Smooth Approximation and Rendering of Large Scattered Data Sets

Haber, Jörg; Zeilfelder, Frank; Davydov, Oleg; Seidel, Hans‐Peter

doi:10.1007/978-3-540-74238-8_11

Cited by 4 publications

(10 citation statements)

References 31 publications

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“…The work of Haber et al 19 achieves several of these goals, however the rendering is restrictively slow for views near the surface that display large areas of the surface. That work does not offer adaptive LOD, thus the entire surface is rendered at the detail required by the near view.…”

Section: Overviewmentioning

confidence: 99%

“…For the scattered data approximation, we use a similar approach to the one presented in 19 . However, instead of fitting the control points of uniformly distributed cubic Bernstein‐Bézier triangles to compute a bivariate cubic spline surface, we now fit the control points of a subdivision surface control mesh, which is adapted to the local variation and distribution of the scattered data.…”

Section: 2 Scattered Data Approximationmentioning

confidence: 99%

“…Our approach to scattered data fitting borrows some ideas from the method presented in 19 . In this section, we describe the key idea of our new approach as well as the main differences to the previous method.…”

Section: Scattered Data Fittingmentioning

confidence: 99%

“…Due to the adaptive construction of the BTT, however, these situations rarely occur. The process of finding the data points that lie inside the local area around a vertex can be efficiently carried out using the same approach and data structures as described in 19 .…”

Section: Scattered Data Fittingmentioning

confidence: 99%

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Efficient Fitting and Rendering of Large Scattered Data Sets Using Subdivision Surfaces

Scheib¹,

Haber

Seidel

2002

Computer Graphics Forum

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We present a method to efficiently construct and render a smooth surface for approximation of large functional scattered data. Using a subdivision surface framework and techniques from terrain rendering, the resulting surface can be explored from any viewpoint while maintaining high surface fairness and interactive frame rates. We show the approximation error to be sufficiently small for several large data sets. Our system allows for adaptive simplification and provides continuous levels of detail, taking into account the local variation and distribution of the data. Categories and Subject Descriptors (according to ACM CCS): G.1.2 [Approximation]: Approximation of surfaces, Least squares approximation, Piecewise polynomial approximation; I.3.3 [Picture/Image Generation]: Display algorithms, Viewing algorithms; I.3.5 [Computational Geometry and Object Modeling]: Surface representation.

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Section: Overviewmentioning

confidence: 99%

Section: 2 Scattered Data Approximationmentioning

confidence: 99%

Section: Scattered Data Fittingmentioning

confidence: 99%

Section: Scattered Data Fittingmentioning

confidence: 99%

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Efficient Fitting and Rendering of Large Scattered Data Sets Using Subdivision Surfaces

Scheib¹,

Haber

Seidel

2002

Computer Graphics Forum

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“…[20], and the references therein, and for instance, the bivariate approaches of [11,13,19,21]) require some knowledge on the structure of these spaces. One such basic structural question in multivariate spline theory is to determine the dimension (i.e.…”

Section: Introductionmentioning

confidence: 99%

Dimension ofC1-splines on type-6 tetrahedral partitions

Hangelbroek

Nürnberger

Rössl

et al. 2004

Journal of Approximation Theory

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We consider a linear space of piecewise polynomials in three variables which are globally smooth, i.e. trivariate C 1 -splines of arbitrary polynomial degree. The splines are defined on type-6 tetrahedral partitions, which are natural generalizations of the four-directional mesh. By using Bernstein-Bézier techniques, we analyze the structure of the spaces and establish formulae for the dimension of the smooth splines on such uniform type partitions.

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Determinants of Above-Ground Biomass and Its Spatial Variability in a Temperate Forest Managed for Timber Production

Soriano‐Luna

Ángeles‐Pérez

Guevara

et al. 2018

Forests

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The proper estimation of above-ground biomass (AGB) stocks of managed forests is a prerequisite to quantifying their role in climate change mitigation. The aim of this study was to analyze the spatial variability of AGB and its uncertainty between actively managed pine and unmanaged pine-oak reference forests in central Mexico. To investigate the determinants of AGB, we analyzed variables related to forest management, stand structure, topography, and climate. We developed linear (LM), generalized additive (GAM), and Random Forest (RF) empirical models to derive spatially explicit estimates and their uncertainty, and compared them. AGB was strongly influenced by forest management, as LiDAR-derived stand structure and stand age explained 80.9% to 89.8% of its spatial variability. The spatial heterogeneity of AGB varied positively with stand structural complexity and age in the managed forests. The type of predictive model had an impact on estimates of total AGB in our study site, which varied by as much as 19%. AGB densities varied from 0 to 492 ± 17 Mg ha−1 and the highest values were predicted by GAM. Uncertainty was not spatially homogeneously distributed and was higher with higher AGB values. Spatially explicit AGB estimates and their association with management and other variables in the study site can assist forest managers in planning thinning and harvesting schedules that would maximize carbon stocks on the landscape while continuing to provide timber and other ecosystem services. Our study represents an advancement toward the development of efficient strategies to spatially estimate AGB stocks and their uncertainty, as the GAM approach was used for the first time with improved results for such a purpose.

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Smooth Approximation and Rendering of Large Scattered Data Sets

Cited by 4 publications

References 31 publications

Efficient Fitting and Rendering of Large Scattered Data Sets Using Subdivision Surfaces

Efficient Fitting and Rendering of Large Scattered Data Sets Using Subdivision Surfaces

Dimension ofC1-splines on type-6 tetrahedral partitions

Determinants of Above-Ground Biomass and Its Spatial Variability in a Temperate Forest Managed for Timber Production

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