitive. A content processing system then generates a vector object by constructing a nonlinear vector graph that specifies a nonlinear connection of the plurality of points with the at least one primitive. In some examples, the vector object is edited by applying an edit to the nonlinear vector graph. Once generated, the content processing system then outputs the vector object for display, e.g., in a user interface.