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Abstract. The common math algorithms library provides a C++ implementation of the most frequently used mathematical algorithms. These include: algorithms to solve a set of linear algebraic equations, algorithms to find the minimum of a function of one or more independent variables, algorithms to find roots of one, or of a set of non-linear equations, algorithm to find the eigenvalues and eigenvectors of a square matrix. The solver for function set is used widely in extrema value evaluation, poin 阅读全文
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Happy New Year! 阅读全文
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Abstract. In calculus, Newton’s method is used for finding the roots of a function. In optimization, Newton’s method is applied to find the roots of the derivative. OPEN CASCADE implement Newton method to find the extrema for a multiple variables function, such as find the extrema point for a curve and a surface.
Key Words. Nonlinear Programming, Newton Method, Extrema, OPEN CASCADE 阅读全文
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Abstract. Multiple variable function with gradient and Hessian matrix is very very import in OPEN CASCADE optimization algorithms. In order to understand these optimization algorithm better, let’s study some basic knowledge about Gradient, Hessian Matrix.
Key Words. Multiple Variable Function, Gradient, Hessian Matrix, 最优化算法, 阅读全文
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Abstract. The least square can be used to solve a set of n linear equations of m unknowns(n >= m). The OPEN CASCADE class math_GaussLeastSquare implements the least square solution of the linear equations by using Gauss LU decomposition algorithm. The paper focus on the Least Square method to solve the linear equations.
Key Words. Least Square, LU Decomposition, Linear Equations 阅读全文
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Abstract. 设计一条复杂曲线时，出于设计和制造上的考虑，常常通过多段曲线组合而成，这就需要解决曲线段之间如何实现光滑连接的问题。评价曲线间连接的光滑度的度量有两种：参数连接性和几何连续性。本文对这两种连续性分别进行介绍。
Key Words. Curve Continuity, Geometric Continuity, 参数连续性、几何连续性 阅读全文
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Abstract. Global curve interpolation to point data is a way to construct curves. The paper focus on the interpolate algorithm in OPEN CASCADE, and give a simple example to demonstrate the usage of the GeomAPI_Interpolate class.
Key Words. Interpolate, NURBS, BSpline, OPEN CASCADE 阅读全文
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Abstract. The Voronoi extension of the Boost.Polygon library provides functionality to construct a Voronoi diagram of a set of points and linear segments in 2D space with some limitations. The paper mainly describles how to compile the boos voronoi visualizer and use it show the example voronoi diagram result.
Key Words. Boost, Voronoi, Visualizer 阅读全文
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Abstract. Clash detection is used for the model collision check. The paper introduce the clash detection in PDMS, and also about how to set the piping component for the operation space clash check.
Key Word. Clash Detection, Collision Detection 阅读全文
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Abstract. Power basis polynomial is the most simple polynomial function. It also be called power series. OpenCASCADE provides basic computation functions for polynomial functions, such as evaluate the result for a given polynomial, Lagrange interpolation, Hermite interpolation, .etc. The package named PLib, means Polynomial functions Library. The paper focus on the Lagrange interpolation usage of PLib.
Key Words. OpenCASCADE, PLib, Interpolation, Lagrange, 插值 阅读全文