How CAD handles solid geometry
In this tutorial I will show why surface and solid models are identical and the encapsulating surface mesh contain all the information of the model.
In other words: Solid geometry is actually surface geometry!
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Step 1:
As the name implies, Solidworks is geared to produce solid geometry. Solid geometry consists of external surfaces that are knitted into a watertight mesh, meaning a mesh without gaps. Every single edge, of an object with more than one outer surface, is defined by the precise intersection of two surfaces.
Draw two cubes by a solid extrusion. This will result in two identical objects.
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Step 2:
We will now convert one of the cubes into surface geometry. There is no direct command in Solidworks to do this; that would be the inverse command to ‘Thicken -> Create solid from enclosed volume’.
One way to create a surface model instantly, is to delete a face of an object with more than one face. Let’s first copy the front face of the right cube with the Surface-Offset command using a distance of 0. This is the same as copying the face. The dialog box even changes name from ‘Offset Surface’ to ‘Copy Surface’.
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Step 3:
The copied face is located exactly in the same place as the existing face. This will often result in a strange moiré-pattern when you click on the faces.
Hide the new face in order to be able to select the front face again.
Delete the front face by using the command ‘Delete Face’. You can now see the inside of the right cube and Solidworks now no longer regards the object as a solid.
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Step 4:
You will notice that I use a bright red outline to signify open edges. This is a general colour scheme setting that I suggest you always use, because it makes open edges much easier to spot and you really do not want any open edges when converting surface geometry to solid geometry, because it will not work. The geometry needs to be ‘watertight’.
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Step 5:
Show the copy of the front face again.
Now use knit the open square and the copied front face into one watertight mesh with the ‘Knit’-command. The Knit-command is to surfaces what the ‘Combine’-command is to solids. But do not check the box ‘Create solid from enclosed volume’.
You will see that the red outlines disappear and the two cubes are 100% identical. But the one on the right is a surface-object and the one on the left is a solid object. So the only difference is that Solidworks treats the inside of the solid cube as solid material even though there is nothing there! It is the direction of the face-normals of the surface geometry that tells Solidworks which areas should be considered solid.
Some 3D software, such as Rhino, allows you to manually view and edit the Face-normals:
So surface and solid models are identical and the encapsulating surface mesh contain all the information of the model. In other words: Solid geometry is actually surface geometry!
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Step 6:
Turning a watertight surface mesh into a solid object is very simple by using the Thicken-command as mentioned. This will immediately make Solidworks block access to the internals of the geometry, as seen by how the cut views change.
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Step 7:
This brings me to the explanation of how the Feature: ‘Delete Face with Delete and Patch selected’ works.
1) The internal, selected surfaces are deleted.
2) This instantly turns the model into a surface model consisting of one holed outer surface
3) This surface can be repaired with the command ‘Untrim Surface’ with the option ‘Merge with original’ selected.
4) This is so, because all surfaces have an underlying UW-grid that determines their shape. This UW-geometry can be visualised by generating Face-curves, command: Tools->Sketch Tools->Face Curves.
5) So all sound geometry is overbuilt; The surface can be extended and used to patch holes and extend its boundaries. It is self-healing and self-contained. But bad geometry has singularities and edges that can’t be extended; this is one major reason why models can’t be thickened from surface to solid.
6) The Untrim Surface command results in a perfect, watertight surface, but it is still a surface and needs to be turned into a solid.
7) The Thicken-command creates the wanted end result and this process is what the Command: ‘Delete Face with Delete and Patch selected’ does and there is no other way because the internal of a solid body is completely empty and has no knowledge about the outer geometry!
