The detection methods of yellow dragon disease spread via wood lice transmission networks like social networks are very important for diverse citrus trees and farmers. Although current methods have some detection accu...
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Rain streaks noise is one of the greatest influence of outdoor scene tasks. In order to improve the effect of the outdoor scene tasks, we need to reduce the impact of the rain streaks noise while ensuring that other i...
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Plants are complex structures,changing their shapes in response to environmental factors such as sunlight,water and neighboring plants. However,some mathematical rules can be found in their growth patterns,one of whic...
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Plants are complex structures,changing their shapes in response to environmental factors such as sunlight,water and neighboring plants. However,some mathematical rules can be found in their growth patterns,one of which is the golden section. The golden section can be observed in branching systems,phyllotaxis,flowers and seeds,and often the spiral arrangement of plant organs. In this study,tree,flower and fruit models have been generated by using the corresponding golden section characteristics,resulting in more natural patterns. Furthermore,the golden section can be found in the bifurcate angles of trees and lobed leaves,extending the golden section theory.
Considering the complexity of the rational B´zier harmonic surfaces, in this paper an approximated algorithm for constructing rational B´zier harmonic surfaces is proposed. By using polynomial curves and sur...
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Considering the complexity of the rational B´zier harmonic surfaces, in this paper an approximated algorithm for constructing rational B´zier harmonic surfaces is proposed. By using polynomial curves and surfaces to approximate rational curves and surfaces and constructing B´zier harmonic surfaces with the Monterde method, the rational B´zier harmonic surface modeling problem can be transformed into an optimization problem of how to minimize a nonlinear function with a limited number of variables under a linear constrained condition. The proposed algorithm is also extended into constructing the rational B´zier biharmonic surfaces. The method is validated by examples of biharmonic surfaces of degree three and harmonic surfaces of degree two and three .The experimental results show that the algorithm proposed performs well in the application of constructing rational B´zier harmonic surfaces and biharmonic surfaces.
The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions wit...
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The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.
In the space Γn=span {1, sin t, cos t, sinh t, cosh t, t, t2, , tn-4}, a kind of algebraic trigonometric hyperbolic basis called ATH Bezier basis is constructed by an integral approach. By the symmetry of the ATH Bez...
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In the space Γn=span {1, sin t, cos t, sinh t, cosh t, t, t2, , tn-4}, a kind of algebraic trigonometric hyperbolic basis called ATH Bezier basis is constructed by an integral approach. By the symmetry of the ATH Bezier basis, we construct an orthogonal basis called quasi-Lengendre basis, then we present the conversion formula between the ATH Bezier basis and the orthogonal basis. In addition, the optimal lower degree approximation of the ATH Bezier curves is investigated.
In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis ...
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In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis functions, we construct a class of shape adjusting surfaces defined over the triangular domain with a shape parameter, namely, quasi-B-B parametric surfaces. These surfaces share many properties with the B-B parametric surfaces. In particular, when shape parameters equal 1, they degenerate to be the B-B parametric surfaces. By changing the value of the shape parameter, we can get different surfaces under the fixed control net.
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