Dean’s Pants

Here are a few useful formulas I’ve derived in the time I’ve squirreled away building in SL. I thought they might be useful to someone out there, and I’d love to have them here for my own reference instead of in the middle of what looks like an high school freshman’s geometry notebook hidden amongst diagrams of parallelograms and triangles. Also of note, I deal only with my ruler in world coordinates, not local or reference.

(Big thanks to SL friend Sanford Foulon who put me on the right track on calculating the visually deceiving values of Y taper.)

To calculate the angle created by applying Y shear to a box primitive:

arc tan ((y * shear) / z) = theta

• y is “Y” size.
• shear is the value in the “Y” box under “Top Shear”.
• theta is the angle created between the XZ plane and the sides of the box originally parallel to the XZ plane (before shearing).

To calculate the angle created by applying Y taper to a box primitive:

arc tan ((y * taper) / (2z)) = theta

• y is the “Y” size.
• taper is the value in the “Y” box under “Taper”.
• theta is the angle created between the XZ plane and the sides of the box originally parallel to the XZ plane (before tapering).

The values of Y sheer and Y taper that will give you a perfectly upright (i.e., parallel to the XZ plane) side:

taper = 2 sheer

If anyone would care to see me derive these or show visual examples, please just comment.