===== Set-theoretic operations in HyperFun =====

Now, we will use HyperFun to construct objects using set-theoretic operations, which were introduced in the previous section. If you do not understand the meaning of a term (union, intersection, subtraction), please refer to the previous pages.

STEP 1: First, let's try to display a cube 10 in length.
<code>
my_model(x[3], a[1])
{
  array box_vertex[3];

  box_vertex[1] = 0.0;
  box_vertex[2] = 0.0;
  box_vertex[3] = 0.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  my_model = box;
}
</code>

Second, let's try to polygonize and set the bounding box larger than the object in the form "-b 12" for example.
<code>hfp set.hf -b 12</code>

{{http://hyperfun.org/Tut_HTML_e/images/set_op_step1.jpg?nolink}}

STEP 2: Please translate the center of the cube to the origin. When you finish, polygonize using the command in Step 1.
<code>
my_model(x[3], a[1])
{
  array box_vertex[3];

  box_vertex[1] = -5.0;
  box_vertex[2] = -5.0;
  box_vertex[3] = -5.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  my_model = box;
}
</code>
{{http://hyperfun.org/Tut_HTML_e/images/set_op_step2.jpg?nolink}}

STEP 3: Let's try to make a sphere which has its center as the origin and a radius of 6.2. First, to display the sphere only, please type //my_model = sphere//
<code>
my_model(x[3], a[1])
{
  array box_vertex[3];
  array sphere_center[3];
  
  box_vertex[1] = -5.0;
  box_vertex[2] = -5.0;
  box_vertex[3] = -5.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  sphere_center[1] = 0.0;
  sphere_center[2] = 0.0;
  sphere_center[3] = 0.0;

  sphere = hfSphere(x, sphere_center, 6.2);
  
  my_model = sphere;
}</code>

{{http://hyperfun.org/Tut_HTML_e/images/set_op_step3.jpg?nolink}}

STEP 4: We will get the union of a box and a sphere. In HyperFun, set-theoretic union operator is |.

<code>
my_model(x[3], a[1])
{
  array box_vertex[3];
  array sphere_center[3];
  
  box_vertex[1] = -5.0;
  box_vertex[2] = -5.0;
  box_vertex[3] = -5.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  sphere_center[1] = 0.0;
  sphere_center[2] = 0.0;
  sphere_center[3] = 0.0;

  sphere = hfSphere(x, sphere_center, 6.2);
  
  my_model = box | sphere;
}
</code>
{{http://hyperfun.org/Tut_HTML_e/images/set_op_step4.jpg?nolink}}

STEP 5: We will get the intersection of a box and a sphere. In HyperFun, set-theoretic intersection operator is &.

<code>
my_model(x[3], a[1])
{
  array box_vertex[3];
  array sphere_center[3];
  
  box_vertex[1] = -5.0;
  box_vertex[2] = -5.0;
  box_vertex[3] = -5.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  sphere_center[1] = 0.0;
  sphere_center[2] = 0.0;
  sphere_center[3] = 0.0;

  sphere = hfSphere(x, sphere_center, 6.2);
  
  my_model = box & sphere;
}</code>

{{http://hyperfun.org/Tut_HTML_e/images/set_op_step5.jpg?nolink}}

STEP 6: We will subtract the sphere from the box. In HyperFun, set-theoretic subtraction operator is \.

<code>
my_model(x[3], a[1])
{
  array box_vertex[3];
  array sphere_center[3];
  
  box_vertex[1] = -5.0;
  box_vertex[2] = -5.0;
  box_vertex[3] = -5.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  sphere_center[1] = 0.0;
  sphere_center[2] = 0.0;
  sphere_center[3] = 0.0;

  sphere = hfSphere(x, sphere_center, 6.2);
  
  my_model = box \ sphere;
}</code>

{{http://hyperfun.org/Tut_HTML_e/images/set_op_step6.jpg?nolink}}

STEP 7: Subtraction of the box from the sphere.
<code>
my_model(x[3], a[1])
{
  array box_vertex[3];
  array sphere_center[3];
  
  box_vertex[1] = -5.0;
  box_vertex[2] = -5.0;
  box_vertex[3] = -5.0;

  box = hfBlock(x, box_vertex, 10.0, 10.0, 10.0);

  sphere_center[1] = 0.0;
  sphere_center[2] = 0.0;
  sphere_center[3] = 0.0;

  sphere = hfSphere(x, sphere_center, 6.2);
  
  my_model = sphere \ box;
}</code>

{{http://hyperfun.org/Tut_HTML_e/images/set_op_step7.jpg?nolink}}