دانلود رایگان مقاله نقشه دوسویی صاف میان چند ضلعی مسطح دلخواه

Abstract

Mapping from one planar polygonal domain to another is a fundamental problem in computer graphics and geometric modelling. Exploiting the properties of harmonic maps, we define smooth and bijective maps with prescribed behaviour along the domain boundary. These maps can be approximated in different ways, and we discuss the respective advantages and disadvantages. We further present a simple procedure for reducing their distortion and demonstrate the effectiveness of our approach by providing examples of applications in image warping and surface cross-parameterization. Moreover, we briefly discuss the extension of our construction to 3D and its application to volumetric shape deformation.

6. Conclusions

The smooth maps f between two polygonal domains in (2) satisfy most of the properties requested by common applications in computer graphics and related fields. They are bijective and symmetric, and we can fully control their boundary behaviour. In addition, the construction of f is transitive in the sense that fk ◦ fk−1 ◦ ... ◦ f1 = g, where fi:i−1 → i , i = 1,...,k and g:0 → k. This guarantees an intuitive behaviour in an interactive image warping application where the user modifies an image in several steps by moving the vertices of the control polygon. The transitivity then assures that the result is independent of the way and the order in which the vertices are moved to arrive at the target positions. Moreover, if the user moves the vertices back to their initial positions, the image will be restored, because g will be the identity.