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three points location theory
autoreconf --install && ./configure && make 原点n坐标为:(Xn,Yn),半径为Rn,则有: F(n): (x - Xn)^2 + (y - Yn)^2 = Rn^2 求两圆相交直线: F(1) - F(0): 2*(X1-X0)*x + (X0^2-X1^2) + 2*(Y1-Y0)*y + (Y0^2 - Y1^2) = R0^2 - R1^2 (R0^2-R1^2)-(X0^2-X1^2)-(Y0^2-Y1^2) X1 - X0 ==> y = ------------------------------------- - --------- * x 2 * (Y1 - Y2) Y1 - Y2 (R0+R1)(R0-R1) - (X0+X1)(X0-X1) - (Y0+Y1)(Y0-Y1) X1 - X0 ==> y = -------------------------------------------------- - --------- * x 2 * (Y1 - Y2) Y1 - Y2 define SUM(X) (X0+X1) define SUB(X) (X0-X1) SUM(X)*SUB(X) + SUM(Y)*SUB(Y) - SUM(R)*SUB(R) -SUB(X) ==> y = ----------------------------------------------- + --------- * x 2 * SUB(Y) SUB(Y) ==> y = A*x + B 有三个圆时,可以得到两个上面的式子。很容易就可以求得中心点。
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