This paper presents an automatic method for computing an anisotropic 2D shape distribution on an arbitrary 2-manifold mesh. Our method allows the user to specify the direction as well as the density of the distributio...This paper presents an automatic method for computing an anisotropic 2D shape distribution on an arbitrary 2-manifold mesh. Our method allows the user to specify the direction as well as the density of the distribution. Using a pre-computed lookup table, our method can efficiently detect collision among the shapes to be distributed on the 3D mesh. In contrast to existing approaches, which usually assume the 2D objects are isotropic and have simple geometry,our method works for complex 2D objects and can guarantee the distribution is conflict-free, which is a critical constraint in many applications. It is able to compute multi-class shape distributions in parallel.Our method does not require global parameterization of the input 3D mesh. Instead, it computes local parameterizations on the fly using geodesic polar coordinates. Thanks to a recent breakthrough in geodesic computation, the local parameterization can be computed at low cost. As a result, our method can be applied to models with complicated geometry and topology. Experimental results on a wide range of3 D models and 2D anisotropic shapes demonstrate the good performance and effectiveness of our method.展开更多
We present a novel algorithm to reconstruct curves with self-intersections and multiple parts from unorganized strip-shaped points,which may have different local shape scales and sampling densities.We first extract an...We present a novel algorithm to reconstruct curves with self-intersections and multiple parts from unorganized strip-shaped points,which may have different local shape scales and sampling densities.We first extract an initial curve,a graph composed of polylines,to model the different structures of the points.Then a least-squares optimization is used to improve the geometric approximation.The initial curve is extracted in three steps:anisotropic farthest point sampling with an adaptable sphere,graph construction followed by non-linear region identification,and edge refinement.Our algorithm produces faithful results for points sampled from non-simple curves without pre-segmenting them.Experiments on many simulated and real data demonstrate the efficiency of our method,and more faithful curves are reconstructed compared to other existing methods.展开更多
文摘This paper presents an automatic method for computing an anisotropic 2D shape distribution on an arbitrary 2-manifold mesh. Our method allows the user to specify the direction as well as the density of the distribution. Using a pre-computed lookup table, our method can efficiently detect collision among the shapes to be distributed on the 3D mesh. In contrast to existing approaches, which usually assume the 2D objects are isotropic and have simple geometry,our method works for complex 2D objects and can guarantee the distribution is conflict-free, which is a critical constraint in many applications. It is able to compute multi-class shape distributions in parallel.Our method does not require global parameterization of the input 3D mesh. Instead, it computes local parameterizations on the fly using geodesic polar coordinates. Thanks to a recent breakthrough in geodesic computation, the local parameterization can be computed at low cost. As a result, our method can be applied to models with complicated geometry and topology. Experimental results on a wide range of3 D models and 2D anisotropic shapes demonstrate the good performance and effectiveness of our method.
基金supported by the National Natural Science Foundation of China-Guangdong Joint Fund (No.U0935004)the National Natural Science Foundation of China (No.60873181)the Fundamental Research Funds for the Central Universities,China
文摘We present a novel algorithm to reconstruct curves with self-intersections and multiple parts from unorganized strip-shaped points,which may have different local shape scales and sampling densities.We first extract an initial curve,a graph composed of polylines,to model the different structures of the points.Then a least-squares optimization is used to improve the geometric approximation.The initial curve is extracted in three steps:anisotropic farthest point sampling with an adaptable sphere,graph construction followed by non-linear region identification,and edge refinement.Our algorithm produces faithful results for points sampled from non-simple curves without pre-segmenting them.Experiments on many simulated and real data demonstrate the efficiency of our method,and more faithful curves are reconstructed compared to other existing methods.
