Numerical methods for colorimetric calculations: A comparison of integration methods

Abstract

Numerical melhodv ,f;w estimating cdnrimetric integrals using various data intervuls Lire reuie wed. Accurucy of Newton-Cotes and Gaussian numerical integrationulgo-rithn1.s ure compared. Tables of colorimetric dataJbr per-Jiwming Guuss-Legendre integrution are presented. Appropriati) numerical examples are presented and applicability t o general and spocial cases is discussed. Tho B-spline method of integration is presented. Errors of integrution are quantified and discussed. 0 1992 John

A color model for rendering linear passive graphic 2D objects

“…• by point sampling of the spectrum: the integration is usually computed by using a Gaussian quadrature [28,20] or a Riemann summation over evenly spaced samples weighted by the distance between the sample wavelength [29]; • by describing the spectra by a set of orthogonal basis functions and using the result of the precomputation of the integration of basis functions with, respectively, the three color matching functions [22].…”

<title>Color perception under various light sources using spectral numerical models</title>

“…Qr) to the incident flux for the wavelength X, while the transmission is described using bi-directional transmittance The total flux diffused in the scattering indicatrix is expressed by cD=f I(Q).dQ (12) ci Scattering Indicatrix C Considering Q as a two-dimensional statistical variable, we express, according to I (Q) distribution function, the cumulative probability function P(Q) of this variable, with associated probability density p(Q). P(Q') = 1f (13) p(Q) O and Jp(cl).dc2=1 (14) Introducing in equation (15) Ie:c2) = i(Q).p(12) (15) cFi(Q1) (16) As the scattering indicatrix has the property of revolution over an axe that is the mean direction of reernitted rays, Q can be expressed in spherical coordinates (zenith 0 and azimuth çø ) in a local reference attached to the scattering indicatrix. The cumulative probability function P is now a function of e only, so we can use its reciprocal function to determine 0 coordinate using a random number generator, while another independant random number is used to determine 9 coordinate.…”