Extensible point location algorithm

Sundareswara, Rashmi; Schrater, Paul

doi:10.1109/gmag.2003.1219670

Cited by 11 publications

(14 citation statements)

References 14 publications

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“…The theoretical complexity of the adjacency walk for nonhomogenous meshes is OððnÞ 1=3 Þ. 18 This constitutes a substantial improvement in terms of scalability over the O(n) brute-force approach. As shown in Fig.…”

Section: Selecting a Tetrahedron For Interpolationmentioning

confidence: 81%

“…18 The barycentric coordinates can directly be used as interpolation weights for estimating the HRTFĤ x at point X as the weighted sum of the HRTFs, H i , measured at A, B, C, and D, respectively,…”

Section: Calculation Of Interpolation Weightsmentioning

confidence: 99%

“…A more efficient way to locate a point in a triangulation is via an adjacency walk. 18 Starting from a random tetrahedron, evaluate the barycentric coordinates and walk to the adjacent tetrahedron across the triangle formed by the vertices with the three largest barycentric coordinates; terminate when all barycentric coordinates are positive [see Fig. 3(b), light gray tetrahedra].…”

Section: Selecting a Tetrahedron For Interpolationmentioning

confidence: 99%

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Head-related transfer function interpolation in azimuth, elevation, and distance

Gamper

2013

The Journal of the Acoustical Society of America

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Although distance-dependent head-related transfer function (HRTF) databases provide interesting possibilities, e.g., for rendering virtual sounds in the near-field, there is a lack of algorithms and tools to make use of them. Here, a framework is proposed for interpolating HRTF measurements in 3-D (i.e., azimuth, elevation, and distance) using tetrahedral interpolation with barycentric weights. For interpolation, a tetrahedral mesh is generated via Delaunay triangulation and searched via an adjacency walk, making the framework robust with respect to irregularly positioned HRTF measurements and computationally efficient. An objective evaluation of the proposed framework indicates good accordance between measured and interpolated nearfield HRTFs.

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Section: Selecting a Tetrahedron For Interpolationmentioning

confidence: 81%

Section: Calculation Of Interpolation Weightsmentioning

confidence: 99%

Section: Selecting a Tetrahedron For Interpolationmentioning

confidence: 99%

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Head-related transfer function interpolation in azimuth, elevation, and distance

Gamper

2013

The Journal of the Acoustical Society of America

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“…The objective is to find a triangle that contains the query point in a triangulation. Several methods have been proposed: Divide and Conquer [1], Directed Acyclic Graphics [2] and Walk-through strategy [3,4]. Among these methods, the Walk-through method is the fastest and simplest.…”

Section: Introductionmentioning

confidence: 99%

A robust backward search method based on walk‐through for point location on a 3D surface mesh

Shan

Guo

et al. 2007

Numerical Meth Engineering

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SUMMARYPoint location is one of the most basic searching problems in computational geometry. It has been largely studied on the aspect of query time in the worst case, and many methods have been proposed, such as counter clockwise wise search and barycentric coordinates search. However, most of them aim at the convex field. For a non-convex problem, such as a concave field or a convex field with holes, these searching schemes may fail. The numerical experience shows that, even for a convex problem, the searching path may lead to an infinite loop for some special case and may not find the element containing the query point. In this paper, a robust backward search method based on Walk-through algorithm is proposed to deal with the searching problems in non-convex fields and to avoid the problems of infinite loop. Another important improvement is to locate the query point on a 3D surface mesh. Several examples demonstrate that the present method is efficient and robust for the workpieces of complex geometry.

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“…Here, we use spherical triangle walk to locate the point [14]. Once the surrounding triangle has been found, the image value can be bilinearily interpolated from its three vertices using the barycentric coordinates of the query point.…”

Section: G Point Location and Mesh Interpolationmentioning

confidence: 99%

Geodesic Active Fields on the Sphere

Zosso

Thiran

2010

2010 20th International Conference on Pattern Recognition

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Abstract-In this paper, we propose a novel method to register images defined on spherical meshes. Instances of such spherical images include inflated cortical feature maps in brain medical imaging or images from omnidirectional cameras. We apply the Geodesic Active Fields (GAF) framework locally at each vertex of the mesh. Therefore we define a dense deformation field, which is embedded in a higher dimensional manifold, and minimize the weighted Polyakov energy. While the Polyakov energy itself measures the hyperarea of the embedded deformation field, its weighting allows to account for the quality of the current image alignment. Iteratively minimizing the energy drives the deformation field towards a smooth solution of the registration problem. Although the proposed approach does not necessarily outperform state-of-the-art methods that are tightly tailored to specific applications, it is of methodological interest due to its high degree of flexibility and versatility.

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Extensible point location algorithm

Cited by 11 publications

References 14 publications

Head-related transfer function interpolation in azimuth, elevation, and distance

Head-related transfer function interpolation in azimuth, elevation, and distance

A robust backward search method based on walk‐through for point location on a 3D surface mesh

Geodesic Active Fields on the Sphere

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