Calculating panel angles

Some structures involve the folding of two-panel angles, in which adjacent panels are folded at angles other than 90 degrees. To ensure that they fold correctly, you need to calculate the angles between the folding panels. You do this with the angle3d function.

The angle3d function

In the function, you enter values for the angles — alpha, beta and gamma — between three merging edges. The function has the following syntax:

angle3d(gamma; beta; alpha)

The panels and angles that define a three-panel corner

Gamma, alpha and beta are the angles at which each panel folds at the corner. The arguments are divided by semicolons, and decimal points are used for angle fractions. In the syntax, the order of the angles belonging to the two panels of the calculated angle can be switched without affecting the calculation result.

IMPORTANT

When you use the function to set the folding of a particular panel, it is essential that the angle of the panel to be folded and that of the panel receiving the folding are entered first in the argument string; the angle value of the third panel is entered last. On their side, the positions of the first two angle values can be switched without consequence to the function's result.
For correct folding, ensure that while entering the function you use the decimal point and list separator formats set in your system's regional settings.

Setting folding angles in three-plane corners with the angle3d function

In the step in which you want to set a folding, go to the the Parameter Data column (in the middle vertical section of the tabular area), and there type the formula with the corresponding angle values (pictured).

The 1up with a map of its panels and angles

The expressions that control the folding of each panel. Notice the order of entering angle values for each panel.

NOTE: In the example, the angle calculated with the angle3d function is subtracted from 180 degrees, because before folding the two panels, they were parts of the same plane.

Run the folding sequence to view the result.