Geometry Processing Of Tubular Objects

Recently, in computer graphics, especially in the subfields as geometry modelingand shape analysis, more and more research interests have diverted from traditionalgeometry processing which based on local features to high level geometry processingwhich aims to first analyze and understand a model in a global sense and then performa global geometry modeling. During this process,3d modeling of man-made objectswhich are ubiquitous in our daily life, e.g. chairs, lamps, bikes and builds, have earnedwidely interests because of their unique properties, such as symmetry, hierarchy instructure, complex topology etc. Current methods usually first segment the man-madeobjects into diferent parts, and then process each part based on the constraints learnedfrom a shape analysis step. Tubular objects, whose skeleton is a1d curve, is an impor-tant component of most man-made shapes. And also, tubular shapes reflect the overallstyle of a model. Thus, a study on the processing of tubular shapes is helpful to furtheranalyze and process a whole man-made shape.In this paper, we propose a skeleton-based method to process tubular shapeswhich are represented by triangular meshes. Our method has built a general frame-work for geometry modeling of tubular shapes. And the results can be readily used ingeometry modeling of man-made shapes which contain tubular components.First, we use the skeleton to sample and remesh a tubular shape, and treat theoutput mesh as an approximation of the original model. In this paper, given a tubularobject, we first extract the mean curvature skeleton which is proposed by Tagliasacchiet al. Similar to Lazarus’s method, we treat the tubular object as a generalized cylin-der in which the trunk is a cylindrical surface and two ends are two hemi-sphericalsurfaces. We then utilize the skeleton to sample the trunk according to a cylindri-cal parameterization and sample each end based on a spherical parameterization. Bysampling in this way, we get a global parameterization of all sampled points. Usingthe connectivity in the parameter domain, we connect all sampled points and get a remeshed representation of the input model.Based on results from previous steps, we use the skeleton to edit the shape of atubular object and achieve morphing between diferent tubular objects. The samplingprocess in previous step has build the correspondence between vertices in the remeshedmodel and the skeleton points. By modifying the skeleton or changing the samplingradius, we can edit the remeshed model to create tubular objects with new shapes.Given two tubular objects which have similar skeleton shape, we apply the sameskeleton-based sampling to each model, and build one to one correspondence betweenall vertices of the remeshed modles. Then, we interpolate between all correspondingvertices and get a morphing sequence between two tubular objects. The generated in-between models can be treated as new models with blended shapes as well as be usedfor animation.In summary, we propose a skeleton-based sampling and remeshing method forman-made tubular shapes. We then use the sampling results to edit the shape andachieve morphing between diferent tubular shapes. By doing these steps, we havebuilt a general geometry processing framework for man-made tubular shapes. Ex-periments results show that, our skeleton-based processing method can achieve goodresults for tubular shapes. Since the sampling is under the guidance of the skeleton,new generated edges in the remeshed model will be close to the principal curvaturelines of the shape. As a result, the remeshed model will reflect the structure of the in-put model. However, since our method is based on ray projection, the remeshed modelmay lose the sharp surface features of the original model. How to keep or recover thegeometry details during sampling and remeshing is one of our future works.