Abstract
A triangular mesh obtained by scanning 3D models typically contains holes. We present an effective technique for filling a hole in a triangular mesh in geometric modeling. Simple triangulation of a hole is refined and remeshed iteratively to generate an initial patch. The generated patch is then enhanced to become a target patch by minimizing the variation of principal curvatures. In discrete approximation, this produces a third-order Laplacian system of sparse symmetric positive definite matrix, and the symmetry can efficiently be used to find the robust solutions to the given Laplacian system. Laplacian smoothing of the target patch is defined as a source patch. The shape difference between two corresponding vertices of the source and the target patches is measured in terms of Euclidean distance and curvature variation. On the basis of the shape difference and a user-specified control parameter, different blending weights are determined for each vertex, and the final patch is generated by blending two patches. We demonstrate the effectiveness of our technique by discussing several examples. The experimental results show that our technique can effectively restore salient geometric features of the original shape.
Highlights
Owing to their simplicity and hardware-accelerated rendering facility, triangular meshes have been widely used for representing the shape of three-dimensional (3D) objects in computer graphics and real-time 3D applications
We present a simple and effective technique for generating a hole patch in a triangular mesh and controlling its shape
We present an effective technique for filling a hole in a triangular mesh based on shape differences
Summary
Owing to their simplicity and hardware-accelerated rendering facility, triangular meshes have been widely used for representing the shape of three-dimensional (3D) objects in computer graphics and real-time 3D applications. The scanned data set cannot be directly used and requires post-processing steps because it contains several artifacts such as holes, gaps, self-intersections, and handles. Most hole-filling algorithms generate a hole patch that is smoothly connected with the hole boundary They do not provide the user with the additional flexibility of controlling the shape of the generated patch. We present a simple and effective technique for generating a hole patch in a triangular mesh and controlling its shape. The final hole patch is generated by blending the source and the target patches on the basis of the shape difference and a user-specified blending parameter. The result of the hole patch generated by using our method is shown, where shape features, such as concavity and convexity, are exaggerated by a user’s control parameter.
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