Self-intersection computation for freeform surfaces based on a regional representation scheme for miter points

Park, Youngjin; Hong, Qingqi; Kim, Myung-Soo; Elber, Gershon

doi:10.1016/j.cagd.2021.101979

Cited by 6 publications

(4 citation statements)

References 17 publications

(17 reference statements)

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“…Several researchers utilized toroidal patches to address complex geometric challenges [28][29][30]. Park et al [28] developed a hybrid bounding volume hierarchy (BVH) for freeform surfaces, employing a rectangle-swept sphere (RSS) at internal nodes and a second-order toroidal patch at leaf nodes to calculate an intersection curve between two freeform surfaces.…”

Section: Related Workmentioning

confidence: 99%

“…Park et al [28] developed a hybrid bounding volume hierarchy (BVH) for freeform surfaces, employing a rectangle-swept sphere (RSS) at internal nodes and a second-order toroidal patch at leaf nodes to calculate an intersection curve between two freeform surfaces. In a follow-up study, Park et al [29] introduced an innovative approach optimized for the efficient computation of self-intersecting curve(s) on a freeform surface. This method utilizes a ternary-structured BVH that incorporates toroidal patches to share rele-vant data, unlike the conventional binary-structured BVH.…”

Section: Related Workmentioning

confidence: 99%

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Camera Path Generation for Triangular Mesh Using Toroidal Patches

Choi,

Kim,

Kim

et al. 2024

Applied Sciences

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Triangular mesh data structures are principal in computer graphics, serving as the foundation for many 3D models. To effectively utilize these 3D models across diverse industries, it is important to understand the model’s overall shape and geometric features thoroughly. In this work, we introduce a novel method for generating camera paths that emphasize the model’s local geometric characteristics. This method uses a toroidal patch-based spatial data structure, approximating the mesh’s faces within a predetermined tolerance ϵ, encapsulating their geometric intricacies. This facilitates the determination of the camera position and gaze path, ensuring the mesh’s key characteristics are captured. During the path construction, we create a bounding cylinder for the mesh, project the mesh’s faces and associated toroidal patches onto the cylinder’s lateral surface, and sequentially select grids of the cylinder containing the highest number of toroidal patches as we traverse the lateral surface. The centers of the selected grids are used as control points for a periodic B-spline curve, which serves as our foundational path. After initial curve generation, we generated camera position and gaze path from the curve by multiplying factors to ensure a uniform camera amplitude. We applied our method to ten triangular mesh models, demonstrating its effectiveness and adaptability across various mesh configurations.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Camera Path Generation for Triangular Mesh Using Toroidal Patches

Choi,

Kim,

Kim

et al. 2024

Applied Sciences

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“…Next, we locate feature points on the parameter domain, which include the intersection points of singular curves and the boundary of the parameter domain, the self-intersecting points of singular curves, the intersection points of different singular curves, and miter points [20]. The loss of feature points could also lead to a non-conforming mesh.…”

Section: Computing Feature Pointsmentioning

confidence: 99%

High-quality quad-mesh generation for self-intersecting parametric surfaces

Nan,

Xu,

et al. 2024

Preprint

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We propose a method for the high-quality quadrangulation of an input self-intersecting parametric surface. We first compute the algebraic representation of self-intersecting curves and cusp curves of the surface by the moving plane method. Sampling points are then generated on the singular curves and the boundary over the parameter domain. In order to ensure the correctness of mesh intersection topology, we compute feature points and the pair-points of the curve sampling points, which are fixed strictly throughout our method. A triangle mesh is generated over the domain with the singular curves as constraint lines, which is the input of quadrilateral mesh generation. We compute a cross-field aligned with the feature lines and construct a coarse layout of quad patches relying on the cross-field. As T-junctions are allowed in the layout, we solve an Integer Linear Program (ILP) problem to determine the number of edges, thereby ensuring that the generated mesh is conforming. Feature lines are preserved perfectly throughout the pipeline by imposing constraints. In conclusion, our method guarantees the neighborhood coordination of mesh intersections, while still producing high-quality quadrilateral meshes.

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“…Other works in this issue propose algorithms for solving computational geometry problems such as computing the precise Hausdorff distance between two freeform surfaces (Son et al (2021)) or the selfintersection of a freeform surface (Park et al (2021)).…”

Section: Topics Of the Special Issuementioning

confidence: 99%