This is an old Steeleye Span song, a favourite of mine, cleverly combining two 19th century weavers songs. The You Tube presentation is noteworthy for two rareities, a video that adds something to the song, and a collection of mostly intelligent comments. Open in You Tube and have a read while you listen.
Read more about the background to the songs here:
As promised in the previous post, here are further details of the PView User Defined Function (UDF), included in the IP2 spreadsheet, which can be downloaded (including full open source code) from IP2.ZIP.
The PView UDF works by multiplying the 3D coordinates of any set of points by a rotation matrix. The resulting array of 2D coordinates can be plotted in an XY (scatter) chart in the usual way. The function input and output is described in the screen shot below, together with a plot of an example; a simple box structure with a doorway, and a spiral line plotted on one wall.
PView input and plot of sample output (click for full size view)
Part of the output array is shown in the next screen shot. The function output is a single array, which must be entered as an array function.
Pview Output array
Following the previous post, I have added several new functions connected with intersections of lines and planes, and a function to generate a perspective plot from 3D coordinates. The new functions have been added to the IP2.xls worksheet, which can be downloaded (including full open source code) from IP2.ZIP.
Note that all the functions return results as an array, and must be entered as an array function:
The new functions are shown in the screen shots below (click any image for full size view):
PDist3D - Perpendicular distance from a point to a plane
PlaneCoeff; Coefficients of a plane specified by 3 points
IPPlaneLine: Intersection point of a plane and a line segment
IPPlanePlane: Intersection line of two planes
PView: Perspective projection of 3D Lines, showing IPPlanePlane output
Further details of the PView function will be given in the next post.
Following a discussion at the Eng-Tips Forum, I have written an Excel User Defined Function (UDF) to find the intersection point of two 3D line segments. The UDF has been added to the IP2 spreadsheet, which is available for free download (including full open source code) from IP2.ZIP.
The method of calculation of the intersection point is:
The screen shots below show for two 3D line segments:
The intersection point found using the new UDF (IP3D):
IP3D example
On spreadsheet calculation for the same two lines, using the UDF IP() (Example 2), and using only built in Excel Functions (Example 3)
On spreadsheet calculation of IP
and graphs of the two lines projected on to the three axis planes:
Projected intersecting lines
What do laterally loaded piles:
Pile loading test
and a safety device for walking on icy pavements:
have in common?
Apart from their obvious utility, both are the subject of learned papers, freely available at the Virginia Tech Digital Library and Archives, along with 18,762 Electronic Theses and Dissertations.
For the full papers see:
Investigation of the Resistance of Pile Caps to Lateral Loading and
Introducing Engineering Design Through an Intelligent Rube Goldberg Implementation
or search the entire archive at: Virginia Tech Digital Library and Archives
Newton Excel Bach, not (just) an Excel Blog 