ªªNumerit[WIN32][1700][1703]Cþúinterp2d qffffff)@ÌÌÌÌÌüj@fffffvq@À?@ffffff9@À?@ffffff9@ffffff)@ffffff)@ð êõ  Úõ Úñ êð êð êð êð êTimes New RomanArialSymbol Courier NewÿÿÿÀÀÀ I ¼»»»»!a@wwwwwcR@Àaô@@@p@ €>ÍÌÌ=ÍÌÌ=€>€>€??0.010.010.010.01I ¼»»»»!a@wwwwwcR@Àaaô@@@p@ €>ÍÌÌ=ÍÌÌ=€>€>€??0.010.010.010.01I ïîîîîêB@ÝÝÝÝÝõ5@Àa}A@_@@P@ €>ÍÌÌ=ÍÌÌ=€>€>€??0.010.010.010.01ÿÿÿÿÿ™v–þ™v–þ™v–þßßßpÿÿÿÿÿÿÿÿ™v–þ™v–þ™v–þßßßpÿÿÿÿÿÿÿÿ™v–þ™v–þ™v–þßßßpÿÿÿÿÿÿÿÿ™v–þ™v–þ™v–þßßßpÿÿÿÿÿÿÿÿ™v–þ™v–þ™v–þßßßpÿÿÿÿÿÿÿÿ™v–þ™v–þ™v–þßßßpÿÿÿÿÿÿÿÿ™v–þ™v–þ™v–þ êOriginal Image ÿÿÿÿÿ™v–þ™v–þ™v–þ ê" ÿÿÿÿÿ™v–þ™v–þ™v–þ ê(ÿÿÿÿÿ™v–þ™v–þ™v–þ êImage magnified ×4 with no interpolationÿÿÿÿÿ™v–þ™v–þ™v–þ ê ÿÿÿÿÿ™v–þ™v–þ™v–þ ê%ÿÿÿÿÿ™v–þ™v–þ™v–þ êImage magnified ×4 with interpolationÿÿÿÿÿ™v–þ™v–þ™v–þ ê! ÿÿ q8ffffff)@ÌÌÌÌÌüj@fffffvq@À?@ffffff9@À?@ffffff9@ffffff)@ffffff)@ð êõ  Úõ Úñ êð êð êð êð êTimes New RomanArialSymbol Courier NewÿÿÿÀÀÀ Y=` This sample program defines a two-dimensional interpolation=` function. It then uses this function to magnify an image by=` a factor of four with minimum degradation in image quality.3` The function interp2d generates a two-dimensional` interpolation.` Input:.` a = 2-d array of values to be interpolated+` x = input coordinates along x-dimension+` y = input coordinates along y-dimension-` xx = output coordinates along x-dimension-` yy = output coordinates along y-dimensionL` - note that the number of rows of 'a' must be equal to the length of 'y'I` and the number of columns of 'a' must be equal to the length of 'x'(` The function returns a 2-d array whose)` [i,j] element is the interpolated value` at the point (xx[j],yy[i]).func interp2d(a,x,y,xx,yy)Nif dim(a) <> 2 or dim(x) <> 1 or dim(y) <> 1 or dim(xx) <> 1 or dim(yy) <> 13wmessage("Interp2d","Parameters dimension error") return 0na = length(a)nx = length(x)ny = length(y)if na[1] <> ny or na[2] <> nx3wmessage("Interp2d","Parameters length mismatch") return 0nxx = length(xx)nyy = length(yy)#aa[nyy,nxx]:0 `` interpolated array if nxx <= nyy"at[ny,nxx]:0 `` temporary array0for ky = 1 to ny at[ky,*] = interp(a[ky,*],x,xx)6for kxx = 1 to nxx aa[*,kxx] = interp(at[*,kxx],y,yy)else"at[nyy,nx]:0 `` temporary array0for kx = 1 to nx at[*,kx] = interp(a[*,kx],y,yy)6for kyy = 1 to nyy aa[kyy,*] = interp(at[kyy,*],x,xx)free at return aa<`-----------------------------------------------------------` Main:` We use 2-d interpolation to magnify an image by a factor9` of four (in each dimension) with minimum degradation in` image quality.` The document shows the image` - before magnification.` - after magnification with no interpolation+` - after magnification with interpolation` Image RGB service functionsfunc red(z) = floor(z/65536)(func green(z) = floor((z mod 65536)/256)func blue(z) = floor(z mod 256):func RGB(r,g,b) = 65536*round(r) + 256*round(g) + round(b)` read a bitmap filea = bitmap("lizard.bmp")` decompose to RGB components ar = red(a) ag = green(a) ab = blue(a)` interpolate each componentf = 4 ` interpolation factorna = length(a)1i = 1 to na[1] `` row coordinates of input array4j = 1 to na[2] `` column coordinates of input array` interpolated coordinatesii = 1 to na[1] len f*na[1]jj = 1 to na[2] len f*na[2] ` interpolateaar = interp2d(ar,j,i,jj,ii)aag = interp2d(ag,j,i,jj,ii)aab = interp2d(ab,j,i,jj,ii)$` fix values (RGB components must be` in the range [0.. 255])where aar > 255 aar = 255where aag > 255 aag = 255where aab > 255 aab = 255where aar < 0 aar = 0where aag < 0 aag = 0where aab < 0 aab = 0` build new imageaa = RGB(aar,aag,aab) c:\num\num1.7\samples\ ÿ ÿÿa aragabfnaijiijjaaraagaabaa  ÿˆ; > <? <@ <C D E  4 eF  4 eH  4  4BfI  4  4Bf K    < L    < M    < P X  ?Q X  ?R X  ?S Y  ?T Y  ?U Y  ?W < interp2d interp2daxyxxyynanxnynxxnyyaaatkykxxkxkyy ÿà Ž ] Ž ]b Ž ]b Ž ]b Ž ]b7  ý =    4 ] 4 ]b7  ý =     4 ,  [7  4 ,   X8 4 4  Ë  N 6!   X8 4 4  Ë  N66 # 4 , $   X8  4 4  Ë  N6 %   X8 4 4  Ë  N6 & ‡' =(>#C‰_oru…ˆ»’¢¥¨¸» redredz ÿ5  C£= greengreenz ÿ 6  D C£= bluebluez ÿ7  D£= RGBRGBrgb ÿ8  ¢B  ¢B@ ¢@= 2@1ð?Interp2dParameters dimension error0Parameters length mismatch65536ð@256p@ lizard.bmp4@255ào@