Equality Testing for Soil Grid Unit Resolutions to Polygon Unit Scales with DNDC Modeling of Regional SOC Pools

Matching soil grid unit resolutions with polygon unit map scales is important to minimize the uncertainty of regional soil organic carbon(SOC) pool simulation due to their strong influences on the modeling.A series of soil grid units at varying cell sizes was derived from soil polygon units at six map scales,namely,1:50 000(C5),1:200 000(D2),1:500 000(P5),1:1 000 000(N1),1:4 000 000(N4) and 1:14 000 000(N14),in the Taihu Region of China.Both soil unit formats were used for regional SOC pool simulation with a De Nitrification-DeC omposition(DNDC) process-based model,which spans the time period from 1982 to 2000 at the six map scales.Four indices,namely,soil type number(STN),area(AREA),average SOC density(ASOCD) and total SOC stocks(SOCS) of surface paddy soils that were simulated by the DNDC,were distinguished from all these soil polygon and grid units.Subjecting to the four index values(IV) from the parent polygon units,the variations in an index value(VIV,%) from the grid units were used to assess its dataset accuracy and redundancy,which reflects the uncertainty in the simulation of SOC pools.Optimal soil grid unit resolutions were generated and suggested for the DNDC simulation of regional SOC pools,matching their respective soil polygon unit map scales.With these optimal raster resolutions,the soil grid units datasets can have the same accuracy as their parent polygon units datasets without any redundancy,when VIV < 1% was assumed to be a criterion for all four indices.A quadratic curve regression model,namely,y = – 0.80 × 10^(–6)x^2 + 0.0228 x + 0.0211(R^2 = 0.9994,P < 0.05),and a power function model R? = 10.394?^(0.2153)(R^2 = 0.9759,P < 0.05) were revealed,which describe the relationship between the optimal soil grid unit resolution(y,km) and soil polygon unit map scale(1:10 000x),the ratio(R?,%) of the optimal soil grid size to average polygon patch size(?,km^2) and the ?,with the highest R^2 among different mathematical regressions,respectively.This knowledge may facilitate the grid partitioning of regions during the investigation and simulation of SOC pool dynamics at a certain map scale,and be referenced to other landscape polygon patches' mesh partition.

Model of Random Polygon Particles for Concrete and Mesh Automatic Subdivision

In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Based on computational geometry, we carry out the automatic generation of the triangle finite element mesh for the model of random polygon particles of concrete. The finite element mesh generated in this paper is also applicable to many other numerical methods.

ADAPTIVE REPAIR APPROACH FOR RECOVERING COMPONENTS FROM DEFECTS

The geometry of each worn part is unique, so that a repair has to be tailored to each part individually. To ensure that a high quality repair is carried out, tool paths have to be generated adaptively for the tmique geometry and pose of the part being repaired. A polygonal modelling approach is introduced to rapidly construct a geometric model of the part to be repaired, together with a defect-free model with identical geometry and poise. The two models are compared so that the defects are identified for direct use by the laser cladding, machining and inspection processes.

Scale effect and geometric shapes of grains

The role-of-mixture approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures, and it is very important for the simulation results to exactly compute phase volume fractions. The nanocrystalline （NC） materials are treated as three-phase composites consisting of grain core phase, grain boundary （GB） phase and triple junction phase, and a two-dimensional three-phase mixture regular polygon model is established to investigate the scale effect of mechanical properties of NC materials due to the geometrical polyhedron characteristics of crystal grain. For different multi-sided geometrical shapes of grains, the corresponding regular polygon model is adopted to obtain more precise phase volume fractions and exactly predict the mechanical properties of NC materials.

Fixing Geometric Errors on Polygonal Models:A Survey

Polygonal models are popular representations of 3D objects. The use of polygonal models in computational applications often requires a model to properly bound a 3D solid. That is, the polygonal model needs to be closed, manifold, and free of self-intersections. This paper surveys a sizeable literature for repairing models that do not satisfy this criteria, focusing on categorizing them by their methodology and capability. We hope to offer pointers to further readings for researchers and practitioners, and suggestions of promising directions for future research endeavors.

Efficient Simplification Methods for Generating High Quality LODs of 3D Meshes

Two simplification algorithms are proposed for automatic decimation of polygonal models, and for generating their LODs. Each algorithm orders vertices according to their priority values and then removes them iteratively. For setting the priority value of each vertex, exploiting normal field of its one-ring neighborhood, we introduce a new measure of geometric fidelity that reflects well the local geometric features of the vertex. After a vertex is selected, using other measures of geometric distortion that are based on normal field deviation and distance measure, it is decided which of the edges incident on the vertex is to be collapsed for removing it. The collapsed edge is substituted with a new vertex whose position is found by minimizing the local quadric error measure. A comparison with the state-of-the-art algorithms reveals that the proposed algorithms are simple to implement, are computationally more efficient, generate LODs with better quality, and preserve salient features even after drastic simplification. The methods are useful for applications such as 3D computer games, virtual reality, where focus is on fast running time, reduced memory overhead, and high quality LODs.