25、圆与球的相交问题及GPS应用解析

圆与球的相交问题及GPS应用解析

1. 线性插值与相关代码

在进行圆与球相交问题的探讨之前，先介绍线性插值的相关内容。线性插值是一种常用的数值计算方法，通过分段线性曲线对给定数据进行插值。以下是实现线性插值的MATLAB/Octave代码：

% Interpolate with a piecewise linear curve
% GetData must be run first
nx = 201; % number of grid points
xlin = linspace(min(x),max(x),nx); % uniformly distributed points
% sort x and y values, based on the order of the x values
xysort = sortrows([x;y]’,1);
% compute the values of y at the given points xlin
ylin = interp1(xysort(:,1),xysort(:,2),xlin);
% Plot the interpolated curve.
% compute the derivatives at the midpoints
dy = diff(ylin)./diff(xlin);
% compute the midpoints of the intervals
xmid = xlin(2:length(xlin))-diff(xlin)/2;
figure(3); plot(x,y,’*’, xlin,ylin,xmid,dy);
legend(’given points’,’