9.5.2

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OBJECTS MENU • SPECIAL MODELING TOOLS • 295
Figure 1: A “perfect”
polygon.
Figure 2: The quadrangle
is no longer a rectangle.
However, all the points
are on the same plane
— the quadrangle is still
planar.
Figure 3: Point B has
been moved into the
depth plane. Now, the
polygon is non-planar.
Figure 4: The angle at
point B is greater than
180° — the polygon
overlaps itself.
Figure 5: All the points
for this polygon are on
a line.
Figure 6: Polygons in
CINEMA 4D have their
own coordinate system.
For planar quadrangles, if the interior angle at points B or D is greater than 180°, problems can occur
when rendering — this is because the polygon overlaps itself, as in Figure 4 above. Another problem
arises if all of the polygon’s points are on the same line. In this case, a surface normal cannot exist
and the polygon is called a degenerated polygon, illustrated in Figure 5.
Polygon coordinate system
Polygons in CINEMA 4D have their own coordinate system, as illustrated in Figure 6. You cannot see
this system in the viewports, but it is important to be aware of it when using modeling tools such as
Matrix Extrude. The origin of the polygon coordinate system is located at the centre of the polygons.
The X-axis is along the line between A and B. The Z-axis is the normal. The Y-axis is perpendicular to
the XZ plane.