Geometric constraint solver using multivariate rational spline functions

2001 ◽  
Author(s):  
Gershon Elber ◽  
Myung-Soo Kim
Keyword(s):  
Geometric Constraint ◽  
Spline Functions ◽  
Constraint Solver ◽  
Rational Spline

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

The Research on a Novel Geometric Constraint Solver

2006 ◽  
Author(s):  
Chunhong Cao ◽  
Bin Zhang ◽  
Xiaolin Li ◽  
Limin Wang ◽  
Wenhui Li
Keyword(s):  
Geometric Constraint ◽  
Constraint Solver

A correct rule-based geometric constraint solver

1997 ◽  
Vol 21 (5) ◽  
pp. 599-609 ◽  
Author(s):  
R. Joan-Arinyo ◽  
A. Soto
Keyword(s):  
Geometric Constraint ◽  
Rule Based ◽  
Constraint Solver ◽  
Correct Rule

LGS: Geometric Constraint Solver

2004 ◽  
pp. 423-430
Author(s):  
Alexey Ershov ◽  
Ilia Ivanov ◽  
Serge Preis ◽  
Eugene Rukoleev ◽  
Dmitry Ushakov
Keyword(s):  
Geometric Constraint ◽  
Constraint Solver
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