(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 22953, 619]*) (*NotebookOutlinePosition[ 23798, 646]*) (* CellTagsIndexPosition[ 23754, 642]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[{ \( (*\ Hermite\ curve\ *) \[IndentingNewLine]\(P1 = {0, 0};\)\), "\[IndentingNewLine]", \(\(P2 = {3, 0};\)\), "\[IndentingNewLine]", \(\(PP1 = {1, 1};\)\), "\[IndentingNewLine]", \(PP2 = {2, 2}; M\ = \ {{2, \(-2\), 1, 1}, {\(-3\), 3, \(-2\), \(-1\)}, {0, 0, 1, 0}, {1, 0, 0, 0}};\), "\[IndentingNewLine]", \(Clear[u]; Clear[U]; U = {u^3, u^2, u, 1};\), "\[IndentingNewLine]", \(\(B\ = \ {P1, P2, PP1, PP2};\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[M]\)], "Input"], Cell[BoxData[ FormBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", \(-2\), "1", "1"}, {\(-3\), "3", \(-2\), \(-1\)}, {"0", "0", "1", "0"}, {"1", "0", "0", "0"} }, ColumnAlignments->{Decimal}], "\[NoBreak]", ")"}], (MatrixForm[ #]&)], TraditionalForm]], "Output"] }, Open ]], Cell[BoxData[ \(For[u = 0; plist = {}, u \[LessEqual] 1.0, u = u + 0.05, plist = Append[plist, U . M . B]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(plist\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0"}, {"0.062125`", "0.040374999999999994`"}, {"0.14700000000000002`", "0.063`"}, {"0.252375`", "0.070125`"}, {"0.37600000000000006`", "0.06399999999999999`"}, {"0.515625`", "0.046875`"}, {"0.669`", "0.02099999999999999`"}, {"0.8338749999999998`", \(-0.011374999999999996`\)}, {"1.0080000000000002`", \(-0.04799999999999996`\)}, {"1.1891249999999998`", \(-0.08662499999999998`\)}, {"1.3749999999999996`", \(-0.12499999999999997`\)}, {"1.5633749999999997`", \(-0.160875`\)}, {"1.7519999999999996`", \(-0.192`\)}, {"1.938625`", \(-0.216125`\)}, {"2.121`", \(-0.2310000000000001`\)}, {"2.296875000000001`", \(-0.2343750000000001`\)}, {"2.4640000000000004`", \(-0.2240000000000001`\)}, {"2.6201250000000003`", \(-0.19762499999999983`\)}, {"2.763000000000001`", \(-0.1529999999999997`\)}, {"2.8903750000000006`", \(-0.08787499999999948`\)}, {"3.0000000000000004`", "4.440892098500626`*^-16"} }, ColumnAlignments->{Decimal}], "\[NoBreak]", ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Graphics[{PointSize[0.025], Thickness[0.01], Line[plist], Point[P1], Point[P2], Line[{P1, P1 + PP1}], Line[{P2, P2 + PP2}]}]\)], "Input"], Cell[BoxData[ FormBox[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[%, Axes \[Rule] Automatic]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.190476 0.215139 0.85514 [ [.21429 .20264 -3 -9 ] [.21429 .20264 3 0 ] [.40476 .20264 -3 -9 ] [.40476 .20264 3 0 ] [.59524 .20264 -3 -9 ] [.59524 .20264 3 0 ] [.78571 .20264 -3 -9 ] [.78571 .20264 3 0 ] [.97619 .20264 -3 -9 ] [.97619 .20264 3 0 ] [.01131 .04411 -24 -4.5 ] [.01131 .04411 0 4.5 ] [.01131 .12962 -24 -4.5 ] [.01131 .12962 0 4.5 ] [.01131 .30065 -18 -4.5 ] [.01131 .30065 0 4.5 ] [.01131 .38617 -18 -4.5 ] [.01131 .38617 0 4.5 ] [.01131 .47168 -18 -4.5 ] [.01131 .47168 0 4.5 ] [.01131 .55719 -18 -4.5 ] [.01131 .55719 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .21514 m .21429 .22139 L s [(1)] .21429 .20264 0 1 Mshowa .40476 .21514 m .40476 .22139 L s [(2)] .40476 .20264 0 1 Mshowa .59524 .21514 m .59524 .22139 L s [(3)] .59524 .20264 0 1 Mshowa .78571 .21514 m .78571 .22139 L s [(4)] .78571 .20264 0 1 Mshowa .97619 .21514 m .97619 .22139 L s [(5)] .97619 .20264 0 1 Mshowa .125 Mabswid .0619 .21514 m .0619 .21889 L s .1 .21514 m .1 .21889 L s .1381 .21514 m .1381 .21889 L s .17619 .21514 m .17619 .21889 L s .25238 .21514 m .25238 .21889 L s .29048 .21514 m .29048 .21889 L s .32857 .21514 m .32857 .21889 L s .36667 .21514 m .36667 .21889 L s .44286 .21514 m .44286 .21889 L s .48095 .21514 m .48095 .21889 L s .51905 .21514 m .51905 .21889 L s .55714 .21514 m .55714 .21889 L s .63333 .21514 m .63333 .21889 L s .67143 .21514 m .67143 .21889 L s .70952 .21514 m .70952 .21889 L s .74762 .21514 m .74762 .21889 L s .82381 .21514 m .82381 .21889 L s .8619 .21514 m .8619 .21889 L s .9 .21514 m .9 .21889 L s .9381 .21514 m .9381 .21889 L s .25 Mabswid 0 .21514 m 1 .21514 L s .02381 .04411 m .03006 .04411 L s [(-0.2)] .01131 .04411 1 0 Mshowa .02381 .12962 m .03006 .12962 L s [(-0.1)] .01131 .12962 1 0 Mshowa .02381 .30065 m .03006 .30065 L s [(0.1)] .01131 .30065 1 0 Mshowa .02381 .38617 m .03006 .38617 L s [(0.2)] .01131 .38617 1 0 Mshowa .02381 .47168 m .03006 .47168 L s [(0.3)] .01131 .47168 1 0 Mshowa .02381 .55719 m .03006 .55719 L s [(0.4)] .01131 .55719 1 0 Mshowa .125 Mabswid .02381 .06121 m .02756 .06121 L s .02381 .07832 m .02756 .07832 L s .02381 .09542 m .02756 .09542 L s .02381 .11252 m .02756 .11252 L s .02381 .14673 m .02756 .14673 L s .02381 .16383 m .02756 .16383 L s .02381 .18093 m .02756 .18093 L s .02381 .19804 m .02756 .19804 L s .02381 .23224 m .02756 .23224 L s .02381 .24934 m .02756 .24934 L s .02381 .26645 m .02756 .26645 L s .02381 .28355 m .02756 .28355 L s .02381 .31776 m .02756 .31776 L s .02381 .33486 m .02756 .33486 L s .02381 .35196 m .02756 .35196 L s .02381 .36906 m .02756 .36906 L s .02381 .40327 m .02756 .40327 L s .02381 .42037 m .02756 .42037 L s .02381 .43748 m .02756 .43748 L s .02381 .45458 m .02756 .45458 L s .02381 .48878 m .02756 .48878 L s .02381 .50589 m .02756 .50589 L s .02381 .52299 m .02756 .52299 L s .02381 .54009 m .02756 .54009 L s .02381 .02701 m .02756 .02701 L s .02381 .0099 m .02756 .0099 L s .02381 .5743 m .02756 .5743 L s .02381 .5914 m .02756 .5914 L s .02381 .6085 m .02756 .6085 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .01 w .02381 .21514 m .03564 .24966 L .05181 .26901 L .07188 .27511 L .09543 .26987 L .12202 .25522 L .15124 .2331 L .18264 .20541 L .21581 .17409 L .25031 .14106 L .28571 .10825 L .3216 .07757 L .35752 .05095 L .39307 .03032 L .42781 .0176 L .46131 .01472 L .49314 .02359 L .52288 .04614 L .5501 .0843 L .57436 .13999 L .59524 .21514 L s .025 w .02381 .21514 Mdot .59524 .21514 Mdot .01 w .02381 .21514 m 0 0 rlineto s .02381 .21514 m .11355 .61803 L s .59524 .21514 m 0 0 rlineto s .59524 .21514 m .68498 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`@00000P@3oool2000006T0oooo000K0?ooo`@00000 00<0oooo0000000000000`0000090?ooo`@00000P`3oool2000006T0oooo000K0?ooo`040000003o ool0000000000080oooo1`0000020?ooo`L00000Q03oool2000006T0oooo000K0?ooo`040000003o ool00000000000D0oooo2`0000260?ooo`800000J@3oool001/0oooo00<000000?ooo`0000000P00 00070?ooo`@00000RP3oool3000006P0oooo000K0?ooo`80000000<0oooo000000000000UP3oool2 000006P0oooo000K0?ooo`030000003oool0oooo00800000UP3oool2000006P0oooo00080?ooo`80 0000103oool00`000000oooo0?ooo`020?ooo`<000001@3oool00`000000oooo0?ooo`02000009H0 oooo0P00001X0?ooo`001`3oool010000000oooo0?ooo`0000090?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool00`00002E0?ooo`<00000I`3oool000L0oooo00@000000?ooo`3oool0 00002@3oool00`000000oooo0?ooo`040?ooo`040000003oool0oooo0?ooo`800000UP3oool20000 06L0oooo00070?ooo`040000003oool0oooo000000T0oooo00<000000?ooo`3oool0103oool20000 0080oooo0P00002F0?ooo`800000I`3oool000L0oooo00@000000?ooo`3oool000002@3oool00`00 0000oooo0?ooo`040?ooo`040000003oool0oooo0?ooo`800000UP3oool2000006L0oooo00070?oo o`040000003oool0oooo000000P0oooo0P0000060?ooo`040000003oool0oooo0?ooo`800000UP3o ool2000006L0oooo00080?ooo`8000002P3oool00`000000oooo0?ooo`040?ooo`040000003oool0 oooo0?ooo`<00000U@3oool3000006H0oooo000K0?ooo`8000000`3oool2000009H0oooo0P00001V 0?ooo`006`3oool00`000000oooo0?ooo`020?ooo`800000UP3oool2000006H0oooo000K0?ooo`03 0000003oool0oooo0080oooo0P00002F0?ooo`800000IP3oool001/0oooo00<000000?ooo`3oool0 0P3oool3000009D0oooo0`00001U0?ooo`006`3oool00`000000oooo0?ooo`030?ooo`800000UP3o ool2000006D0oooo000K0?ooo`800000103oool2000009H0oooo0P00001U0?ooo`006`3oool00`00 0000oooo0?ooo`030?ooo`800000UP3oool2000006D0oooo000K0?ooo`030000003oool0oooo00<0 oooo0`00002E0?ooo`<00000I03oool001/0oooo00<000000?ooo`3oool0103oool2000009H0oooo 0P00001T0?ooo`006`3oool2000000D0oooo0P00002F0?ooo`800000I03oool001/0oooo00<00000 0?ooo`3oool0103oool2000009H0oooo0P00001T0?ooo`006`3oool00`000000oooo0?ooo`040?oo o`800000UP3oool2000006@0oooo000K0?ooo`030000003oool0oooo00@0oooo0`00002E0?ooo`<0 0000H`3oool001/0oooo00<000000?ooo`3oool01@3oool2000009H0oooo0P00001S0?ooo`006`3o ool2000000H0oooo0P00002F0?ooo`800000H`3oool001/0oooo00<000000?ooo`3oool01@3oool2 000009H0oooo0P00001S0?ooo`00203oool2000000@0oooo00@000000?ooo`3oool0oooo1@000004 0?ooo`030000003oool0oooo00D0oooo0`00002E0?ooo`<00000HP3oool000L0oooo00@000000?oo o`3oool00000203oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo00H0oooo0P00 002F0?ooo`800000HP3oool000L0oooo00@000000?ooo`3oool000002@3oool00`000000oooo0?oo o`040?ooo`030000003oool0oooo00H0oooo0P00002F0?ooo`800000HP3oool000L0oooo00@00000 0?ooo`3oool000002P3oool00`000000oooo0?ooo`030?ooo`8000001`3oool2000009H0oooo0P00 001R0?ooo`001`3oool010000000oooo0?ooo`0000070?ooo`050000003oool0oooo0?ooo`000000 103oool00`000000oooo0?ooo`060?ooo`800000UP3oool200000680oooo00070?ooo`040000003o ool0oooo000000L0oooo00D000000?ooo`3oool0oooo000000040?ooo`030000003oool0oooo00H0 oooo0`00002E0?ooo`<00000H@3oool000P0oooo0P0000090?ooo`<000001@3oool00`000000oooo 0?ooo`070?ooo`800000UP3oool200000640oooo000K0?ooo`800000203oool2000009H0oooo0P00 001Q0?ooo`006`3oool00`000000oooo0?ooo`070?ooo`800000UP3oool200000640oooo000K0?oo o`030000003oool0oooo00L0oooo0`00002E0?ooo`<00000H03oool001/0oooo00<000000?ooo`3o ool0203oool2000009H0oooo0P00001P0?ooo`006`3oool00`000000oooo0?ooo`080?ooo`800000 UP3oool200000600oooo000K0?ooo`8000002@3oool2000009H0oooo0P00001P0?ooo`006`3oool0 0`000000oooo0?ooo`080?ooo`800000UP3oool200000600oooo000K0?ooo`030000003oool0oooo 00P0oooo0`00002E0?ooo`<00000G`3oool001/0oooo00<000000?ooo`3oool02@3oool2000009H0 oooo0P00001O0?ooo`006`3oool2000000X0oooo0P00002F0?ooo`800000G`3oool001/0oooo00<0 00000?ooo`3oool02@3oool2000009H0oooo0P00001O0?ooo`006`3oool00`000000oooo0?ooo`09 0?ooo`<00000U@3oool3000005h0oooo000K0?ooo`030000003oool0oooo00X0oooo0P00002F0?oo o`800000GP3oool001/0oooo00<000000?ooo`3oool02P3oool2000009H0oooo0P00001N0?ooo`00 6`3oool2000000/0oooo0P00002F0?ooo`800000GP3oool001/0oooo00<000000?ooo`3oool02P3o ool2000009H0oooo0P00001N0?ooo`00203oool2000000@0oooo00<000000?ooo`3oool00P3oool3 000000D0oooo00<000000?ooo`3oool02P3oool3000009D0oooo0`00001M0?ooo`001`3oool01000 0000oooo0?ooo`0000070?ooo`050000003oool0oooo0?ooo`000000103oool00`000000oooo0?oo o`0;0?ooo`800000UP3oool2000005d0oooo00070?ooo`040000003oool0oooo000000/0oooo00<0 00000?ooo`3oool00P3oool2000000`0oooo0P00002F0?ooo`800000G@3oool000L0oooo00@00000 0?ooo`3oool000002@3oool2000000D0oooo00<000000?ooo`3oool02`3oool2000009H0oooo0P00 001M0?ooo`001`3oool010000000oooo0?ooo`00000;0?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool02`3oool3000009D0oooo0`00001L0?ooo`001`3oool010000000oooo0?ooo`00 00070?ooo`050000003oool0oooo0?ooo`000000103oool00`000000oooo0?ooo`0<0?ooo`800000 UP3oool2000005`0oooo00080?ooo`8000002@3oool3000000D0oooo00<000000?ooo`3oool0303o ool2000009H0oooo0P00001L0?ooo`006`3oool2000000d0oooo0P00002F0?ooo`800000G03oool0 01/0oooo00<000000?ooo`3oool0303oool2000009H0oooo0P00001L0?ooo`006`3oool00`000000 oooo0?ooo`0<0?ooo`<00000U@3oool3000005/0oooo000K0?ooo`030000003oool0oooo00d0oooo 0P00002F0?ooo`800000F`3oool001/0oooo0P00000>0?ooo`800000UP3oool2000005/0oooo000K 0?ooo`030000003oool0oooo00d0oooo0P00002F0?ooo`800000F`3oool001/0oooo00<000000?oo o`3oool03@3oool3000009D0oooo0`00001J0?ooo`006`3oool00`000000oooo0?ooo`0>0?ooo`80 0000UP3oool2000005X0oooo000K0?ooo`030000003oool0oooo00h0oooo0P00002F0?ooo`800000 FP3oool001/0oooo0P00000?0?ooo`800000UP3oool2000005X0oooo000K0?ooo`030000003oool0 oooo00h0oooo0`00002E0?ooo`<00000F@3oool001/0oooo00<000000?ooo`3oool03`3oool20000 09H0oooo0P00001I0?ooo`006`3oool00`000000oooo0?ooo`0?0?ooo`800000UP3oool2000005T0 oooo000K0?ooo`800000403oool2000009H0oooo0P00001I0?ooo`006`3oool00`000000oooo0?oo o`0?0?ooo`800000UP3oool2000005T0oooo000K0?ooo`030000003oool0oooo00l0oooo0`00002E 0?ooo`<00000F03oool000P0oooo0P0000040?ooo`030000003oool0oooo00<0oooo0`0000040?oo o`030000003oool0oooo0100oooo0P00002F0?ooo`800000F03oool000L0oooo00@000000?ooo`3o ool000002P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0100oooo0P00002F0?oo o`800000F03oool000L0oooo00@000000?ooo`3oool000001`3oool5000000@0oooo0P00000A0?oo o`800000UP3oool2000005P0oooo00070?ooo`040000003oool0oooo000000L0oooo00@000000?oo o`3oool000001@3oool00`000000oooo0?ooo`0@0?ooo`<00000U@3oool3000005L0oooo00070?oo o`040000003oool0oooo000000P0oooo00<000000?ooo`0000001@3oool00`000000oooo0?ooo`0A 0?ooo`800000UP3oool2000005L0oooo00070?ooo`040000003oool0oooo000000T0oooo0P000005 0?ooo`030000003oool0oooo0140oooo0P00002F0?ooo`800000E`3oool000P0oooo0P00000;0?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool04@3oool2000009H0oooo0P00001G0?oo o`006`3oool200000180oooo0P00002F0?ooo`800000E`3oool001/0oooo00<000000?ooo`3oool0 4@3oool3000009D0oooo0`00001F0?ooo`006`3oool00`000000oooo0?ooo`0B0?ooo`800000UP3o ool2000005H0oooo000K0?ooo`030000003oool0oooo0180oooo0P00002F0?ooo`800000EP3oool0 01/0oooo0P00000C0?ooo`800000UP3oool2000005H0oooo000K0?ooo`030000003oool0oooo0180 oooo0`00002E0?ooo`<00000E@3oool001/0oooo00<000000?ooo`3oool04`3oool2000009H0oooo 0P00001E0?ooo`006`3oool00`000000oooo0?ooo`0C0?ooo`800000UP3oool2000005D0oooo000K 0?ooo`030000003oool0oooo01<0oooo0P00002F0?ooo`800000E@3oool001/0oooo0P00000D0?oo o`800000UP3oool2000005D0oooo000K0?ooo`030000003oool0oooo01<0oooo0`00002E0?ooo`<0 0000E03oool001/0oooo00<000000?ooo`3oool0503oool2000009H0oooo0P00001D0?ooo`00"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.539323, -0.279142, \ 0.0197364, 0.00439614}}], Cell[BoxData[ FormBox[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], TraditionalForm]], "Output"] }, Open ]] }, FrontEndVersion->"4.0 for Macintosh", ScreenRectangle->{{0, 1024}, {0, 748}}, WindowSize->{520, 626}, WindowMargins->{{Automatic, -8}, {Automatic, 25}}, MacintoshSystemPageSetup->"\<\ 02P0001804P000000^L2D_ogooL33`9K8085:0?l0000005X0FP000003X<;VP5d 038;VTRX04/00@4100000BL?00400@000000000000000000000000000040I0<0 00000000000@XP404@000000000eDflP\>" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1717, 49, 495, 9, 155, "Input"], Cell[CellGroupData[{ Cell[2237, 62, 46, 1, 27, "Input"], Cell[2286, 65, 377, 10, 85, "Output"] }, Open ]], Cell[2678, 78, 130, 2, 43, "Input"], Cell[CellGroupData[{ Cell[2833, 84, 38, 1, 27, "Input"], Cell[2874, 87, 1326, 26, 347, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4237, 118, 166, 2, 59, "Input"], Cell[4406, 122, 167, 4, 26, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4610, 131, 64, 1, 27, "Input"], Cell[4677, 134, 18090, 476, 186, 4124, 299, "GraphicsData", "PostScript", \ "Graphics"], Cell[22770, 612, 167, 4, 26, "Output"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)