interpolation methods Catmull - Rom spline, ebook
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(C) 2011 Jan-Willem Krans (janwillem32 <at> hotmail.com)This file is part of Video pixel shader pack.This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, version 2.This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.interpolation methods, Catmull-Rom splineiteration pyramid:p p p p p ps s sr r rq/qNote: the interval (p2+.5, p3) is handled by the mirror function 1.-t, all valid values for t are in the interval [p2, p2+.5]weights function:t2 = pow(t, 2);t3 = pow(t, 3);w0 = t2-(t3+t)/2.;w1 = t3*1.5+1.-t2*2.5;w2 = t2*2+t/2.-t3*1.5;w3 = (t3-t2)/2.;convolution function spline4, t is in the interval [m1, m2):n = ((((m1-m2)*3+m3-m0)*t+m0*2+m2*4-m1*5-m3)*t+m2-m0)*t/2.+m1;control points:.5 weights:t = .5;t2 = .25;t3 = .125;filling in the weights:w0 = -1/16.;w1 = 9/16.;w2 = 9/16.;w3 = -1/16.;----------------s0 (window: p0, p1, p2, p3):s0 = (p1*9+p2*9-p0-p3)/16.;s1 (window: p1, p2, p3, p4):s1 = (p2*9+p3*9-p1-p4)/16.;s2 (window: p2, p3, p4, p5):s2 = (p3*9+p4*9-p2-p5)/16.;----------------r0 (window: p1, s0, p2, s1):r0 = (s0*9+p2*9-p1-s1)/16.;r0 = (p1*66+p2*216+p4-p0*9-p3*18)/256.;r1 (spline5, window: s0, p2, s1, p3):r1 = (p2*9+s1*9-s0-p3)/16.;r1 = (p0+p2*216+p3*66-p1*18-p4*9)/256.;r2 (window: p2, s1, p3, s2):r2 = (s1*9+p3*9-p2-s2)/16.;r2 = (p2*66+p3*216+p5-p1*9-p4*18)/256.;----------------f(t) q0, spline6, interval [p2, p2+.25] (window: r0, p2, r1, s1):q0 = (((p0*3/256.-p1*7/128.+p2*3/32.-p3*9/128.+p4*5/256.)*t+p1*19/128.+p3*21/128.-p0*7/256.-p2/4.-p4*9/256.)*t+(p3-p1)*21/128.+(p0-p4)*5/256.)*t+p2;f(t) q1, spline6, interval (p2+.25, p2+.5] (window: p2, r1, s1, r2):q1 = (((((p0+p4)*3+p2*26+p5-p1*15-p3*18)*t+p1*35+p3*30-p0*5-p2*58-p4-p5)*t+p3*144-(p1+p4)*16-p2*112)*t+p0*2+p2*432+p3*132-p1*36-p4*18)/512.;
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