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A constant speed parametrization (CSP) mapping of boundary surfaces is proposed for moment-method analysis of antennas and scatterers, along with its approximation using large higher-order Lagrange-type curved quadrilateral patches. The importance of the proper placement of interpolation nodes that ensures minimum mapped parametric space distortion (arc-length parametrization) is explained and demonstrated on simple examples. The CSP mapping results in on average five times lower radar cross section (RCS) error for a spherical scatterer than with the ray casting (central projection) parametrization mapping. The extension of the CSP concept to arbitrary surfaces is illustrated in modeling of the double-ogive target.