Cochlodinium polykrikoides is a notoriously harmful algal species that inflicts severe damage on the aquacultures of the coastal seas of Korea and Japan. Information on their expected movement tracks and boundaries of...Cochlodinium polykrikoides is a notoriously harmful algal species that inflicts severe damage on the aquacultures of the coastal seas of Korea and Japan. Information on their expected movement tracks and boundaries of influence is very useful and important for the effective establishment of a reduction plan. In general, the information is supported by a red-tide（a.k.a algal bloom） model. The performance of the model is highly dependent on the accuracy of parameters, which are the coefficients of functions approximating the biological growth and loss patterns of the C. polykrikoides. These parameters have been estimated using the bioassay data composed of growth-limiting factor and net growth rate value pairs. In the case of the C. polykrikoides, the parameters are different from each other in accordance with the used data because the bioassay data are sufficient compared to the other algal species. The parameters estimated by one specific dataset can be viewed as locally-optimized because they are adjusted only by that dataset. In cases where the other one data set is used, the estimation error might be considerable. In this study, the parameters are estimated by all available data sets without the use of only one specific data set and thus can be considered globally optimized. The cost function for the optimization is defined as the integrated mean squared estimation error, i.e., the difference between the values of the experimental and estimated rates. Based on quantitative error analysis, the root-mean squared errors of the global parameters show smaller values, approximately 25%–50%, than the values of the local parameters. In addition, bias is removed completely in the case of the globally estimated parameters. The parameter sets can be used as the reference default values of a red-tide model because they are optimal and representative. However, additional tuning of the parameters using the in-situ monitoring data is highly required.As opposed to the bioassay data, it is necessary because the bioassay data have limitations in terms of the in-situ coastal conditions.展开更多
We propose a novel method to compute globally injective parameterizations with arbitrary positional constraints on disk topology meshes.Central to this method is the use of a scaffold mesh that reduces the globally in...We propose a novel method to compute globally injective parameterizations with arbitrary positional constraints on disk topology meshes.Central to this method is the use of a scaffold mesh that reduces the globally injective constraint to a locally flipfree condition.Hence,given an initial parameterized mesh containing flipped triangles and satisfying the positional constraints,we only need to remove the flips of a overall mesh consisting of the parameterized mesh and the scaffold mesh while always meeting positional constraints.To successfully apply this idea,we develop two key techniques.Firstly,an initialization method is used to generate a valid scaffold mesh and mitigate difficulties in eliminating flips.Secondly,edgebased remeshing is used to optimize the regularity of the scaffold mesh containing flips,thereby improving practical robustness.Compared to state-of-the-art methods,our method is much more robust.We demonstrate the capability and feasibility of our method on a large number of complex meshes.展开更多
A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined...A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.展开更多
基金The part of the project "Development of Korea Operational Oceanographic System(KOOS),Phase 2",funded by the Ministry of Oceans and Fisheries,Koreathe part of the project entitled "Cooperative Project on Korea-China Bilateral Committee on Ocean Science",funded by the Ministry of Oceans and Fisheries,Korea and China-Korea Joint Research Ocean Research Center
文摘Cochlodinium polykrikoides is a notoriously harmful algal species that inflicts severe damage on the aquacultures of the coastal seas of Korea and Japan. Information on their expected movement tracks and boundaries of influence is very useful and important for the effective establishment of a reduction plan. In general, the information is supported by a red-tide（a.k.a algal bloom） model. The performance of the model is highly dependent on the accuracy of parameters, which are the coefficients of functions approximating the biological growth and loss patterns of the C. polykrikoides. These parameters have been estimated using the bioassay data composed of growth-limiting factor and net growth rate value pairs. In the case of the C. polykrikoides, the parameters are different from each other in accordance with the used data because the bioassay data are sufficient compared to the other algal species. The parameters estimated by one specific dataset can be viewed as locally-optimized because they are adjusted only by that dataset. In cases where the other one data set is used, the estimation error might be considerable. In this study, the parameters are estimated by all available data sets without the use of only one specific data set and thus can be considered globally optimized. The cost function for the optimization is defined as the integrated mean squared estimation error, i.e., the difference between the values of the experimental and estimated rates. Based on quantitative error analysis, the root-mean squared errors of the global parameters show smaller values, approximately 25%–50%, than the values of the local parameters. In addition, bias is removed completely in the case of the globally estimated parameters. The parameter sets can be used as the reference default values of a red-tide model because they are optimal and representative. However, additional tuning of the parameters using the in-situ monitoring data is highly required.As opposed to the bioassay data, it is necessary because the bioassay data have limitations in terms of the in-situ coastal conditions.
基金supported by the National Natural Science Foundation of China(61802359,62025207)USTC Research Funds of the Double First-Class Initiative(YD0010002003).
文摘We propose a novel method to compute globally injective parameterizations with arbitrary positional constraints on disk topology meshes.Central to this method is the use of a scaffold mesh that reduces the globally injective constraint to a locally flipfree condition.Hence,given an initial parameterized mesh containing flipped triangles and satisfying the positional constraints,we only need to remove the flips of a overall mesh consisting of the parameterized mesh and the scaffold mesh while always meeting positional constraints.To successfully apply this idea,we develop two key techniques.Firstly,an initialization method is used to generate a valid scaffold mesh and mitigate difficulties in eliminating flips.Secondly,edgebased remeshing is used to optimize the regularity of the scaffold mesh containing flips,thereby improving practical robustness.Compared to state-of-the-art methods,our method is much more robust.We demonstrate the capability and feasibility of our method on a large number of complex meshes.
基金Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds forYoung Innovation Group, Education Department of Anhui Prov-ince (No. 2005TD03) and the Natural Science Foundation of An-hui Provincial Education Department (No. 2006KJ252B), China
文摘A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
