1 | // $Id: surf.lib,v 1.3 1999-05-26 16:23:25 obachman Exp $ |
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2 | // |
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3 | // author : Hans Schoenemann |
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4 | // |
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5 | /////////////////////////////////////////////////////////////////////////////// |
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6 | version="$Id: surf.lib,v 1.3 1999-05-26 16:23:25 obachman Exp $"; |
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7 | info=" |
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8 | LIBRARY: surf.lib PROCEDURES FOR GRAPHICS WITH SURF (by Stephan Endrass) |
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9 | |
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10 | plot(I); plots curves and surfaces |
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11 | "; |
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12 | |
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13 | /////////////////////////////////////////////////////////////////////////////// |
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14 | static proc num_of_vars(ideal I) |
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15 | { |
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16 | intvec v; |
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17 | int i; |
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18 | poly p; |
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19 | for(i=size(I);i>0;i--) |
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20 | { |
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21 | p=I[i]; |
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22 | while(p!=0) |
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23 | { |
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24 | v=v+leadexp(p); |
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25 | p=p-lead(p); |
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26 | } |
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27 | } |
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28 | return(v); |
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29 | } |
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30 | |
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31 | proc plot(ideal I) |
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32 | "USAGE: plot(I); I ideal |
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33 | RETURN: |
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34 | NOTE: |
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35 | EXAMPLE: example plot; shows an example |
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36 | " |
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37 | { |
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38 | string l="/tmp/surf"+string(system("pid")); |
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39 | def base=basering; |
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40 | intvec v=num_of_vars(I); |
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41 | int i,j,n; |
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42 | for(i=size(v);i>0;i--) |
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43 | { |
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44 | if (v[i]!=0) { n++; } |
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45 | } |
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46 | if (n==0 or n>3) |
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47 | { |
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48 | "Cannot plot equations with", n, "variables"; |
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49 | return(); |
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50 | } |
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51 | ring r=0,(x,y,z),dp; |
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52 | short=0; |
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53 | map phi=base,0; |
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54 | j=1; |
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55 | for(i=1;i<=size(v);i++) |
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56 | { |
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57 | if (v[i]!=0) |
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58 | { |
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59 | phi[i]=var(j); |
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60 | j++; |
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61 | if(j==4) break; |
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62 | } |
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63 | } |
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64 | ideal I=simplify(phi(I),2); |
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65 | if (ncols(I)==1 and n<=2) // curve |
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66 | { |
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67 | write(":w "+l,"clip=none;"); |
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68 | write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;"); |
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69 | write(l, |
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70 | "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;"); |
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71 | write(l, "curve_green=0; curve_blue=0; curve_width=4.5;"); |
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72 | write(l,"curve=",I[1],";"); |
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73 | write(l,"draw_curve;"); |
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74 | } |
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75 | else |
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76 | { |
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77 | if (ncols(I)==1 and n==3) // surface |
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78 | { |
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79 | write(":w "+l, |
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80 | "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;"); |
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81 | write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;"); |
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82 | write(l,"rot_x=0.14; rot_y=-0.3;"); |
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83 | write(l,"surface=",I[1],";"); |
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84 | write(l,"draw_surface;"); |
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85 | } |
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86 | else |
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87 | { |
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88 | "cannot plot",ncols(I),"equations in",n,"variables"; |
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89 | return(); |
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90 | } |
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91 | } |
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92 | // "calling surf (by Stephan Endrass) for drawing"; |
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93 | i=system("sh","surf "+l+" >/dev/null 2>&1"); |
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94 | i=system("sh","/bin/rm "+l); |
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95 | } |
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96 | example |
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97 | { "EXAMPLE:"; echo =2; |
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98 | // --------- plane curves ------------ |
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99 | ring rr0 = 0,(x1,x2),dp; |
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100 | |
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101 | ideal I = x1^3 - x2^2; |
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102 | plot(I); |
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103 | ideal J = x1^2-x1-x2^3; |
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104 | plot(J); |
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105 | |
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106 | ring rr1 = 0,(x,y,z),dp; |
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107 | ideal I(1) = 2x2-1/2x3 +1-y+1; |
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108 | plot(I(1)); |
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109 | ideal I(2) = x3-x-y; |
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110 | plot(I(2)); |
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111 | |
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112 | // ---- Singular Logo -------------- |
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113 | poly logo = ((x+3)^3 + 2*(x+3)^2 - y^2)*(x^3 - y^2)*((x-3)^3-2*(x-3)^2-y^2); |
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114 | plot(logo); |
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115 | |
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116 | |
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117 | // --------- implicit curves ------------ |
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118 | // implicit curves |
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119 | ideal I(1) = y,-x2; |
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120 | plot(I(1)); |
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121 | ideal I(2) = x2,-y2 +4; |
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122 | plot(I(2)); |
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123 | |
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124 | //the lemniscate |
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125 | |
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126 | ideal I(3) = x4+2x2y2 + y4, x2-y2; |
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127 | plot(I(3)); |
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128 | |
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129 | // a critical part |
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130 | // adjust the plotregion properly to get a good picture |
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131 | |
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132 | poly f = (x-y)*(x2+y); |
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133 | plot(f,1); |
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134 | ideal J = jacob(f); |
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135 | J; |
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136 | plot(J); // bad resolution |
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137 | |
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138 | // ----------- surfaces ------------------- |
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139 | ideal J(1) = 3xy4 + 2xy2, x5y3 + x + y6,10x2; |
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140 | plot(J(1)); |
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141 | |
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142 | // Steiner surface |
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143 | |
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144 | ideal J(2) = x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z; |
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145 | plot(J(2)); |
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146 | |
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147 | plot(x*(x2-y2)+z2); |
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148 | |
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149 | // E7 |
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150 | plot(x^3-x*y^3+z^2); |
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151 | |
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152 | // Whitney umbrella |
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153 | plot(z^2-x^2*y); |
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154 | |
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155 | // A1 |
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156 | plot(y2-xz); |
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157 | |
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158 | |
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159 | } |
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160 | /////////////////////////////////////////////////////////////////////////////// |
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161 | |
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162 | |
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