An algorithm for triangulating multiple 3D polygons

Zou, Ming; Ju, Tao; Carr, Nathan

doi:10.1111/cgf.12182

Cited by 20 publications

(13 citation statements)

References 15 publications

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“…To get better-looking patches, we utilize the parallel-transport normal families that attains the intra-bridge cost for each curve on the cycle. We then use a dynamic programming algorithm [Zou et al 2013] to compute a triangulation that matches these normals as best as possible while minimizing the average dihedral angle between triangles. This initial triangulation is then refined and smoothed while still maintaining the normal constraints [Andrews et al 2011].…”

Section: Interactive Toolmentioning

confidence: 99%

A general and efficient method for finding cycles in 3D curve networks

et al. 2013

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Figure 1: A curve network (misc2) representing a genus-7 mechanical part (left), cycles found by our algorithm (middle), and surface patches generated from the cycles (right). The curve network contains 410 curves. Our algorithm completed in half a second. AbstractGenerating surfaces from 3D curve networks has been a longstanding problem in computer graphics. Recent attention to this area has resurfaced as a result of new sketch based modeling systems. In this work we present a new algorithm for finding cycles that bound surface patches. Unlike prior art in this area, the output of our technique is unrestricted, generating both manifold and nonmanifold geometry with arbitrary genus. The novel insight behind our method is to formulate our problem as finding local mappings at the vertices and curves of our network, where each mapping describes how incident curves are grouped into cycles. This approach lends us the efficiency necessary to present our system in an interactive design modeler, whereby the user can adjust patch constraints and change the manifold properties of curves while the system automatically re-optimizes the solution.

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Section: Interactive Toolmentioning

confidence: 99%

A general and efficient method for finding cycles in 3D curve networks

et al. 2013

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“…The software used a triangulated surface to determine the defect borders through the method of morphological thinning [17]. Defect area was then calculated using minimum weight triangulation [18]. Details on the software reliability, validity and user interface are explained in the appendix.…”

Section: Discussionmentioning

confidence: 99%

Long-Term Characterization of Cranial Defects After Surgical Correction for Single-Suture Craniosynostosis

et al. 2019

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Introduction-Craniosynostosis is typically corrected surgically within the first year of life through cranial vault reconstruction. These procedures often leaves open calvarial defects at the time of surgery, which are anticipated to close over time in a large proportion of cases. However, residual calvarial defects may result as long-term sequelae from cranial vault remodeling. When larger defects are present, they may necessitate further reconstruction for closure.Better understanding of the calvarial osseous healing process may help to identify which defects will resolve or shrink to acceptable size and which will require further surgery. Our study aims to assess the long-term changes in defect size after cranial vault reconstruction for craniosynostosis.Methods-One year post-operative and long-term computed tomography scans were retrieved from the craniofacial anomalies archive. Analysis used custom software. All defects above the size of 1 cm 2 were analyzed and tracked for calvarial location, surface area, and circularity. Monte Carlo simulation was performed to model the effect of initial defect size on the rate of defect closure.Results-We analyzed a total of 74 defects. The average initial defect surface area was 3.27 ± 3.40 cm 2 . The average final defect surface area was 1.71 ± 2.54 cm 2 . The average percent decrease was 55.06 ± 28.99 %. There was a significant difference in the percentage decrease of defects in the parietal and fronto-parietal locations: 68.4% and 43.7%, respectively (p = 0.001). Monte Carlo simulation results suggest that less than 10% of defects above the size of 9 cm 2 will close to the size of 2.5 cm 2 or less.Conclusions-We describe and make available a novel, validated method of measuring cranial defects. We find that the large majority of initial defects greater than 9cm 2 remain at least one square inch in size (2.5cm 2 ) one year post-operatively. Additionally, there appear to be regional differences in closure rates across the cranium, with front-parietal defects closing more slowly than those in the parietal region. This information will aid surgeons in the decision-making process regarding cranioplasty after craniosynostosis correction.

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“…A second challenge is to generate the surface geometry that interpolates the cycle boundaries. We adopt the method by Zou et al [62] for this task, which applies a dynamic programming algorithm to generate a triangulation that satisfies various geometric criteria. Alternative solutions include the generation of a quad mesh aligned with the input curves [9].…”

Section: Related Workmentioning

confidence: 99%

“…Once a cycle is detected, we generate a triangle mesh over it with the method by Zou et al [62], using their public implementation. We then refine the generated surface by applying isotropic re-meshing followed by curvature-flow smoothing [15,33] to generate minimal (soap-film) surfaces.…”

Section: Surface Geometrymentioning

confidence: 99%

CASSIE: Curve and Surface Sketching in Immersive Environments

Arora

Stanko

et al. 2021

Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems

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Figure 1: Freehand 3D sketching in AR/VR allows rapid conceptualization of design ideas (a). However, 3D inputs are prone to large inaccuracies (a, inset) and sketches cannot be utilized in downstream design pipelines. Our novel 3D sketching system, CASSIE, allows the creation of clean, well-connected 3D curve networks by performing automatic stroke neatening (b). These curve networks are augmented by our on-the-fly cycle detection and surfacing method (c) which improves shape perception by providing occlusion cues. We evaluated CASSIE with 12 users and utilized it for creating 3D concepts for a variety of application domains (d).

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An algorithm for triangulating multiple 3D polygons

Cited by 20 publications

References 15 publications

A general and efficient method for finding cycles in 3D curve networks

A general and efficient method for finding cycles in 3D curve networks

Long-Term Characterization of Cranial Defects After Surgical Correction for Single-Suture Craniosynostosis

CASSIE: Curve and Surface Sketching in Immersive Environments

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