hermite surface
- To: mathgroup at smc.vnet.net
- Subject: [mg24944] hermite surface
- From: "J. Seng Ja" <csb998306 at ait.ac.th>
- Date: Thu, 24 Aug 2000 05:08:16 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I try to generate or ploting the hermite surface with Bezier boundary curves by using mathematica. But cannot success. I need help for the generating hermite surface and gregory surfaces by mathemaica.Here is the attachment that I try to generate. ahngaij (*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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. 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info at 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[ 10147, 259]*) (*NotebookOutlinePosition[ 10795, 282]*) (* CellTagsIndexPosition[ 10751, 278]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ \(A = {{1 - 3 t^2 + 2 t^3}, \n\ \ \ \ \ \ \ \ \ \ \ {3 t^2 - 2 t^3}, \n\ \ \ \ \ \ \ \ \ \ \ {t - 2 t^2 + t^3}, \n \ \ \ \ \ \ \ \ \ \ \ {\(-t^2\) + t^3}}\n\), \(B = {{1 - 3 u^2 + 2 u^3}, \n\ \ \ \ \ \ \ \ \ \ \ {3 u^2 - 2 u^3}, \n\ \ \ \ \ \ \ \ \ \ \ {u - 2 u^2 + u^3}, \n \ \ \ \ \ \ \ \ \ \ \ {\(-u^2\) + u^3}}\n\), \(Bernstein[n_]\ = \(\(n!\)/\(i!\)\)/\(\((n - i)\)!\)\ u^\((i)\) \((1 - u)\)^\((n - i)\)\n \), \(Bezier[n_, u_]\ = Sum[Bernstein[n, i]\ p[\([i + 1]\)], {i, 0, n}]\n\), \(Expand[Bz[3, 0]]\n\), \(DerBezier[n_, u_] = n\ \ Sum[Bezier[n - 1, i, u] \((p[\([i + 2]\)] - p[\([i + 1]\)])\), \n \t{i, 0, n - 1}]\t\n\), \(H[3 _, u_] = {Bezier[3, 0], Bezier[3, 1], DerBezier[3, 0], DerBezier[3, 1]}\n\), \(HermiteCurve = H[3 _, u_].B\n\n\), \(ParametricPlot3D[HermiteCurve, {u, 0, 1}, AspectRatio -> Automatic\n \t\t]\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\)}], "Input"], Cell[BoxData[ \({{1 - 3\ t\^2 + 2\ t\^3}, {3\ t\^2 - 2\ t\^3}, {t - 2\ t\^2 + t\^3}, { \(-t\^2\) + t\^3}}\)], "Output"], Cell[BoxData[ \({{1 - 3\ u\^2 + 2\ u\^3}, {3\ u\^2 - 2\ u\^3}, {u - 2\ u\^2 + u\^3}, { \(-u\^2\) + u\^3}}\)], "Output"], Cell[BoxData[ \(\(\((1 - u)\)\^\(\(-i\) + n\)\ u\^i\ \(n!\)\)\/\(\(i!\)\ \(\((\(-i\) + n)\)!\)\)\)], "Output"], Cell[BoxData[ \(Part::"pspec" \( : \ \) "Part specification \!\(1 + i\) is neither an integer nor a list of \ integers."\)], "Message"], Cell[BoxData[ \(\[Sum]\+\(i = 0\)\%n Bernstein[n, i]\ p\[LeftDoubleBracket]i + 1\[RightDoubleBracket]\)], "Output"], Cell[BoxData[ \(Part::"partd" \( : \ \) "Part specification \!\(p \\[LeftDoubleBracket] 1 \ \\[RightDoubleBracket]\) is longer than depth of object."\)], "Message"], Cell[BoxData[ \(Part::"partd" \( : \ \) "Part specification \!\(p \\[LeftDoubleBracket] 2 \ \\[RightDoubleBracket]\) is longer than depth of object."\)], "Message"], Cell[BoxData[ \(Part::"partd" \( : \ \) "Part specification \!\(p \\[LeftDoubleBracket] 3 \ \\[RightDoubleBracket]\) is longer than depth of object."\)], "Message"], Cell[BoxData[ \(General::"stop" \( : \ \) "Further output of \!\(Part :: \"partd\"\) will be suppressed during \ this calculation."\)], "Message"], Cell[BoxData[ \(p\[LeftDoubleBracket]1\[RightDoubleBracket] - 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