Structure Preserving Manipulation and Interpolation for Multi-element 2D Shapes

This paper presents a method that generates natural and intuitive deformations via direct manipulation and smooth interpolation for multi-element 2D shapes. Observing that the structural relationships between different parts of a multi-element 2D shape are important for capturing its feature semantics, we introduce a simple structure called a feature frame to represent such relationships. A constrained optimization is solved for shape manipulation to find optimal deformed shapes under user-specified handle constraints. Based on the feature frame, local feature preservation and structural relationship maintenance are directly encoded into the objective function. Beyond deforming a given multi-element 2D shape into a new one at each key frame, our method can automatically generate a sequence of natural intermediate deformations by interpolating the shapes between the key frames. The method is computationally efficient, allowing real-time manipulation and interpolation, as well as generating natural and visually plausible results.