**3D Geometry**

- 3D Analogue to the Trapezoid (part 1): Irregular Triangular Prism
- Volume of an Irregular Triangular Prism: Proof of formula in part 1
- 3D Analogue to the Trapezoid (part 2): Frustum of a Pyramid/Truncated Pyramid
- 3D Analogue to the Trapezoid (part 3): Conditions for applying volume formula for the frustum of a pyramid: 2 parallel faces ("top" and "bottom"), consecutive edges of "sides" coplanar.
- Volume of a Tetrahedron: A tetrahedron is a minimal 3-dimensional solid much like triangles are a minimal 2-dimensional area. The volume calculation is one-sixth of the absolute value of the scalar triple product.
- The Un-Pyramid: If you want to know the volume of a
*really*irregular triangular prism, you may be looking for the volume of a*skew-cut slanted pyramid with a triangular base*. - Unfolded Approximation to a Hemisphere: A Maxima program for calculating the fold-creases for an approximated hemisphere. A flexible substrate could be cut or folded (as appropriate) at these lines to produce a segmented approximation to a hemisphere. (Segmented like an orange.)
- Rotation of Planar Regions: A Polyhedron in AutoCAD: How to rotate faces of a polyhedral surface together by using appropriate construction lines. Demonstration of the creation of a polyhedron.
- Angle Between Intersecting Planes: It matters how you look at an angle when you're working in 3D.
- Defining a User Coordinate System: This post isn't about the AutoCAD commands, but about the mathematics involved.
- Introducing the Twisted Plane: This is also called bilinear interpolation.
- Volume Under a Twisted Plane: A simple formula that you might even guess.
- Snap Perpendicular Code: Find the point on a line which is closest to a given point (not on the same line).

**AutoCAD (DIY style)**

- Defining a User Coordinate System: What's really involved in defining a UCS?
- Snap Perpendicular Code: Find the point on a line which is closest to a given point (not on the same line).
- Snap Tangent: Given a start point, S, and a circle, find the point(s), P, on the circle (or arc) such that the line through SP is tangent to the arc.
- Find the Intersection of a Plane with a Line
- Bulge Value (code 42) in LWPolyline: understanding the bulge value in light weight polyline lines.
- Dynamic Zoom in LispWorks' CAPI: although this is specific to a certain API, the method can be transferred to any environment. This is the classic navigation method used by the current generation of CAD users and available in some other environments as well (in some form).
- Polylines: Radius-Bulge Turnaround: Go from the bulge value to the radius of an arc section of polyline and back again. Convert either way.
- Plotting a LWPOLYLINE in Maxima: You would never need to do this to make your own CAD system, but it might be fun anyway.

**Building Science**

- Convective Heat Transfer on a Building Envelope (Wind Chill?): The wind chill equation for human skin cannot be naively applied to a building envelope. It has everything to do with temperature difference.
- Convective Heat Transfer: Buildings in the Cold: Heat flux is a physical quantity and is a more useful means of determining the effect of wind on objects of arbitrary surface temperature. It is best to avoid the idea of modeling the effects of wind by using a colder temperature than ambient. Actually, the wind chill concept is backwards if you are trying to use steady-state heat equations. The windy condition is normal. The no wind condition results in the exterior of the building being
*warmer*than ambient (and warmer than the high wind condition). - Degree of Saturation vs Relative Humidity: These are easily confused measures which ASHRAE Fundamentals breezes through. I took the time to work out the details.