Torabi Architect.
Implicit Surface Documents Apr 2009
arrowBounding box rollout .

 

The uniform polygonization algorithm decomposes the bounding box of the implicit shape using a simplified cell complex. It then identities the set of cells that are intersected by the implicit surface and for each of these cells, it generates an element of the polygonal mesh approximating the surface. These settings deal with size and resolution of implicit bounding box.
Parameters from and to defines the restricted area that implicit surface must be polygonized.
There are three groups of these parameters that allow you to set the bounding box dimensions separately in three dimensional space. The bounding box trims implicit surface in intersection of its six faces. That can make truncated objects in some cases. To avoid this problem you may need to adjust the size of the bounding box to fit the whole object inside. In this case implicit surface should create a solid object like sphere in the example.

  Implicit Bounding box rollout

sphere by radius 3 units has been generated based on implicit presentation:


x^2+y^2+z^2-9=0
As you can see in the image intervals [-2.5, 2.5] cannot fit the whole object and it makes truncated sphere.

Subdivision parameter set the number of partitions that intersect with implicit surface in the specific direction. There are three different subdivision values that enable you to control density of mesh in three dimensional space separately. Another reason for having three groups of these parameter is that you can make objects with any proportion you want while you keep control of the subdivisions on areas that needs more or less partitions.
sphere in bounding box

Example 1: The surface doesn’t need any subdivision along Z direction because the formula is independent of Z parameter (extrusion). We can use higher value of subdivision for X and Y directions to achieve smooth result.

 

uniform subdivisionno subdivision along z axis

Left:X,Y,Z-subdivision:13 time: 4.368 seconds

Right :X-subdivision:41 Y-subdivision:71 Z-subdivision:1 time: 2.6 seconds  

x^2+y^2-2*x*sin(x*y)-4=0

 

 
final result

Example 2: surface wanted to be in linear proportional object.  The subdivisions have been set to make the surface as much as possible smooth and optimized in the same time.

Example 2 setting

 

example 2

sin(x-y+z)+cos(2*y)+sin(3*z)=0

Example 3:

The amount of subdivision can also affect on topology in areas that implicit surface doesn’t reach to a good level of details.

Left:lower subdivision amount has created two separate surface


Right: higher subdivision amount makes one continues surface

Implicit Example 3

  x_y*(x-z^3-1)+z^4-z^2=0

Example 4:

Sometimes a minor adjustment is needed to remove artifacts. x*(z+1)-y*(z-1)

Left :X,Y and Z subdivisions: 11,12,11

Right :X,Y and Z subdivisions:11,11,11

 

implicit example 4
   
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