1 | \documentclass{article} |
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2 | % |
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3 | % surfex_doc.tex |
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4 | % |
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5 | % {\sc surfex} --- A Short Documentation |
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6 | % |
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7 | |
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8 | \usepackage[latin1]{inputenc} |
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9 | \usepackage{latexsym} |
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10 | \usepackage{amsfonts} |
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11 | \usepackage{color} |
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12 | \usepackage{dsfont} |
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13 | \usepackage{varioref} |
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14 | \usepackage{epsfig} |
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15 | \usepackage[active]{srcltx} |
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16 | \usepackage{hyperref} |
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17 | \usepackage[english]{babel} |
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18 | \usepackage{verbatim} |
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19 | \usepackage{fancyhdr} |
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20 | |
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21 | \InputIfFileExists{surfex_doc.cfg} |
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22 | {\typeout{Use surfex_doc.cfg to configure the system type.}} |
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23 | {\input{surfex_doc_linux.cfg}} |
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24 | |
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25 | %\newcommand{\Linux}[1]{}\newcommand{\Windows}[1]{#1} |
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26 | |
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27 | \newcommand{\surfex}{{\sc surfex}} |
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28 | \newcommand{\attention}{\emph{Attention!}} |
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29 | |
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30 | \newcommand{\inshell}[1]{{\\\qquad\qquad{\tt #1}}} |
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31 | \newcommand{\curver}{0.89.02 } |
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32 | \newcommand{\curverfile}{0\_89\_02} |
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33 | \Linux{\newcommand{\INSTALL}{INSTALL\_LINUX}} |
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34 | \Windows{\newcommand{\INSTALL}{INSTALL\_WINDOWS}} |
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35 | |
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36 | \newcommand{\dZ}{{\mathds Z}} |
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37 | \newcommand{\dN}{{\mathds N}} |
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38 | \newcommand{\dP}{{\mathds P}} |
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39 | \newcommand{\dC}{{\mathds C}} |
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40 | \newcommand{\dR}{{\mathds R}} |
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41 | \newcommand{\dQ}{{\mathds Q}} |
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42 | \newcommand{\smcdot}{{\textup{$\cdot$}}} |
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43 | |
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44 | \newtheorem{theorem}{Theorem} |
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45 | \newtheorem{corollary}[theorem]{Corollary} |
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46 | \newtheorem{remark}[theorem]{Remark} |
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47 | |
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48 | \pagestyle{fancy} |
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49 | |
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50 | \begin{document} |
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51 | |
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52 | \title{{\sc surfex v.\ \curver for \Windows{Windows}\Linux{Linux/Unix}}\\ |
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53 | --- A Short Documentation ---} |
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54 | \author{Oliver Labs} |
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55 | %\address{Universit\"at des Saarlandes, Saarbr\"ucken (Germany)} |
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56 | |
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57 | \maketitle |
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58 | |
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59 | %\begin{abstract} |
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60 | \abstract{ |
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61 | \noindent {\sc surfex} is a tool for interactive high quality real algebraic |
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62 | surface |
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63 | visualization. |
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64 | It is a meta-software which combines the strenghts of several visualization |
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65 | tools such as {\sc surf}, {\sc javaview}%, {\sc singsurf} |
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66 | . |
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67 | |
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68 | \noindent We also implemented a {\sc Singular} library called {\sc surfex.lib} |
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69 | which enhances the quality of the visualization of {\sc surfex} using |
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70 | pre-computation of the singular locus etc. |
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71 | |
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72 | \noindent The latest version and information on {\sc surfex} and {\sc |
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73 | surfex.lib} is available from our website: |
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74 | \href{http://www.surfex.AlgebraicSurface.net}{\tt |
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75 | www.surfex.AlgebraicSurface.net}. |
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76 | %\end{abstract} |
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77 | \begin{center} |
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78 | \includegraphics[width=0.8\textwidth]{surfex_simple} |
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79 | \end{center} |
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80 | } |
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81 | |
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82 | %\tableofcontents{} |
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83 | |
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84 | % We do not want indentation at the beginning of each paragraph: |
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85 | \setlength{\parindent}{0pt} |
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86 | % Instead, we prefer a small vertical space between paragraphs: |
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87 | \setlength{\parskip}{1ex plus 0.5ex minus 0.2ex} |
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88 | |
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89 | |
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90 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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91 | % |
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92 | % |
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93 | % |
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94 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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95 | \section{Getting Started} |
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96 | |
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97 | |
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98 | |
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99 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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100 | % |
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101 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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102 | \subsection{Download} |
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103 | |
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104 | You can download the version \curver of our visualization software {\sc |
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105 | surfex} as one file called {\tt surfex\_\curverfile.tar.gz} from our website: |
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106 | \begin{center} |
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107 | \href{http://www.surfex.AlgebraicSurface.net}{\tt |
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108 | www.surfex.AlgebraicSurface.net} |
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109 | \end{center} |
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110 | |
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111 | |
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112 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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113 | % |
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114 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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115 | \subsection{Prerequisites} |
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116 | |
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117 | The current version of \surfex{} |
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118 | uses the raytracer {\sc surf} as a back-end for computing the beautiful |
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119 | images. |
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120 | This software has to be installed on your system if you want to use |
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121 | \surfex{}. |
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122 | If you want to produce movies using \surfex{}, |
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123 | then you will also need to have the image conversion tool {\sc convert} |
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124 | installed which is part of the {\sc ImageMagick} package. |
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125 | |
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126 | |
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127 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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128 | % |
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129 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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130 | \subsubsection{{\sc Java} (required)} |
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131 | |
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132 | \surfex{} is a {\sc Java} program. |
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133 | This has the advantage that it is not much work to provide the software for |
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134 | many operating systems and also that it can easily be adapted to work over the |
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135 | internet. |
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136 | |
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137 | The current version of \surfex{} requires the Java Runtime Environment |
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138 | (JRE), version 1.4.2 or later. |
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139 | You can download it from \href{http://www.java.sun.com}{www.java.sun.com}. |
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140 | |
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141 | |
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142 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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143 | % |
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144 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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145 | \subsubsection{{\sc surf} (required)} |
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146 | |
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147 | \Windows{ |
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148 | Thanks to the {\sc Singular} Team, the raytracer {\sc surf} is now also |
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149 | available for Windows. |
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150 | This enables us to provide \surfex{} for Windows: |
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151 | |
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152 | The most convenient way to install {\sc surf} is to install the {\bf full |
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153 | version} of {\sc Singular for Windows} (which includes in particular {\sc |
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154 | surf}). |
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155 | It uses the Linux emulation {\sc cygwin}. |
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156 | The {\sc Singular} team provides their great software on their website: |
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157 | \href{https://www.singular.uni-kl.de}{\tt www.singular.uni-kl.de}. |
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158 | It is very easy to install; just follow the instructions. |
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159 | |
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160 | Please, remember the directory to which {\sc Singular} installed the {\sc |
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161 | Cygwin} for later use; |
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162 | at the moment, the standard seems to be {\tt c:$\backslash$cygwin}. |
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163 | } |
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164 | |
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165 | \Linux{ |
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166 | The canonical way to install {\sc surf} under Linux is to download the |
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167 | latest version from the {\sc surf} website: |
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168 | \href{http://surf.sourceforge.net}{\tt http://surf.sourceforge.net}. |
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169 | After having downloaded the source code from this site, you will have to |
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170 | compile and install it. |
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171 | The version 1.0.5 usually compiles easily on recent Linux installations with a |
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172 | recent c++ compiler. |
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173 | Just follow the instructions in the {\tt \INSTALL{}} file contained in the downloaded |
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174 | package. |
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175 | |
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176 | However, for some systems there exist pre-compiled versions, see e.g.\ the |
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177 | {\sc Singular} website: \href{https://www.singular.uni-kl.de}{\tt |
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178 | www.singular.uni-kl.de}. |
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179 | These versions run on many Linux systems. |
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180 | |
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181 | The standard name of the current version of the {\sc surf} binary is {\tt |
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182 | surf-1.0.5}. |
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183 | Please, {\bf rename it to {\tt surf}} in order to allow \surfex{} to find it, |
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184 | independantly of the current version. |
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185 | } |
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186 | |
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187 | |
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188 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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189 | % |
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190 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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191 | \subsubsection{{\sc convert} (optional, for producing movies)} |
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192 | |
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193 | For producing movies of algebraic surfaces, \surfex{} uses the great image |
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194 | conversion tool {\sc convert} which is part of the {\sc ImageMagick} package. |
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195 | You can download it from: |
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196 | \href{http://www.imagemagick.org}{\tt www.imagemagick.org}. |
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197 | |
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198 | \Windows{ |
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199 | The easiest way is to download and install a Windows binary release (do NOT |
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200 | use the cygwin binary!). |
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201 | Please, use the Q16-verion. |
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202 | At the time of the writing of this documentation, the current version is |
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203 | 6.2.7-6 and the corresponding file is: |
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204 | ImageMagick-6.2.7-6-Q16-windows-static.exe |
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205 | |
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206 | Its installation is very easy; just double-click the downloaded file. |
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207 | } |
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208 | |
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209 | \Linux{ |
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210 | The easiest way is to download and install a binary release in the form of a |
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211 | rpm package. |
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212 | At the time of the writing of this documentation, the current version is |
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213 | 6.2.7-6 and the corresponding file is: ImageMagick-6.2.7-6.i386.rpm |
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214 | |
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215 | To install it, type (as superuser (root)): |
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216 | \inshell{rpm -i ImageMagick-6.2.7-6.i386.rpm} |
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217 | } |
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218 | |
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219 | |
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220 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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221 | % |
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222 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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223 | \subsection{Install} |
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224 | |
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225 | If you have {\sc Java} and {\sc surf} (and, optionally, {\sc convert}) installed on your |
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226 | system as described above, the installation of \surfex{} should be very easy. |
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227 | Just follow the steps below: |
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228 | |
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229 | \begin{itemize} |
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230 | \Windows{ |
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231 | \item |
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232 | Copy the downloaded file {\tt surfex\_\curverfile.tar.gz} to the directory for |
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233 | the temporary files of your {\sc cygwin} (if the {\sc cygwin} directory is |
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234 | {\tt c:$\backslash$cygwin}, then the temporary directory will be {\tt |
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235 | c:$\backslash$cygwin$\backslash$tmp}). |
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236 | |
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237 | \item Open a bash shell: |
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238 | It is available from the Windows Start Menu via the {\sc Singular} sub-menu: |
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239 | Programs $\to$ Singular CAS $\to$ Cygwin $\to$ Bash. |
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240 | |
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241 | \item |
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242 | Uncompress the downloaded file by typing the following command into the |
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243 | shell: |
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244 | \inshell{tar -xzvf /tmp/surfex\_\curverfile.tar.gz} |
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245 | } |
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246 | |
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247 | \Linux{ |
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248 | \item |
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249 | Open a shell, preferably the bash shell. |
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250 | This shell is available on most Linux systems. |
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251 | You can start a bash by typing |
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252 | \inshell{bash}\\ |
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253 | into a shell. |
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254 | |
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255 | \item |
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256 | Change to the directory, say {\tt /home/yourlogin/software} into which you |
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257 | downloaded the file |
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258 | {\tt surfex\_\curverfile.tar.gz}, e.g.\ by typing |
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259 | \inshell{cd /home/yourlogin/software}\\ |
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260 | into a shell. |
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261 | |
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262 | \item |
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263 | Uncompress the downloaded file by typing the following command into the |
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264 | shell: |
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265 | \inshell{tar -xzvf surfex\_\curverfile.tar.gz} |
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266 | } |
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267 | \item |
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268 | This should have created a directory called {\tt |
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269 | surfex\_\curverfile}. |
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270 | Change to this directory by typing the following into the shell: |
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271 | \inshell{cd surfex\_\curverfile} |
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272 | \item |
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273 | Run the {\tt \INSTALL{}} script by typing the following into the shell: |
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274 | \inshell{./\INSTALL}\\ |
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275 | If {\tt \INSTALL{}} works well, it will produce a script |
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276 | called {\tt surfex} in the current directory, and it will copy this script to |
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277 | a directory which is contained in your bash path. |
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278 | \item |
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279 | You can now start surfex by typing: |
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280 | \inshell{surfex} |
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281 | \end{itemize} |
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282 | |
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283 | |
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284 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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285 | % |
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286 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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287 | \subsection{Start} |
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288 | |
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289 | If you have installed \surfex{} correctly then you can start it by typing |
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290 | \inshell{surfex}\\ |
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291 | into a shell. |
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292 | Three windows will show up (see e.g., fig.\ \vref{fig:surfex_simple}), and a default |
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293 | surface will be shown. |
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294 | You can also invoke \surfex{} directly with an equation: |
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295 | \inshell{surfex -e x\^{}3+y\^{}2-z\^{}2}\\ |
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296 | If this equation contains parenthesis then you might have to enclose the equation |
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297 | in quotes: \inshell{surfex -e "(x+y)*(x-y)+z\^{}3"}\\ |
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298 | If you already have a \surfex{}-file, say {\tt example.sux}, then you can |
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299 | open this file by typing: |
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300 | \inshell{surfex example.sux} |
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301 | |
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302 | |
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303 | |
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304 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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305 | % |
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306 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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307 | \subsection{Examples} |
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308 | |
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309 | The directory {\tt \curverfile} which was made during the installation process |
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310 | should contain a sub-folder called {\tt examples}. |
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311 | |
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312 | Furthermore, we will give many more examples on our website in the future, |
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313 | see |
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314 | \href{http://www.surfex.AlgebraicSurface.net}{\tt |
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315 | www.surfex.AlgebraicSurface.net}. |
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316 | |
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317 | |
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318 | |
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319 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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320 | % |
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321 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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322 | \subsection{Documentation} |
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323 | |
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324 | The latest version of the documentation which you are currently reading is |
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325 | available from our website: |
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326 | \href{http://www.surfex.AlgebraicSurface.net}{\tt |
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327 | www.surfex.AlgebraicSurface.net} |
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328 | |
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329 | |
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330 | |
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331 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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332 | % |
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333 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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334 | \section{The Interface} |
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335 | |
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336 | |
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337 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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338 | % |
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339 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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340 | \subsection{Three Windows} |
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341 | |
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342 | \begin{figure}[htbp] |
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343 | \begin{center} |
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344 | \includegraphics[width=0.8\textwidth]{surfex_simple} |
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345 | \caption{The \surfex{} interface.} |
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346 | \label{fig:surfex_simple} |
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347 | \end{center} |
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348 | \end{figure} |
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349 | |
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350 | After having started \surfex, you see three windows, entitled {\tt surfex}, {\tt |
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351 | triangulation}, {\tt raytraced surface}. |
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352 | |
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353 | The {\tt raytraced surface} window shows a raytraced view of the surfaces |
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354 | (produced using {\sc surf}). |
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355 | |
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356 | The {\tt triangulation} window currently only shows a sphere. |
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357 | By dragging the mouse on this window you can rotate the surface which is |
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358 | shown in the {\tt raytraced surface} window. |
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359 | |
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360 | The main window is the {\tt surfex} window: |
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361 | here, you specify the equations and most of the other data. |
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362 | We describe this in detail in the next subsection. |
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363 | |
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364 | |
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365 | |
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366 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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367 | % |
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368 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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369 | \subsection{The {\tt surfex} Window} |
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370 | |
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371 | |
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372 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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373 | % |
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374 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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375 | \subsubsection{The Menu} |
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376 | |
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377 | \ \\\includegraphics[scale=0.75]{surfex_menu_bar} |
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378 | |
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379 | In the current version, the menu does not have much functionality. |
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380 | Only the {\tt file} menu contains some important items: |
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381 | for opening \surfex{} files, and for saving raytraced images and movies. |
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382 | |
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383 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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384 | % |
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385 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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386 | \subsubsection{The Project Title} |
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387 | |
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388 | \ \\\includegraphics[scale=0.6]{surfex_project_title} |
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389 | |
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390 | |
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391 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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392 | % |
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393 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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394 | \subsubsection{The Actions Bar} |
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395 | |
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396 | \ \\\includegraphics[scale=0.35]{surfex_actions_bar} |
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397 | |
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398 | The main actions are performed using the actions bar. |
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399 | From left to right, the buttons have the following functionalities: |
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400 | \begin{itemize} |
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401 | \item save the current project, |
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402 | \item save the current raytraced image (in a higher resolution, if you whish), |
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403 | \item save a movie, based on the current image (in a higher resolution, if you whish), |
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404 | \item add a parameter to the project, |
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405 | \item add an equation to the project, |
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406 | \item add a curve to the project, |
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407 | \item add an isolated point to the project, |
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408 | \item raytrace the image once, |
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409 | \item raytrace permanently; i.e., always produce new raytraced images whenever |
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410 | you have changed anything. |
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411 | \end{itemize} |
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412 | |
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413 | |
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414 | \subsubsection{The General Properties Bar} |
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415 | |
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416 | \ \\\includegraphics[scale=0.6]{surfex_general_prop_bar} |
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417 | |
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418 | Using the general properties bar you can perform actions which do not |
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419 | only have an effect on one single object, but on all varieties |
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420 | simultaneously. |
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421 | From left to right: |
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422 | \begin{itemize} |
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423 | \item antialiasing: after the computation of the raytraced image, perform an |
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424 | antialiasing (which enhances the quality, but which takes time). |
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425 | \item preview-quality: 1 (best quality), \dots, 8 (lowest quality). |
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426 | \item background-color: set the background color of the raytraced image. |
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427 | \end{itemize} |
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428 | |
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429 | |
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430 | \subsubsection{The Parameters Window} |
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431 | |
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432 | \ \\\includegraphics[scale=0.5]{surfex_parameters} |
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433 | |
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434 | The name of the parameter (here {\tt p1}) is the leftmost information given |
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435 | for each parameter. |
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436 | It cannot be changed in the current version. |
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437 | |
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438 | But you may specify the range of the parameter, and, of course, the value |
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439 | of the parameter itself. |
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440 | In the current version, the parameter can only be changed using the slider and |
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441 | not via the keyboard. |
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442 | |
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443 | \attention{} |
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444 | Once you have changed the lower or upper bound for a |
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445 | parameter by typing in some decimal number, you have to press RETURN (while |
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446 | the cursor is still in the text field in which you entered the new number). |
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447 | |
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448 | |
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449 | \subsubsection{The Equations Window} |
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450 | |
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451 | \ \\\includegraphics[scale=0.35]{surfex_equations} |
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452 | |
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453 | A checkbox is the leftmost element for each equation. |
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454 | Using this one, you can decide wether the surface should be shown in the |
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455 | picture or not. |
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456 | |
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457 | By clicking on one of the two colored buttons one can specify the inside (i.e. |
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458 | looking towards the points on which the equation takes positive values) and |
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459 | the outside color of the surface. |
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460 | |
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461 | The {\tt del} button is currently disabled. |
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462 | |
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463 | The {\tt opts} button opens an options dialogue box. |
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464 | At the moment, one can only specify the transparency there (in \%). |
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465 | If this is set to 100 \% then the surface is not visible at all in the |
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466 | picture. |
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467 | |
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468 | At the right of this button you can see the name of the equation. |
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469 | |
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470 | \paragraph{Equation Syntax} |
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471 | |
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472 | The equation itself may be entered into the big text field. |
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473 | You have to give all operators explicitly: {\tt +}, {\tt -}, {\tt *}, |
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474 | {\tt \^{}} (i.e., e.g., {\tt 3xy} is not allowed). |
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475 | As parenthesis you may use {\tt (} and {\tt )}. |
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476 | |
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477 | Furthermore, you may include the names of the parameters (in the numerator or |
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478 | denominator) and of the other equations (in the numerator). |
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479 | |
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480 | You may even apply trigonometric functions ({\tt sin}, {\tt cos}, {\tt tan}, |
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481 | {\tt arccos}, {\tt arcsin}, {\tt arctan}) or {\tt sqrt} to decimal numbers or |
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482 | parameters (these are actually those supported by {\sc surf}).\\ |
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483 | E.g., if you have two parameters {\tt p1} and {\tt p2}, and two equations {\tt |
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484 | f1} and {\tt f2}, then the equation of the third equation may e.g.\ look as |
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485 | follows: {\tt cos(p1)*f1 + (sqrt(p2)+1)*f2}. |
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486 | |
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487 | {\sc surf} also allows the usage of some functions which yield a polynomial: |
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488 | \begin{itemize} |
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489 | \item {\tt hesse} (produces the Hessian of a surface), |
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490 | \item |
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491 | {\tt diff(p,x)}, {\tt diff(p,y)}, {\tt diff(p,z)} (the partial |
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492 | differentials, where {\tt p} is some polynomial), |
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493 | \item {\tt rotate(p,v,xAxis)}, {\tt rotate(p,v,yAxis)}, {\tt |
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494 | rotate(p,v,zAxis)}, where {\tt p} is some polynomial and {\tt v} is |
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495 | some decimal number (or parameter!); in this way, you can produce your own |
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496 | non-standard rotation movie. |
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497 | \end{itemize} |
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498 | |
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499 | E.g., |
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500 | {\tt diff(f1,x)*p1 + diff(f1,y)*p2 + diff(f1,z)*p3} |
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501 | is the equation of the polar of the surface {\tt f1} with respect to the point |
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502 | with coordinates {\tt p1}, {\tt p2}, {\tt p3} (which can be specified using |
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503 | the parameter sliders). |
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504 | |
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505 | |
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506 | \subsubsection{The Curves Window} |
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507 | |
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508 | \ \\\includegraphics[scale=0.35]{surfex_curves} |
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509 | |
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510 | Similar to the equations, you can specify if you want to see the curve or not |
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511 | by using the checkbox at the left. |
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512 | |
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513 | There is also a color button. |
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514 | |
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515 | Each curve is then specified by giving the numbers of some equations. |
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516 | |
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517 | \attention{} |
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518 | It is important to note that the curve will be drawn on the first of the |
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519 | surfaces specified. |
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520 | This means in particular that the curve will only be shown if the checkbox of |
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521 | this surface is checked, although its transparency can be 100 \%. |
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522 | This last feature can be used to draw space curves without showing the |
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523 | surface. |
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524 | |
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525 | |
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526 | \subsubsection{The Solitary Points Window} |
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527 | |
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528 | \ \\\includegraphics[scale=0.35]{surfex_points} |
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529 | |
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530 | Solitary points can be shown as small spheres in the picture. |
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531 | At the moment, their properties have to be the same as those of one of the |
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532 | surfaces. |
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533 | You have to select its number from the drop down list at the left. |
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534 | The coordinates of the points can contain polynomials in the parameters. |
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535 | |
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536 | The slider can be used to give the radius of the small sphere representing the |
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537 | solitary point. |
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538 | At the moment, all solitary points have to be represented by spheres which |
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539 | have the same radius. |
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540 | |
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541 | |
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542 | \end{document} |
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543 | %%% Local Variables: |
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544 | %%% mode: latex |
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545 | %%% TeX-master: t |
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546 | %%% End: |
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