Constrained Texture Mapping And Foldover-free Condition

Texture mapping has been widely used in image processing and graphics to enhance the realism of CG scenes. However to perfectly match the feature points of a 3D model with the corresponding pixels in texture images, the parameterisation which maps a 3D mesh to the texture space must satisfy the positional constraints. Despite numerous research efforts, the construction of a mathematically robust foldover-free parameterisation subject to internal constraints is still a remaining issue. In this paper, we address this challenge by developing a two-step parameterisation method. First, we produce an initial parameterisation with a method traditionally used to solve structural engineering problems, called the bar-network. We then derive a mathematical foldover-free condition, which is incorporated into a Radial Basis Function based scheme. This method is therefore able to guarantee that the resulting parameterization meets the hard constraints without foldovers

What you seam is what you get

3D paint systems opened the door to new texturing tools, directly operating on 3D objects. However, although time and effort was devoted to mesh parameterization, UV unwrapping is still known to be a tedious and time-consuming process in Computer Graphics production. We think that this is mainly due to the lack of well-adapted segmentation method. To make UV unwrapping easier, we propose a new system, based on three components : * A novel spectral segmentation method that proposes reasonable initial seams to the user; * Several tools to edit and constrain the seams. During editing, a parameterization is interactively updated, allowing for direct feedback. Our interactive constrained parameterization method is based on simple (yet original) modifications of the ABF++ method, that make it behave as an interactive constraint solver; * A method to map the two halves of symmetric objects to the same texels in UV space, thus halving texture memory requirements for symmetric objects

Mesh parameterization by minimizing the synthesized distortion metric with the coefficient-optimizing algorithm

2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

An RBF-based reparameterization method for constrained texture mapping

Texture mapping has long been used in computer graphics to enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous research efforts, the construction of a mathematically robust, foldover‐free parameterization that is subject to positional constraints continues to be a challenge. In the present paper, this foldover problem is addressed by developing radial basis function (RBF) based reparameterization. Given initial 2D embedding of a 3D surface, the proposed method can reparameterize 2D embedding into a foldover ‐free 2D mesh, satisfying a set of user‐specified constraint points. In addition, this approach is mesh‐free. Therefore, generating smooth texture mapping results is possible without extra smoothing optimization

Interactive Geometry Remeshing

We present a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry. First, the original (arbitrary genus) mesh is substituted by a series of 2D maps in parameter space. Using these maps, our algorithm is then able to take advantage of established signal processing and halftoning tools that offer real-time interaction and intricate control. The user can easily combine these maps to create a control map – a map which controls the sampling density over the surface patch. This map is then sampled at interactive rates allowing the user to easily design a tailored resampling. Once this sampling is complete, a Delaunay triangulation and fast optimization are performed to perfect the final mesh. As a result, our remeshing technique is extremely versatile and general, being able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semiregularity, curvature sensitive resampling, and feature preservation. We provide a high level of control over the sampling distribution allowing the user to interactively custom design the mesh based on their requirements thereby increasing their productivity in creating a wide variety of meshes