Geometric shape morphing is a special geometric operation that interpolates two geometric shapes to generate in-between shapes, which can be used in various design applications such as pipe-like surface design or motion simulation in CAD/CAM. It has been well known that Minkowski sum can be used to design collision-free motion path and to modify geometric shapes. Recently, we developed a geometric modeling technique to interactively control geometric shape morphing based on Minkowski sum. The basic idea develops from the linear interpolation on two geometric shapes where the traditional algebraic sum is replaced by Minkowski sum. We extended this scheme into n-th degree B？zier and blossom control with multiple control shapes. In this paper, we introduce mathematical models of the proposed control structure and some of their properties. Moreover, we present a fast and efficient computation method based on direction map analysis, which has been optimized for repeated generation of in-betweens to outperform previous algorithms.

Abstract 
1. Introduction 
2. Geometric Preliminaries 
3. Computation Method based on Direction Map 
4. Conclusion 
Acknowledgement 
References

• Joo-Haeng Lee | 이주행
• Jae Yeol Lee | 이재열
• Hyun Kim | 김현
• Hyoung-Sun Kim | 김형선