cad/: added description to 2nd series of tests and a pointer from the 1st series

- test1/README: added pointer to 2nd series of tests
- test2/README: described findings and theories so far

cad/test1/README

@@ -1,5 +1,5 @@
-Comparison of Free scripted 3D CAD systems
+Comparison of Free scripted 3D CAD systems, part 1
-==========================================
+==================================================
 
 Werner Almesberger <werner@almesberger.net>
 
@@ -14,6 +14,10 @@ Introduction
 This file and the sources of the models can be found in
 http://projects.qi-hardware.com/index.php/p/wernermisc/source/tree/master/cad/test1/
 
+Later experiments showed that small changes to the model can lead to
+quite different results. The continuation is at
+http://projects.qi-hardware.com/index.php/p/wernermisc/source/tree/master/cad/test2/
+
 
 Objectives
 ----------
@@ -320,6 +324,15 @@ work went into the addition of fillets and chamfers. Neither of the
 two systems provides operations to automate such tasks.
 
 
+The story continues
+-------------------
+
+Later experiments showed that small changes to the model can lead to
+quite different and generally better results. The continuation of
+this evaluation is at
+http://projects.qi-hardware.com/index.php/p/wernermisc/source/tree/master/cad/test2/
+
+
 References
 ==========
 

cad/test2/README

@@ -0,0 +1,121 @@
+Comparison of Free scripted 3D CAD systems, part 2
+==================================================
+
+Werner Almesberger <werner@almesberger.net>
+
+This is the continuation of my evaluation of scripted 3D CAD systems.
+It shows new findings and improvements since the last test.
+
+
+Introduction
+============
+
+This file and the sources of the models can be found in
+http://projects.qi-hardware.com/index.php/p/wernermisc/source/tree/master/cad/test2/
+
+
+New findings and hypotheses
+===========================
+
+
+The road to hell is paved with good intentions
+----------------------------------------------
+
+The original model tried to prevent the creation of artefacts through
+rounding errors. It turned out that this isn't only unnecessary with
+Cadmium, but it massively slows down the rendering.
+
+Also, after removing these preventions the bug the "noise" parameter
+worked around no longer appeared.
+
+This is a comparison of run time (in seconds) and mesh size:
+
+                real    user    system  faces   vertices
+Before:         4901.0  4904.4     1.5  8362    3183
+After:           316.3   315.9     0.3  2942    1473
+
+This makes Cadmium only about 3.7 times slower than OpenSCAD's CGAL
+rendering, a marked improvement from the previous factor of 57. The
+resulting mesh is now less than half the size of the mesh generated
+by OpenSCAD.
+
+Furthermore, the model is much easier to design and more
+understandable without these extra tolerances.
+
+
+Context: preventing artefacts
+-----------------------------
+
+When subtracting volumes from each other, surfaces that coincide in
+both the original volume and the one subtracted from it, can remain
+as arbitrarily thin artefacts.
+
+This 2D example illustrates the effect:
+
+- given an original shape A like this
+
+  +---------------+
+  |               |
+  |               |
+  |               |
+  |               |
+  |               |
+  +---------------+
+
+- we want to subtract the following shape from it:
+
+         +--------+
+         |        |
+         +--------+
+ 
+- expecting this to result in something like
+
+  +---------------+
+  |               |
+  |      +--------+
+  |      |
+  |      +--------+
+  |               |
+  +---------------+
+
+- however, if the subtraction isn't perfectly exact, we may get this
+  instead:
+
+  +---------------+
+  |               |
+  |      +--------+
+  |      |        |<--- very thin surface
+  |      +---^----+
+  |          |    |
+  +----------|----+
+             |
+          empty space
+
+- to avoid this problem, we could enlarge the shape that is
+  subtracted:
+
+         +---------+
+         |         |
+         +---------+
+
+
+Artefacts in OpenSCAD's mesh may also be rounding errors
+--------------------------------------------------------
+
+The artefacts found in the mesh produced by OpenSCAD may also be
+caused from rounding errors. In this case, the problem would be parts
+that are fused along a common surface. As in the above example, this
+could be solved by making the parts overlap a little.
+
+Whether this is truly the source of the artefacts still needs to be
+verified.
+
+
+OpenCSG problems may be an OpenGL compatibility issue
+-----------------------------------------------------
+
+It could be that OpenCSG showing volumes to be removed just with a
+different color without actually removing them is caused by using
+OpenGL emulation in Mesa. This needs further investigation.
+
+---------------------------------------------------------------------