/ Aminet 35 / Aminet 35 (2000)(Schatztruhe)[!][Feb 2000].iso / Aminet / gfx / misc / gnuplot-src.lha / gnuplot-3.7.1src / gnuplot-3.7.1.lha / gnuplot-3.7.1 / demo / spline.dem

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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 23 0a 23 20 24 49 64 3a | 20 73 70 6c 20 61 72 72 |#.# $Id:| spl arr|
|00000010| 6f 77 73 20 00 f8 26 a8 | 08 00 70 2c 31 2e 32 2e |ows ..&.|..p,1.2.|
|00000020| 31 20 31 39 39 39 2f 31 | 30 2f 31 31 20 31 33 3a |1 1999/1|0/11 13:|
|00000030| 32 34 3a 30 39 20 6c 68 | 65 63 6b 69 6e 67 20 45 |24:09 lh|ecking E|
|00000040| 78 70 20 24 0a 23 0a 23 | 20 53 6f 6d 65 20 63 75 |xp $.#.#| Some cu|
|00000050| 72 76 65 20 70 6c 6f 74 | 74 69 6e 67 20 75 73 69 |rve plot|ting usi|
|00000060| 6e 67 20 63 6f 6d 6d 6f | 6e 20 63 75 62 69 63 20 |ng commo|n cubic |
|00000070| 70 6f 6c 79 6e 6f 6d 69 | 61 6c 20 62 61 73 69 73 |polynomi|al basis|
|00000080| 20 66 75 6e 63 74 69 6f | 6e 20 66 6f 72 20 63 61 | functio|n for ca|
|00000090| 67 64 2e 0a 23 0a 23 09 | 09 09 09 47 65 72 73 68 |gd..#.#.|...Gersh|
|000000a0| 6f 6e 20 45 6c 62 65 72 | 2c 20 41 75 67 2e 20 31 |on Elber|, Aug. 1|
|000000b0| 39 39 32 0a 23 0a 73 65 | 74 20 78 72 61 6e 67 20 |992.#.se|t xrang |
|000000c0| 5b 30 3a 31 5d 0a 73 65 | 74 20 67 72 69 64 0a 73 |[0:1].se|t grid.s|
|000000d0| 65 74 20 6b 65 79 20 62 | 6f 78 0a 0a 73 65 74 20 |et key b|ox..set |
|000000e0| 79 72 61 6e 67 65 5b 2d | 30 2e 32 3a 31 2e 34 5d |yrange[-|0.2:1.4]|
|000000f0| 0a 6d 30 28 78 29 20 3d | 20 31 0a 6d 31 28 78 29 |.m0(x) =| 1.m1(x)|
|00000100| 20 3d 20 78 0a 6d 32 28 | 78 29 20 3d 20 78 2a 2a | = x.m2(|x) = x**|
|00000110| 32 0a 6d 33 28 78 29 20 | 3d 20 78 2a 2a 33 0a 73 |2.m3(x) |= x**3.s|
|00000120| 65 74 20 74 69 74 6c 65 | 20 22 54 68 65 20 63 75 |et title| "The cu|
|00000130| 62 69 63 20 4d 6f 6e 6f | 6d 69 61 6c 20 62 61 73 |bic Mono|mial bas|
|00000140| 69 73 20 66 75 6e 63 74 | 69 6f 6e 73 22 0a 70 6c |is funct|ions".pl|
|00000150| 6f 74 20 6d 30 28 78 29 | 2c 20 6d 31 28 78 29 2c |ot m0(x)|, m1(x),|
|00000160| 20 6d 32 28 78 29 2c 20 | 6d 33 28 78 29 0a 70 61 | m2(x), |m3(x).pa|
|00000170| 75 73 65 20 2d 31 20 22 | 50 72 65 73 73 20 72 65 |use -1 "|Press re|
|00000180| 74 75 72 6e 20 74 6f 20 | 63 6f 6e 74 69 6e 75 65 |turn to |continue|
|00000190| 22 0a 0a 68 30 30 28 78 | 29 20 3d 20 78 2a 2a 32 |"..h00(x|) = x**2|
|000001a0| 20 2a 20 28 20 32 20 2a | 20 78 20 2d 20 33 29 20 | * ( 2 *| x - 3) |
|000001b0| 2b 20 31 0a 68 30 31 28 | 78 29 20 3d 20 2d 78 2a |+ 1.h01(|x) = -x*|
|000001c0| 2a 32 20 2a 20 28 32 20 | 2a 20 78 20 2d 20 33 29 |*2 * (2 |* x - 3)|
|000001d0| 0a 68 31 30 28 78 29 20 | 3d 20 78 20 2a 20 28 78 |.h10(x) |= x * (x|
|000001e0| 20 2d 20 31 29 2a 2a 32 | 0a 68 31 31 28 78 29 20 | - 1)**2|.h11(x) |
|000001f0| 3d 20 78 2a 2a 32 20 2a | 20 28 78 20 2d 20 31 29 |= x**2 *| (x - 1)|
|00000200| 0a 0a 73 65 74 20 74 69 | 74 6c 65 20 22 54 68 65 |..set ti|tle "The|
|00000210| 20 63 75 62 69 63 20 48 | 65 72 6d 69 74 65 20 62 | cubic H|ermite b|
|00000220| 61 73 69 73 20 66 75 6e | 63 74 69 6f 6e 73 22 0a |asis fun|ctions".|
|00000230| 70 6c 6f 74 20 68 30 30 | 28 78 29 2c 20 68 30 31 |plot h00|(x), h01|
|00000240| 28 78 29 2c 20 68 31 30 | 28 78 29 2c 20 68 31 31 |(x), h10|(x), h11|
|00000250| 28 78 29 0a 70 61 75 73 | 65 20 2d 31 20 22 50 72 |(x).paus|e -1 "Pr|
|00000260| 65 73 73 20 72 65 74 75 | 72 6e 20 74 6f 20 63 6f |ess retu|rn to co|
|00000270| 6e 74 69 6e 75 65 22 0a | 0a 62 65 7a 30 28 78 29 |ntinue".|.bez0(x)|
|00000280| 20 3d 20 28 31 20 2d 20 | 78 29 2a 2a 33 0a 62 65 | = (1 - |x)**3.be|
|00000290| 7a 31 28 78 29 20 3d 20 | 33 20 2a 20 28 31 20 2d |z1(x) = |3 * (1 -|
|000002a0| 20 78 29 2a 2a 32 20 2a | 20 78 0a 62 65 7a 32 28 | x)**2 *| x.bez2(|
|000002b0| 78 29 20 3d 20 33 20 2a | 20 28 31 20 2d 20 78 29 |x) = 3 *| (1 - x)|
|000002c0| 20 2a 20 78 2a 2a 32 0a | 62 65 7a 33 28 78 29 20 | * x**2.|bez3(x) |
|000002d0| 3d 20 78 2a 2a 33 0a 73 | 65 74 20 74 69 74 6c 65 |= x**3.s|et title|
|000002e0| 20 22 54 68 65 20 63 75 | 62 69 63 20 42 65 7a 69 | "The cu|bic Bezi|
|000002f0| 65 72 20 62 61 73 69 73 | 20 66 75 6e 63 74 69 6f |er basis| functio|
|00000300| 6e 73 22 0a 70 6c 6f 74 | 20 62 65 7a 30 28 78 29 |ns".plot| bez0(x)|
|00000310| 2c 20 62 65 7a 31 28 78 | 29 2c 20 62 65 7a 32 28 |, bez1(x|), bez2(|
|00000320| 78 29 2c 20 62 65 7a 33 | 28 78 29 0a 70 61 75 73 |x), bez3|(x).paus|
|00000330| 65 20 2d 31 20 22 50 72 | 65 73 73 20 72 65 74 75 |e -1 "Pr|ess retu|
|00000340| 72 6e 20 74 6f 20 63 6f | 6e 74 69 6e 75 65 22 0a |rn to co|ntinue".|
|00000350| 0a 62 73 70 30 28 78 29 | 20 3d 20 28 20 31 20 2d |.bsp0(x)| = ( 1 -|
|00000360| 20 33 20 2a 20 78 20 2b | 20 33 20 2a 20 78 2a 2a | 3 * x +| 3 * x**|
|00000370| 32 20 2d 20 78 2a 2a 33 | 20 29 20 2f 20 36 3b 0a |2 - x**3| ) / 6;.|
|00000380| 62 73 70 31 28 78 29 20 | 3d 20 28 20 34 20 2d 20 |bsp1(x) |= ( 4 - |
|00000390| 36 20 2a 20 78 2a 2a 32 | 20 2b 20 33 20 2a 20 78 |6 * x**2| + 3 * x|
|000003a0| 2a 2a 33 20 29 20 2f 20 | 36 3b 0a 62 73 70 32 28 |**3 ) / |6;.bsp2(|
|000003b0| 78 29 20 3d 20 28 20 31 | 20 2b 20 33 20 2a 20 78 |x) = ( 1| + 3 * x|
|000003c0| 20 2b 20 33 20 2a 20 78 | 2a 2a 32 20 2d 20 33 20 | + 3 * x|**2 - 3 |
|000003d0| 2a 20 78 2a 2a 33 20 29 | 20 2f 20 36 0a 62 73 70 |* x**3 )| / 6.bsp|
|000003e0| 33 28 78 29 20 3d 20 78 | 2a 2a 33 20 2f 20 36 0a |3(x) = x|**3 / 6.|
|000003f0| 73 65 74 20 74 69 74 6c | 65 20 22 54 68 65 20 63 |set titl|e "The c|
|00000400| 75 62 69 63 20 75 6e 69 | 66 6f 72 6d 20 42 73 70 |ubic uni|form Bsp|
|00000410| 6c 69 6e 65 20 62 61 73 | 69 73 20 66 75 6e 63 74 |line bas|is funct|
|00000420| 69 6f 6e 73 22 0a 70 6c | 6f 74 20 62 73 70 30 28 |ions".pl|ot bsp0(|
|00000430| 78 29 2c 20 62 73 70 31 | 28 78 29 2c 20 62 73 70 |x), bsp1|(x), bsp|
|00000440| 32 28 78 29 2c 20 62 73 | 70 33 28 78 29 0a 70 61 |2(x), bs|p3(x).pa|
|00000450| 75 73 65 20 2d 31 20 22 | 50 72 65 73 73 20 72 65 |use -1 "|Press re|
|00000460| 74 75 72 6e 20 74 6f 20 | 63 6f 6e 74 69 6e 75 65 |turn to |continue|
|00000470| 22 0a 0a 79 30 20 3d 20 | 31 0a 79 31 20 3d 20 30 |"..y0 = |1.y1 = 0|
|00000480| 2e 32 0a 79 32 20 3d 20 | 30 2e 38 0a 79 33 20 3d |.2.y2 = |0.8.y3 =|
|00000490| 20 30 0a 0a 78 30 20 3d | 20 30 0a 78 31 20 3d 20 | 0..x0 =| 0.x1 = |
|000004a0| 30 2e 33 33 0a 78 32 20 | 3d 20 30 2e 36 36 0a 78 |0.33.x2 |= 0.66.x|
|000004b0| 33 20 3d 20 31 0a 0a 78 | 76 30 20 3d 20 2d 30 2e |3 = 1..x|v0 = -0.|
|000004c0| 33 0a 79 76 30 20 3d 20 | 30 2e 35 0a 78 76 31 20 |3.yv0 = |0.5.xv1 |
|000004d0| 3d 20 2d 30 2e 34 0a 79 | 76 31 20 3d 20 30 2e 32 |= -0.4.y|v1 = 0.2|
|000004e0| 0a 0a 73 65 74 20 61 72 | 72 6f 77 20 66 72 6f 6d |..set ar|row from|
|000004f0| 20 78 30 2c 79 30 20 74 | 6f 20 78 31 2c 79 31 20 | x0,y0 t|o x1,y1 |
|00000500| 6e 6f 68 65 61 64 0a 73 | 65 74 20 61 72 72 6f 77 |nohead.s|et arrow|
|00000510| 20 66 72 6f 6d 20 78 31 | 2c 79 31 20 74 6f 20 78 | from x1|,y1 to x|
|00000520| 32 2c 79 32 20 6e 6f 68 | 65 61 64 0a 73 65 74 20 |2,y2 noh|ead.set |
|00000530| 61 72 72 6f 77 20 66 72 | 6f 6d 20 78 32 2c 79 32 |arrow fr|om x2,y2|
|00000540| 20 74 6f 20 78 33 2c 79 | 33 20 6e 6f 68 65 61 64 | to x3,y|3 nohead|
|00000550| 0a 0a 63 75 62 5f 62 65 | 7a 69 65 72 5f 78 28 74 |..cub_be|zier_x(t|
|00000560| 29 20 3d 20 62 65 7a 30 | 28 74 29 20 2a 20 78 30 |) = bez0|(t) * x0|
|00000570| 20 2b 20 62 65 7a 31 28 | 74 29 20 2a 20 78 31 20 | + bez1(|t) * x1 |
|00000580| 2b 20 62 65 7a 32 28 74 | 29 20 2a 20 78 32 20 2b |+ bez2(t|) * x2 +|
|00000590| 20 62 65 7a 33 28 74 29 | 20 2a 20 78 33 0a 63 75 | bez3(t)| * x3.cu|
|000005a0| 62 5f 62 65 7a 69 65 72 | 5f 79 28 74 29 20 3d 20 |b_bezier|_y(t) = |
|000005b0| 62 65 7a 30 28 74 29 20 | 2a 20 79 30 20 2b 20 62 |bez0(t) |* y0 + b|
|000005c0| 65 7a 31 28 74 29 20 2a | 20 79 31 20 2b 20 62 65 |ez1(t) *| y1 + be|
|000005d0| 7a 32 28 74 29 20 2a 20 | 79 32 20 2b 20 62 65 7a |z2(t) * |y2 + bez|
|000005e0| 33 28 74 29 20 2a 20 79 | 33 0a 63 75 62 5f 62 73 |3(t) * y|3.cub_bs|
|000005f0| 70 6c 69 6e 5f 78 28 74 | 29 20 3d 20 62 73 70 30 |plin_x(t|) = bsp0|
|00000600| 28 74 29 20 2a 20 78 30 | 20 2b 20 62 73 70 31 28 |(t) * x0| + bsp1(|
|00000610| 74 29 20 2a 20 78 31 20 | 2b 20 62 73 70 32 28 74 |t) * x1 |+ bsp2(t|
|00000620| 29 20 2a 20 78 32 20 2b | 20 62 73 70 33 28 74 29 |) * x2 +| bsp3(t)|
|00000630| 20 2a 20 78 33 0a 63 75 | 62 5f 62 73 70 6c 69 6e | * x3.cu|b_bsplin|
|00000640| 5f 79 28 74 29 20 3d 20 | 62 73 70 30 28 74 29 20 |_y(t) = |bsp0(t) |
|00000650| 2a 20 79 30 20 2b 20 62 | 73 70 31 28 74 29 20 2a |* y0 + b|sp1(t) *|
|00000660| 20 79 31 20 2b 20 62 73 | 70 32 28 74 29 20 2a 20 | y1 + bs|p2(t) * |
|00000670| 79 32 20 2b 20 62 73 70 | 33 28 74 29 20 2a 20 79 |y2 + bsp|3(t) * y|
|00000680| 33 0a 0a 73 65 74 20 70 | 61 72 61 6d 65 74 72 69 |3..set p|arametri|
|00000690| 63 0a 73 65 74 20 74 72 | 61 6e 67 65 20 5b 30 3a |c.set tr|ange [0:|
|000006a0| 31 5d 0a 73 65 74 20 74 | 69 74 6c 65 20 22 54 68 |1].set t|itle "Th|
|000006b0| 65 20 63 75 62 69 63 20 | 42 65 7a 69 65 72 2f 42 |e cubic |Bezier/B|
|000006c0| 73 70 6c 69 6e 65 20 62 | 61 73 69 73 20 66 75 6e |spline b|asis fun|
|000006d0| 63 74 69 6f 6e 73 20 69 | 6e 20 75 73 65 22 0a 70 |ctions i|n use".p|
|000006e0| 6c 6f 74 20 63 75 62 5f | 62 65 7a 69 65 72 5f 78 |lot cub_|bezier_x|
|000006f0| 28 74 29 2c 20 63 75 62 | 5f 62 65 7a 69 65 72 5f |(t), cub|_bezier_|
|00000700| 79 28 74 29 20 77 69 74 | 68 20 6c 69 6e 65 73 20 |y(t) wit|h lines |
|00000710| 32 2c 5c 0a 20 20 20 20 | 20 63 75 62 5f 62 73 70 |2,\.    | cub_bsp|
|00000720| 6c 69 6e 5f 78 28 74 29 | 2c 20 63 75 62 5f 62 73 |lin_x(t)|, cub_bs|
|00000730| 70 6c 69 6e 5f 79 28 74 | 29 20 77 69 74 68 20 6c |plin_y(t|) with l|
|00000740| 69 6e 65 73 20 33 0a 70 | 61 75 73 65 20 2d 31 20 |ines 3.p|ause -1 |
|00000750| 22 50 72 65 73 73 20 72 | 65 74 75 72 6e 20 74 6f |"Press r|eturn to|
|00000760| 20 63 6f 6e 74 69 6e 75 | 65 22 0a 0a 73 65 74 20 | continu|e"..set |
|00000770| 6e 6f 61 72 72 6f 77 0a | 23 0a 23 20 4e 6f 74 65 |noarrow.|#.# Note|
|00000780| 20 74 68 65 20 61 72 72 | 6f 77 73 20 68 65 72 65 | the arr|ows here|
|00000790| 2c 20 73 63 61 6c 65 64 | 20 62 79 20 31 2f 33 20 |, scaled| by 1/3 |
|000007a0| 73 6f 20 74 68 65 79 20 | 77 69 6c 6c 20 66 69 74 |so they |will fit|
|000007b0| 20 69 6e 74 6f 20 70 6c | 6f 74 74 69 6e 67 20 61 | into pl|otting a|
|000007c0| 72 65 61 0a 23 0a 73 65 | 74 20 61 72 72 6f 77 20 |rea.#.se|t arrow |
|000007d0| 66 72 6f 6d 20 78 31 2c | 79 31 20 74 6f 20 78 31 |from x1,|y1 to x1|
|000007e0| 2b 78 76 30 2f 33 2c 79 | 31 2b 79 76 30 2f 33 0a |+xv0/3,y|1+yv0/3.|
|000007f0| 73 65 74 20 61 72 72 6f | 77 20 66 72 6f 6d 20 78 |set arro|w from x|
|00000800| 32 2c 79 32 20 74 6f 20 | 78 32 2b 78 76 31 2f 33 |2,y2 to |x2+xv1/3|
|00000810| 2c 79 32 2b 79 76 31 2f | 33 0a 73 65 74 20 61 72 |,y2+yv1/|3.set ar|
|00000820| 72 6f 77 20 66 72 6f 6d | 20 78 31 2c 79 31 20 74 |row from| x1,y1 t|
|00000830| 6f 20 78 31 2b 78 76 30 | 2c 79 31 2b 79 76 30 0a |o x1+xv0|,y1+yv0.|
|00000840| 73 65 74 20 61 72 72 6f | 77 20 66 72 6f 6d 20 78 |set arro|w from x|
|00000850| 32 2c 79 32 20 74 6f 20 | 78 32 2b 78 76 31 2c 79 |2,y2 to |x2+xv1,y|
|00000860| 32 2b 79 76 31 0a 0a 63 | 75 62 5f 68 65 72 6d 69 |2+yv1..c|ub_hermi|
|00000870| 74 5f 78 31 28 74 29 20 | 3d 20 68 30 30 28 74 29 |t_x1(t) |= h00(t)|
|00000880| 20 2a 20 78 31 20 2b 20 | 68 30 31 28 74 29 20 2a | * x1 + |h01(t) *|
|00000890| 20 78 32 20 2b 20 68 31 | 30 28 74 29 20 2a 20 78 | x2 + h1|0(t) * x|
|000008a0| 76 30 20 2b 20 68 31 31 | 28 74 29 20 2a 20 78 76 |v0 + h11|(t) * xv|
|000008b0| 31 0a 63 75 62 5f 68 65 | 72 6d 69 74 5f 79 31 28 |1.cub_he|rmit_y1(|
|000008c0| 74 29 20 3d 20 68 30 30 | 28 74 29 20 2a 20 79 31 |t) = h00|(t) * y1|
|000008d0| 20 2b 20 68 30 31 28 74 | 29 20 2a 20 79 32 20 2b | + h01(t|) * y2 +|
|000008e0| 20 68 31 30 28 74 29 20 | 2a 20 79 76 30 20 2b 20 | h10(t) |* yv0 + |
|000008f0| 68 31 31 28 74 29 20 2a | 20 79 76 31 0a 63 75 62 |h11(t) *| yv1.cub|
|00000900| 5f 68 65 72 6d 69 74 5f | 78 32 28 74 29 20 3d 20 |_hermit_|x2(t) = |
|00000910| 68 30 30 28 74 29 20 2a | 20 78 31 20 2b 20 68 30 |h00(t) *| x1 + h0|
|00000920| 31 28 74 29 20 2a 20 78 | 32 20 2b 20 68 31 30 28 |1(t) * x|2 + h10(|
|00000930| 74 29 20 2a 20 78 76 30 | 2a 33 20 2b 20 68 31 31 |t) * xv0|*3 + h11|
|00000940| 28 74 29 20 2a 20 78 76 | 31 2a 33 0a 63 75 62 5f |(t) * xv|1*3.cub_|
|00000950| 68 65 72 6d 69 74 5f 79 | 32 28 74 29 20 3d 20 68 |hermit_y|2(t) = h|
|00000960| 30 30 28 74 29 20 2a 20 | 79 31 20 2b 20 68 30 31 |00(t) * |y1 + h01|
|00000970| 28 74 29 20 2a 20 79 32 | 20 2b 20 68 31 30 28 74 |(t) * y2| + h10(t|
|00000980| 29 20 2a 20 79 76 30 2a | 33 20 2b 20 68 31 31 28 |) * yv0*|3 + h11(|
|00000990| 74 29 20 2a 20 79 76 31 | 2a 33 0a 73 65 74 20 74 |t) * yv1|*3.set t|
|000009a0| 69 74 6c 65 20 22 54 68 | 65 20 63 75 62 69 63 20 |itle "Th|e cubic |
|000009b0| 48 65 72 6d 69 74 65 20 | 62 61 73 69 73 20 66 75 |Hermite |basis fu|
|000009c0| 6e 63 74 69 6f 6e 73 20 | 69 6e 20 75 73 65 22 0a |nctions |in use".|
|000009d0| 70 6c 6f 74 20 63 75 62 | 5f 68 65 72 6d 69 74 5f |plot cub|_hermit_|
|000009e0| 78 31 28 74 29 2c 20 63 | 75 62 5f 68 65 72 6d 69 |x1(t), c|ub_hermi|
|000009f0| 74 5f 79 31 28 74 29 20 | 77 69 74 68 20 6c 69 6e |t_y1(t) |with lin|
|00000a00| 65 73 20 32 2c 5c 0a 20 | 20 20 20 20 63 75 62 5f |es 2,\. |    cub_|
|00000a10| 68 65 72 6d 69 74 5f 78 | 32 28 74 29 2c 20 63 75 |hermit_x|2(t), cu|
|00000a20| 62 5f 68 65 72 6d 69 74 | 5f 79 32 28 74 29 20 77 |b_hermit|_y2(t) w|
|00000a30| 69 74 68 20 6c 69 6e 65 | 73 20 33 0a 70 61 75 73 |ith line|s 3.paus|
|00000a40| 65 20 2d 31 20 22 50 72 | 65 73 73 20 72 65 74 75 |e -1 "Pr|ess retu|
|00000a50| 72 6e 20 74 6f 20 63 6f | 6e 74 69 6e 75 65 22 0a |rn to co|ntinue".|
|00000a60| 72 65 73 65 74 0a       |                         |reset.  |        |
+--------+-------------------------+-------------------------+--------+--------+