Intersection-Free Morphing of Planar Graphs

نویسندگان

  • Cesim Erten
  • Stephen G. Kobourov
  • Chandan Pitta
چکیده

Given two different drawings of a planar graph we consider the problem of morphing one drawing into the other. We designed and implemented an algorithm for intersection-free morphing of planar graphs. Our algorithm uses a combination of different techniques to achieve smooth transformations: rigid morphing, compatible triangulations, as well as morphing based on interpolation of the convex representations of the graphs. Our algorithm can morph between drawings with straightline segments, bends, and curves. Our system is implemented in Java and available as an applet at http://gmorph.cs.arizona.edu.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Morphing Planar Graphs in Spherical Space

We consider the problem of intersection-free planar graph morphing, and in particular, a generalization from Euclidean space to spherical space. We show that there exists a continuous and intersectionfree morph between two sphere drawings of a maximally planar graph, provided that both sphere drawings have convex inscribed polytopes, where sphere drawings are the spherical equivalent of plane d...

متن کامل

On cycles in intersection graphs of rings

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

متن کامل

Intrinsic Morphing of Compatible Triangulations

Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentri...

متن کامل

Nodally 3-connected planar graphs and convex combination mappings

A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a planar graph is nodally 3-connected then such a mapping is an embedding. Floater generalised this result to convex combination mappings in which every internal vertex is a proper weighted average of its neighbours. He also...

متن کامل

Planar Graphs as L-intersection or L-contact graphs

The x-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel x shapes in the plane. A subfamily of these graphs are {x, |,−}-contact graphs which are the contact graphs of axis parallel x, |, and − shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are x-intersection gra...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003