Mesh Editing with Poisson-Based Gradient Field Manipulation

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Three-dimensional geometric models are the base data for applications in computer graphics, computer aided design, visualization, multimedia, and other related fields. This report will focus on computerized modeling editing of discrete (digital) geometry, in particular polygonal meshes. In this report, I will survey the state-of-the-art techniques for creating, manipulating, editing and analyzing digital geometry models.
The mesh editing techniques we discussed here are : Poisson Shape Interpolation[1], Mesh Editing with Poisson-Based Gradient Field Manipulation[2], Mesh Editing based on Discrete Laplace and Poisson Models[3], Mesh Editing with Curvature Flow Laplacian[4] and Mean Value coordinates for Closed triangular meshes[5]. All the five techniques will be discussed in detail in section 2-6. In section 7, we’ll do a comprehensive comparison of these five techniques and conclude in section 8. Poisson Shape Interpolation
Shape interpolation which is also known as shape blending or morphing is used in many aspects of computer graphics industry widely. Provided two input models, the shape interpolation will produce a set of shapes in sequence to demonstrate how the source model is changed to the target model smoothly. It can also be applied to forecast new product from known products.

It’s well known that in B-rep(boundary representation) shape interpolation[6], there are two major issues which are correspondence problem and trajectory problem. The

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