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<div class="header">
<div class="headertitle"><div class="title">Mesh_3/implicit_functions.cpp</div></div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"> </div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Sphere (r=1)</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> sphere_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) {</div>
<div class="line"> <span class="keywordtype">double</span> x2=x*x, y2=y*y, z2=z*z;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> x2+y2+z2-1;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Ellipsoid (r=1)</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> ellipsoid_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) {</div>
<div class="line"> <span class="keywordtype">double</span> x2=x*x, y2=y*y, z2=z*z;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> x2+2*y2+4*z2-1;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Torus (r=2)</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> torus_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) {</div>
<div class="line"> <span class="keywordtype">double</span> x2=x*x, y2=y*y, z2=z*z;</div>
<div class="line"> <span class="keywordtype">double</span> x4=x2*x2, y4=y2*y2, z4=z2*z2;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> x4 + y4 + z4 + 2 *x2* y2 + 2*</div>
<div class="line"> x2*z2 + 2*y2* z2 - 5 *x2 + 4* y2 - 5*z2+4;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// "Chair" (r=6)</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> chair_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) {</div>
<div class="line"> <span class="keywordtype">double</span> x2=x*x, y2=y*y, z2=z*z;</div>
<div class="line"> <span class="keywordtype">double</span> x4=x2*x2, y4=y2*y2, z4=z2*z2;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> x4-1.2*x2*y2+3.6*x2*z2-7.50*x2+y4+3.6*y2*z2-7.50*y2+.2*z4-7.50*z2+64.0625-16.0*z*y2+16.0*x2*z;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// "Tanglecube" (r=4)</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> tanglecube_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) {</div>
<div class="line"> <span class="keywordtype">double</span> x2=x*x, y2=y*y, z2=z*z;</div>
<div class="line"> <span class="keywordtype">double</span> x4=x2*x2, y4=y2*y2, z4=z2*z2;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> x4 - 5*x2 + y4 - 5*y2 + z4 - 5*z2 + 11.8;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> cube_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z){</div>
<div class="line"> <span class="keywordflow">if</span>( x < 1 && -x < 1 &&</div>
<div class="line"> y < 1 && -y < 1 &&</div>
<div class="line"> z < 1 && -z < 1 )</div>
<div class="line"> <span class="keywordflow">return</span> -1.;</div>
<div class="line"> <span class="keywordflow">return</span> 1.;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"><span class="comment">// Barth's octic surface (degree 8)</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> octic_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// r=2</span></div>
<div class="line"> <span class="keywordtype">double</span> x2=x*x, y2=y*y, z2=z*z;</div>
<div class="line"> <span class="keywordtype">double</span> x4=x2*x2, y4=y2*y2, z4=z2*z2;</div>
<div class="line"> <span class="keywordtype">double</span> x6=x4*x2, y6=y4*y2, z6=z4*z2;</div>
<div class="line"> <span class="keywordtype">double</span> x8=x4*x4, y8=y4*y4, z8=z4*z4;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> 43.30495169 *x2* y2 + 43.30495169 *x2* z2 + 43.30495169 *y2 * z2 + 44.36067980 *x6* y2 + 44.36067980* x6 * z2 + 66.54101970* x4* y4 + 66.54101970* x4 * z4 + 44.36067980 *x2 * y6 - 11.70820393* x2 - 11.70820393* y2 - 11.70820393* z2 + 37.65247585 *x4 + 37.65247585 *y4 + 37.65247585* z4 + 11.09016995* x8 + 11.09016995 *y8 + 11.09016995* z8 + 133.0820394 *x2* y4* z2 + 133.0820394 *x2 * y2 * z4 + 44.36067980* x2 * z6 + 44.36067980 *y6 * z2 + 66.54101970 *y4 * z4 + 44.36067980 *y2 * z6 + 133.0820394* x4* y2 * z2 - 91.95742756 *x4 * y2 - 91.95742756 *x4 *z2 - 91.95742756* x2 * y4 - 91.95742756 *x2 *z4 - 91.95742756* y4 * z2 - 183.9148551* x2 *y2 *z2 - 30.65247585 *x6 - 30.65247585* y6 - 91.95742756 *y2 * z4 - 30.65247585* z6 + 1.618033988;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// "Heart"</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> heart_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// radius = 2</span></div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> (2*x*x+y*y+z*z-1)*(2*x*x+y*y+z*z-1)*(2*x*x+y*y+z*z-1) - (0.1*x*x+y*y)*z*z*z;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Klein's bottle</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> klein_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// radius = 4</span></div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> (x*x+y*y+z*z+2*y-1)*((x*x+y*y+z*z-2*y-1)*(x*x+y*y+z*z-2*y-1)-8*z*z)+16*x*z*(x*x+y*y+z*z-2*y-1);</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Ring</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> ring_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// radius = ?</span></div>
<div class="line"> <span class="keywordtype">double</span> e=0.1;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> f1 = x*x+y*y+z*z-1;</div>
<div class="line"> <span class="keywordtype">double</span> f2 = x;</div>
<div class="line"> </div>
<div class="line"> f1 = f1*f1-e*e;</div>
<div class="line"> f2 = f2*f2-e*e;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">if</span> (f1 < 0 && f2 < 0)</div>
<div class="line"> <span class="keywordflow">return</span> -1.;</div>
<div class="line"> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (f1 > 0 || f2 > 0)</div>
<div class="line"> <span class="keywordflow">return</span> 1.;</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <span class="keywordflow">return</span> 0.;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// False knot</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> false_knot_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// radius = 1</span></div>
<div class="line"> <span class="keywordtype">double</span> d=1.2, e=0.1;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> f1 = x*(x*x-z*z)-2*x*z*z-y*y+d*d-x*x-z*z-y*y;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> m2 = z*(x*x-z*z)+2*x*x*z;</div>
<div class="line"> <span class="keywordtype">double</span> f2 = 4*y*y*(d*d-x*x-z*z-y*y) - m2*m2;</div>
<div class="line"> </div>
<div class="line"> f1 = f1*f1-e*e;</div>
<div class="line"> f2 = f2*f2-e*e;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">if</span> (f1 < 0 && f2 < 0)</div>
<div class="line"> <span class="keywordflow">return</span> -1.;</div>
<div class="line"> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (f1 > 0 || f2 > 0)</div>
<div class="line"> <span class="keywordflow">return</span> 1.;</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <span class="keywordflow">return</span> 0.;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Knot 1</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">void</span> puiss(<span class="keywordtype">double</span>& x, <span class="keywordtype">double</span>& y, <span class="keywordtype">int</span> n) {</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> xx = 1, yy = 0;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">while</span>(n>0) {</div>
<div class="line"> <span class="keywordflow">if</span> (n&1) {</div>
<div class="line"> <span class="keywordtype">double</span> xxx = xx, yyy = yy;</div>
<div class="line"> xx = xxx*x - yyy*y;</div>
<div class="line"> yy = xxx*y + yyy*x;</div>
<div class="line"> }</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> xxx = x, yyy = y;</div>
<div class="line"> x=xxx*xxx-yyy*yyy;</div>
<div class="line"> y=2*xxx*yyy;</div>
<div class="line"> </div>
<div class="line"> n/=2;</div>
<div class="line"> }</div>
<div class="line"> </div>
<div class="line"> x = xx;</div>
<div class="line"> y = yy;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> knot1_function (<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, <span class="keywordtype">double</span> c) { <span class="comment">// radius = 4</span></div>
<div class="line"> <span class="keywordtype">double</span> e=0.1;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> x, y, z, t, den;</div>
<div class="line"> den=1+a*a+b*b+c*c;</div>
<div class="line"> x=2*a/den;</div>
<div class="line"> y=2*b/den;</div>
<div class="line"> z=2*c/den;</div>
<div class="line"> t=(1-a*a-b*b-c*c)/den;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> x3=x, y3=y, z2=z, t2=t;</div>
<div class="line"> puiss(x3,y3,3);</div>
<div class="line"> puiss(z2,t2,2);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> f1 = z2-x3;</div>
<div class="line"> <span class="keywordtype">double</span> f2 = t2-y3;</div>
<div class="line"> </div>
<div class="line"> f1 = f1*f1;</div>
<div class="line"> f2 = f2*f2;</div>
<div class="line"> e=e*e/(den-1);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">if</span> (f1+f2-e < 0)</div>
<div class="line"> <span class="keywordflow">return</span> -1.;</div>
<div class="line"> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (f1+f2-e > 0)</div>
<div class="line"> <span class="keywordflow">return</span> 1.;</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <span class="keywordflow">return</span> 0.;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"><span class="comment">/*</span></div>
<div class="line"><span class="comment">double knot1_function (double x, double y, double z) { // radius = 4</span></div>
<div class="line"><span class="comment"> double e=0.1;</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> double c1, c2, c3, c4, den;</span></div>
<div class="line"><span class="comment"> den=1+x*x+y*y+z*z;</span></div>
<div class="line"><span class="comment"> c1=2*x/den;</span></div>
<div class="line"><span class="comment"> c2=2*y/den;</span></div>
<div class="line"><span class="comment"> c3=2*z/den;</span></div>
<div class="line"><span class="comment"> c4=(1-x*x-y*y-z*z)/den;</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> double f1 = c1*(c1*c1-c2*c2)-2*c1*c2*c2-c3*c3+c4*c4;</span></div>
<div class="line"><span class="comment"> double f2 = c2*(c1*c1-c2*c2)+2*c1*c1*c2-2*c3*c4;</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> f1 = f1*f1;</span></div>
<div class="line"><span class="comment"> f2 = f2*f2;</span></div>
<div class="line"><span class="comment"> e=e*e/(den-1);</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment"> if (f1+f2-e < 0)</span></div>
<div class="line"><span class="comment"> return -1.;</span></div>
<div class="line"><span class="comment"> else if (f1+f2-e > 0)</span></div>
<div class="line"><span class="comment"> return 1.;</span></div>
<div class="line"><span class="comment"> else</span></div>
<div class="line"><span class="comment"> return 0.;</span></div>
<div class="line"><span class="comment">}</span></div>
<div class="line"><span class="comment">*/</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> knot1_surf1_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// radius = 4</span></div>
<div class="line"> <span class="keywordtype">double</span> c1, c2, c3, c4, den;</div>
<div class="line"> den=1+x*x+y*y+z*z;</div>
<div class="line"> c1=2*x/den;</div>
<div class="line"> c2=2*y/den;</div>
<div class="line"> c3=2*z/den;</div>
<div class="line"> c4=(1-x*x-y*y-z*z)/den;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> c1*(c1*c1-c2*c2)-2*c1*c2*c2-c3*c3+c4*c4;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> knot1_surf2_function (<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z) { <span class="comment">// radius = 4</span></div>
<div class="line"> <span class="keywordtype">double</span> c1, c2, c3, c4, den;</div>
<div class="line"> den=1+x*x+y*y+z*z;</div>
<div class="line"> c1=2*x/den;</div>
<div class="line"> c2=2*y/den;</div>
<div class="line"> c3=2*z/den;</div>
<div class="line"> c4=(1-x*x-y*y-z*z)/den;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> c2*(c1*c1-c2*c2)+2*c1*c1*c2-2*c3*c4;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Knot 2</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> knot2_function (<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, <span class="keywordtype">double</span> c) { <span class="comment">// radius = 4</span></div>
<div class="line"> <span class="keywordtype">double</span> e=0.025;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> x, y, z, t, den;</div>
<div class="line"> den=1+a*a+b*b+c*c;</div>
<div class="line"> x=2*a/den;</div>
<div class="line"> y=2*b/den;</div>
<div class="line"> z=2*c/den;</div>
<div class="line"> t=(1-a*a-b*b-c*c)/den;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> x7=x, y7=y, x13=x, y13=y;</div>
<div class="line"> puiss(x7,y7,7);</div>
<div class="line"> puiss(x13,y13,13);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> z3=z, t3=t;</div>
<div class="line"> puiss(z3,t3,3);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> f1t = (z3-x7)*(z3-x7+100*x13) - (t3-y7)*(t3-y7+100*y13);</div>
<div class="line"> <span class="keywordtype">double</span> f2t = (z3-x7)*(t3-y7+100*y13) + (t3-y7)*(z3-x7+100*x13);</div>
<div class="line"> <span class="keywordtype">double</span> f1 = f1t*(z3-x7-100*x13) - f2t*(t3-y7-100*y13);</div>
<div class="line"> <span class="keywordtype">double</span> f2 = f1t*(t3-y7-100*y13) + f2t*(z3-x7-100*x13);</div>
<div class="line"> </div>
<div class="line"> f1 = f1*f1;</div>
<div class="line"> f2 = f2*f2;</div>
<div class="line"> e=e*e/(den-1);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">if</span> (f1+f2-e < 0)</div>
<div class="line"> <span class="keywordflow">return</span> -1.;</div>
<div class="line"> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (f1+f2-e > 0)</div>
<div class="line"> <span class="keywordflow">return</span> 1.;</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <span class="keywordflow">return</span> 0.;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="comment">// Knot 3</span></div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">double</span> knot3_function (<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, <span class="keywordtype">double</span> c) { <span class="comment">// radius = 4</span></div>
<div class="line"> <span class="keywordtype">double</span> e=0.025;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> x, y, z, t, den;</div>
<div class="line"> den=1+a*a+b*b+c*c;</div>
<div class="line"> x=2*a/den;</div>
<div class="line"> y=2*b/den;</div>
<div class="line"> z=2*c/den;</div>
<div class="line"> t=(1-a*a-b*b-c*c)/den;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> x19=x, y19=y, z17=z, t17=t;</div>
<div class="line"> puiss(x19,y19,19);</div>
<div class="line"> puiss(z17,t17,17);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">double</span> f1 = z17-x19;</div>
<div class="line"> <span class="keywordtype">double</span> f2 = t17-y19;</div>
<div class="line"> </div>
<div class="line"> f1 = f1*f1;</div>
<div class="line"> f2 = f2*f2;</div>
<div class="line"> e=e*e/(den-1);</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">if</span> (f1+f2-e < 0)</div>
<div class="line"> <span class="keywordflow">return</span> -1.;</div>
<div class="line"> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (f1+f2-e > 0)</div>
<div class="line"> <span class="keywordflow">return</span> 1.;</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <span class="keywordflow">return</span> 0.;</div>
<div class="line">}</div>
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