T-FLEX Parametric CAD. Fundamentals. 2D Design

Functions
The resulting function construction, as in the case of splines, is a polyline. The “Start” and “Finish”
parameters define respectively the start and end values of the variable parameter, defining the beginning and
the end ranges of calculating the polyline coordinates.
The “Polyline generation” group of parameters defines the way of calculating the intermediate point
coordinates when creating the polyline:
Equal steps. This way implies the variable parameter to change from the start to the end value in equal
increments. The number of steps is specified by the user. It defines the number of segments in the
polyline being created. The more the number of steps, the higher-accuracy will be the polyline
representation along the bends and the longer time will take various operations handling the created
polyline.
The number of points used in the polyline creation is always equal to the number of segments plus one,
and, therefore, is greater by one than the specified number of steps. The first point always corresponds to
the start value of the variable parameter. The coordinates of the rest of points are based on the values of
the variable parameter defined by the formula:
Current value = Start value + I * Step
Step = (End value – Start value) / Number of steps,
I is the current step number (1,2,…, Number of steps).
If polyline point coordinates are calculated using a database, the value of the variable parameter is
usually the line number in the database. In this case, the current value of the variable parameter is
replaced by the largest integer less than or equal to it. As a result, data could come at uneven steps
from the database. To avoid this, always define the function parameters in such a way that the
number of steps was equal to the difference between the end and the start values of the variable
parameter.
Optimized to curvature. One could notice that the above approach is not always convenient for curves of
complex shape, as the tessellation density was constant along “smooth” and “curved” zones
unnecessarily. Optimization to curvature yields finer tessellation along high-curvature zones and,
respectively, coarser otherwise. The criterion of the accuracy and quality in this case is the “Tolerance”
parameter that defines the maximum permitted deviation of the calculated polyline coordinates from the
true curve coordinates. The lesser is the tolerance, the more segments will be in complicated zones of the
curve.
Once the polyline is built, it can directly be used as a construction entity. However, a possibility is provided
for using the calculated polyline points for spline creation. For this, turn on the option “Generate spline
from polyline”, define its type and the number of tessellation segments between two neighboring points of
the spline for the spline tessellation polyline. This tessellation polyline will be the final output construction
entity. Spline generation may be needed when a smooth curve is desired, while the number of defining points
is limited.
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