Calculator Programs For Stamp Collectors

Author:	Mitch Richling
Updated:	2024-11-21 16:49:41

1. Metadata
2. Introduction
3. The Main Menu
4. [CAL]: Image Calibration
5. [LENG]: Measuring lengths
6. [PERF]: Measuring & Converting Perforations
- - 6.0.1. Example: Measuring Standard & Kiusalas Perforations
7. [ANGL]: Measuring Angles
- 7.1. Examples
- 7.2. Philatelic Application: Parallel Lines (Take 1)
  - 7.2.1. Example
8. [DCRD]: Design Coordinates
- 8.1. Example
9. [QUAD]: A Philatelic Power Tool
- 9.1. Philatelic Application: Parallel Lines (Take 2)
- 9.2. Philatelic Application: Rotary Press vs. Flat Plate (Take 2)
10. Code
- 10.1. Menu Code
- 10.2. Local Functions
11. EOF

1. Metadata

The home for this HTML file is: https://richmit.github.io/hp42/phil.html

Files related to this document may be found on github: https://github.com/richmit/hp42

Directory contents:

`src`	-	The org-mode file that generated this HTML document
`src_42s`	-	Ready to convert source listings for 42s code in this document
`docs`	-	This html document and associated PDF
`bin`	-	Importable RAW program files

2. Introduction

This application might be best described as an image metrology tool with a focus on philatelic applications. It supports a few standard measurements useful for philately (length & angle) as well as some specialized functionality for philatelists (perforation measurement, kiusalas gauge conversion, Thirkell & design coordinates, design size, & parallel edge checks). While I do most of this kind of work on my laptop with ImageJ (Fiji actually), I frequently use this calculator application with the digital microscope on my "stamp table" or when I'm away from my laptop.

MS	ML	Menu	Description	Require Cal?
LBL 85	LBL 92	ANGL	Angle given complex pixel coordinate	Never
LENG:PX>D	LBL 91	LENG:PX>D	Length given real pixel count or complex pixel coordinate	Always
LENG:D>PX	LBL 66	LENG:D>PX	Pixel count given Length or complex coordinate	Always
LENG:▒▒▒▒		LENG:▒▒▒▒		N/A
LENG:▒▒▒▒		LENG:▒▒▒▒		N/A
LENG:▒▒▒▒		LENG:▒▒▒▒		N/A
LENG:CAL	LBL 95	LENG:CAL	Set or display image calibration	Never
QUAD:UL	LBL 57	QUAD:UL		Never
QUAD:UR	LBL 58	QUAD:UR		Never
QUAD:LR	LBL 59	QUAD:LR		Never
QUAD:LL	LBL 60	QUAD:LL		Never
QUAD:▒▒▒▒		QUAD:▒▒▒▒		N/A
QUAD:CAL	LBL 95	QUAD:CAL	Set or display image calibration	Never
QUAD:∡TB	LBL 62	QUAD:∡TB	Compute angle difference between top an bottom sides	Never
QUAD:∡LR	LBL 63	QUAD:∡LR	Compute angle difference between left an right sides	Never
QUAD:WIDE	LBL 64	QUAD:WIDE	Compute width (left, right, average)	Always
QUAD:TALL	LBL 65	QUAD:TALL	Compute height (top, bottom, average)	Always
QUAD:▒▒▒▒		QUAD:▒▒▒▒		N/A
QUAD:▒▒▒▒		QUAD:▒▒▒▒		N/A
PERF:D<>P	LBL 96	PERF:D<>P	Convert between perforations & distance	Only if D=px
PERF:P<>K		PERF:P<>K	Convert between perforations & Kiusalas	Never
PERF:LBL 87	LBL 98	PERF:C:??	Set perforation count (C)	Never
PERF:LBL 89	LBL 99	PERF:D:??	Cycle distance units: px mm mil um in cm	Never
PERF:LBL 86	LBL 88	PERF:I:??	Cycle image length units when D=px: mm mil um in cm	Never
PERF:LBL 67	LBL 95	PERF:CAL	Set or display image calibration when when D=px	Never
DCRD:PX>DC	LBL 75	DCRD:PX>DC	Design Coordinate given complex pixel coordinate	Always
DCRD:DC>PX	LBL 49	DCRD:DC>PX	Complex pixel coordinate given Design Coordinate	Always
DCRD:T>MM		DCRD:T>MM	Thirkell grid (letter+number) to coord in millimeters	Never
DCRD:MM>T		DCRD:MM>T	Coord in millimeters to Thirkell grid (letter+number)	Never
DCRD:ORIG	LBL 90	DCRD:ORIG		N/A
DCRD::CAL	LBL 95	DCRD:CAL	Set or display image calibration	Never
CAL	LBL 95	CAL	Set or display image calibration	Never

Notes:

Please ignore the first two columns in the table – they are used to auto-generate the menu code for the application.
Image calibration is not required all the time – see the last column of the table
In examples I will generally leave off key strokes to get to the correct menu. i.e. I'll say [PX>D] instead of [LENG] [PX>D]
Parameter setting functions don't drop the stack. Hitting [SHIFT] before one of these keys will report the current value.
Functions like [PX>DC] that require a complex argument will do a [COMPLEX] when given real arguments.

4. `[CAL]`: Image Calibration

Note: The [CAL] function is located on most menu pages so it is always handy.

Image coordinates are measured in pixels. The upper left point is pixel \((0, 0)\). X values increase as we move to the right. Y values increase as we move down. This is the most common coordinate system used in computer graphics.

This application works with images with square pixels only. When using a scanner make sure the X & Y DPI settings are the same!

Calibration is retained between runs of the application. If the application is started up without calibration data, then a default will be set (2400 DIP scan with units in mm resulting in a calibration factor of 94.4881889764).

4.1. Known DPI

When using a scanner, the scanner DPI settings may be used to roughly calibrate an image.

4.1.1. Examples

2400 DPI scans and using inches as the unit: 2400 [ENTER] 1 [CAL]
2400 DPI scans and using mm as the unit: 2400 [ENTER] 25.4 [CAL]
1000 DPcm scans using mm as the unit: 1000 [ENTER] 10 [CAL]

4.2. Using a target

Including a calibration target in the image field is the most common way to calibrate microscope images. For high magnification expensive, etched glass reticle are generally used. For the lower magnifications normally used my stamp collectors, a simple scale may be included in the image frame. I simply lay the stamps on top of a plastic ruler.

When using a calibration target it is rare that the target is precisely lined up horizontally or vertically, so providing a simple pixel count for it's length is impossible. Instead we provide the pixel coordinates of two points on the target.

4.2.1. Example

We have a 1mm ruler in the frame. The 0 mark of the ruler is at pixel coordinates (123, 456) and the 3 mark of the ruler is at pixel coordinates (567, 345). If we wish to work directly in mm, then we do this:

Enter the 0 coordinate: 123 [ENTER] 456 [COMPLEX] – assuming "RECT" mode
Enter the 1 coordinate: 234 [ENTER] 345 [COMPLEX]
Enter physical distance: 3
Press the CAL menu key: [CAL]

If we wanted to work in cm instead of mm, we would use a distance of 0.3 instead.

If we wanted to work in mil instead of mm, we would use a distance of 118.11 instead

4.3. Using a Stamp!

The techniques documented here can be very useful, but must be used with care. Stamp paper can warp and deform – depending on printing process, storage conditions, etc…

Suppose you have an image of a stamp (perhaps from an auction website) that should have an design width of 22mm. You determine the upper left of the design is at pixel coordinates (300, 100), and the upper right of the design is at pixel coordinates (536, 101). Also suppose you wish to work in inches (you will see why in a moment):

322 [ENTER] 125 [COMPLEX] 582 [ENTER] 126 [COMPLEX] [-] 22 [ENTER] 25.4 [÷] [CAL]

Now notice the value on the screen is 300.1840. Many stamp images posted on auction sites are scanned at 300 DPI, and the fact this is so close to 300 tells us that we probably have a 300 DPI scan. We can now use 300 as our calibration data, or use the computed value.

You can use this technique with any feature of a stamp with a known measurement – not just design size. For example, some souvenir sheets have very precise paper sizes allowing the width or height of the paper to be used for calibration.

The perforations may also be used as a calibration aid. For example if we know the stamp in question has a perforation of 70 on the Kiusalas gauge, then we know 10 perforations should measure very close to 16mm.

4.4. Calibration factor

The "calibration factor", returned by [SHIFT] [CAL], is the current image calibration data in units of pixels/length.

4.4.1. Examples

2400 DPI scans and using inches as the unit: 2400
2400 DPI scans and using mm as the unit: 94.4881889764
1000 DPcm scans using mm as the unit: 100

5. `[LENG]`: Measuring lengths

5.1. Horizontal or Vertical Lengths

For horizontal & vertical lengths in the image, one simply needs to provided a pixel count as a real number.

For stamps it can be handy to rotate the image so that interesting lengths are at 0 or 90 degrees. For example, when working with US Washington-Franklin issues it is a good idea to line up the design frame with the horizontal.

5.1.1. Examples

2400 DPI image working in inches:
- 1200 [PX>D] → 0.5
- 2400 [PX>D] → 1.0
The same image working in mm:
- 1200 [PX>D] → 12.7
- 2400 [PX>D] → 25.4

5.2. Generic distances

To measure the length of a non-horizontal/vertical line, we provide a complex number to the [PX>D] function. One might think of the coordinates as specifying a line from the origin, upper left image pixel at (0, 0), to the given coordinates. Alternately one might think of the coordinates as the width & height of the line. The signs of the coordinates are ignored – i.e. the absolute value of each coordinate is used.

          * P2  -            (0, 0) *
         /      |                    \
        /       |                     \
       /        h                      \
      /         |                       \
     /          |                        \
P1  *           -                         * (x, y)
    |--w--|

To measure the length of a line segment given by two points, we simply enter both points as complex numbers and subtract them. We then give the difference to the [PX>D] function.

5.2.1. Examples

For a 2400 DPI image working in mm (2400 [ENTER] 25.4 [CAL]):
- 123 [ENTER] 456 [COMPLEX] 234 [ENTER] 345 [COMPLEX] [-] [PX>D] → 1.7300 mm
For a 2400 DPI image working in inches (2400 [ENTER] 1 [CAL]):
- 1 [ENTER] 1 [COMPLEX] 100 [ENTER] 100 [COMPLEX] [-] [PX>D] → 0.0583 in
To compute the length in raw pixels, set cal to 1 (1 [ENTER] [CAL]):
- 1 [ENTER] 1 [COMPLEX] 100 [ENTER] 100 [COMPLEX] [PX>D] → 140.0 PX

5.3. Philatelic Application: Rotary Press vs. Flat Plate (Take 1)

For an alternative approach see: Philatelic Application: Rotary Press vs. Flat Plate (Take 2)

5.3.1. Example 1

Scenario: We have a Washington-Franklin, and we would like to know if it was printed on a rotary press. We have a 2400 DPI scan.

For reference, here are the measurements for the various printing options:

Press	Width	Height
Flat	18.5-19mm	22mm
Rot Vert	18.5-19mm	22.5-23mm
Rot Horz	19.5-20mm	22mm

5.3.1.1. Method 1 (Stamp design not aligned)

We begin by locating the coordinates for three frame corners:

Corner	Coordinates
Upper left	(150, 160)
Upper right	(1903, 161)
Lower left	(149, 2239)

Calibration. If we have not already calibrated, we need to do that first
- 2400 25.4 [CAL]
Now we compute the width of our stamp design
- 150 [ENTER] 160 [COMPLEX] [ENTER] [ENTER] 1903 [ENTER] 161 [COMPLEX] [-] [PX>D] → 18.55 mm
- Note we duplicated the first coordinate so we can use it later…
Now we compute the height of our stamp design
- [X<>Y] 149 [ENTER] 2239 [COMPLEX] [-] [PX>D] → 22.00 mm

Our stamp is 18.55mm x 22.00mm – and so it must be a flat plate stamp.

5.3.1.2. Method 2 (Stamp design aligned)

In this case the lower and upper frame lines of the design are perfectly horizontal. In this case we only need two points.

We begin by locating the coordinates for three frame corners (UL & LR, or UR & LL):

Corner	Coordinates
Upper left	(150, 160)
Lower right	(1902, 2240)

Calibration. If we have not already calibrated, we need to do that first
- 2400 25.4 [CAL]
Now we compute the width of our stamp design
- 150 [ENTER] 160 [COMPLEX] 1902 [ENTER] 2240 [COMPLEX] [-] [COMPLEX] [PX>D] → 22.01mm
Now we compute the width of our stamp design
- [Rv] [Rv] [PX>D] → 18.54mm

Our stamp is 18.54mm x 22.01mm – and so it must be a flat plate stamp.

6. `[PERF]`: Measuring & Converting Perforations

Perforations are usually measured in units of perfs/2cm; however, other units are used in some specialized areas of philately. For example, the Kiusalas gauge measures perforations in units of mil/perf – a more natural measure for USPS bureau issues. This application provides tools to convert between standard perforations and Kiusalas perforations ([P<>K]).

Also provided is a way to approximate standard perforation measurement by measuring the distance (D) spanned by a number of perforations (C).

Below is an illustration of how to measure distance and count perforations. First pick a recognizable feature in your starting and ending perforations, and measure the distance between them. The first distance in the illustration measures the distance between "perf bottoms". Take careful note of how we count – the number of "bottoms" in this case.

##                                                                                                              ##
##      | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |     ##
##      |. . . . . . . . . . . . . . . . . . . . . . C = 4 . . . . . . . . . . . . . . . . . . . . . . . .|     ##
##      | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |     ##
##      |. . . . . ------- . . . . . . . .-------. . . . . . . . ------- . . . . . . . .-------. . . . . .|     ##
##      | . . . .-/       \-. . . . . . -/       \- . . . . . .-/       \-. . . . . . -/       \- . . . . |     ##
##      |. . . ./           \. . . . . /           \ . . . . ./           \. . . . . /           \ . . . .|     ##
##      | . . ./      1      \. . . . /      2      \ . . . ./      3      \. . . . /      4      \ . . . |     ##
##      |. . . |             | . . . .|             |. . . . |             | . . . .|             |. . . .|     ##
##      +------+             +--------+             +--------+             +--------+             +-------+     ##
##                    |--------------------------- D = Distance ---------------------------|                    ##
##             |--------------------------- D = Distance ---------------------------|                           ##
##                           |--------------------------- D = Distance ---------------------------|             ##
##                                                                                                              ##

Distance (\(D\)), perforation count (\(C\)), traditional perforations (\(P\)) measured in perfs/2cm, and Kiusalas perforations (\(K\)) measured in mil/perf are related:

\[ K = \frac{5000 D}{127 (C - 1)} \] \[ P = \frac{20 (C - 1)}{D} \] \[ P = \frac{100000}{127 K} \]

6.0.1. Example: Measuring Standard & Kiusalas Perforations

Scenario: We have a Washington-Franklin that should be perforated Kiusalas 70, and we wish to verify perfs. We have a 2400 DPI scan.

We find the coordinate of the first perf bottom at (150, 160) and 10 perfs over we have another bottom at (1662, 161).

Calibration. If we have not already calibrated, we need to do that first
- 2400 25.4 [CAL]
Now we compute our perfs
- 150 [ENTER] 160 [COMPLEX] 1662 [ENTER] 161 [COMPLEX] [D<>P] → 11.24859
Next we compute the Kiusalas value
- [P<>K] → 70.0000

And it looks like our stamp really is perforated Kiusalas 70!

7. `[ANGL]`: Measuring Angles

Angles are measured with respect the horizontal – the negative of the argument of the complex number representing the pixel coordinate. We use the negative because pixel y-coordinates go up in the down direction.

TIP: [ANGL] requires a complex number. If you give it something else it will call COMPLEX to convert the lower two stack levels into a complex number. This saves the user two key presses – i.e. you don't have to hit [SHIFT] [COMPLEX] to convert to complex before you use [ANGL].

7.1. Examples

123 [ENTER] 123 [COMPLEX] [ANGLE] → -45 – assuming degree angle mode

7.2. Philatelic Application: Parallel Lines (Take 1)

For an alternative approach see: Philatelic Application: Parallel Lines (Take 2).

Why?

Verify that the two cut edges of a US coil stamp are parallel
Verify that perforations are parallel
Verify that the cut edge of a souvenir sheet is parallel with an engraved margin line
Verify that design edges are parallel – to make sure an image has no perspective distortion

7.2.1. Example

P1 *    * P3                                       P1 *    * P3
   |    |              P1 *-----* P2                 /    /
   |    |      _OR_                     _OR_        /    /
   |    |              P3 *-----* P4               /    /
P2 *    * P4                                   P2 *    * P4

Angle 1: P1.x [ENTER] P1.y [COMPLEX] P2.x [ENTER] P2.y [COMPLEX] [-] [ANGLE] [STO 00]
Angle 2: P3.x [ENTER] P3.y [COMPLEX] P4.x [ENTER] P4.y [COMPLEX] [-] [ANGLE] [STO 00]
Difference: [RCL- 00] [ABS]

The result will be the absolute angle by which the two lines differ – i.e. if we have parallel lines it should be 0.

8. `[DCRD]`: Design Coordinates

Design Coordinates are used to locate points on a stamp referenced to the design. A few different schemes are in use with the "Thirkell" philatelic position finder probably the most popular. Most of these systems work the same way. They use the upper left corner of the stamp design as the origin of a coordinate system – i.e. they measure distance to the right and down from the upper left corner of the design. The most common unit of measurement is millimeters; however, a few also add a grid system on top. For example the Thirkell uses a 3mm grid.

+^^^^^^^^^^^^^^^^^^^^^^^^+
(          * P3          )
(   O *------------+     ) 
(     |            |     )   - Design coordinates are used locate points on the stamp
(     |            |     )    - for a point (x,y) is (x-O_x, y-O_y)
(     |   * P1     |     )    - The most common units are mm
(     |            |     )    - Axis orientation: Coordinate values get bigger to the right or down
(     |            |     )    - These kinds of coordinates are frequently used to locate plate flaws                                                               
(     |            |     )  - Special cases                                                                                                                        
(     +------------+     )    - Points above or to the left of O will have negative coordinates -- Ex: P3                                                          
(                   P2 * )    - Points need not be inside the design -- Ex: P2 & P3                                                                                  
+vvvvvvvvvvvvvvvvvvvvvvvv+

When working with design coordinates you must first tell the application the coordinates of the origin by entering a complex number representing the pixel coordinates of the upper left corner of the design and hitting the [ORIG] button. If you shift press this button then it will display the current origin.

Now you can convert pixel coordinates to and from design coordinates.

Two functions are also available to convert standard millimeter design coordinates to and from Thirkell coordinates: [MM>T] & [T>MM]. Note that Thirkell coordinates are reversed – i.e. the first coordinate (the letter) is on the vertical axis and the second coordinate (the integer) is on the horizontal axis. These functions work in millimeters directly, and do not require the image to be calibrated; however, if you wish to use these functions in concert with [PX>DC] & [DC>PX] then you must calibrate your image and work in millimeters!

TIP: [MM>T], [PX>DC] & [DC>PX] require a complex number. If you provide something else they will call COMPLEX to convert the lower two stack levels into a complex number. This saves the user two key presses – i.e. you don't have to hit [SHIFT] [COMPLEX] to convert to complex before you use [ANGL].

8.1. Example

Scenario: You wish to report a new plate flaw to the nice people that make the Zumstein catalog using the Thirkell grid. We have a 2400 DPI scan.

First we locate the upper left hand corner of the design and our plate flaw:

Item	Pixel Coordinates
Upper left corner of design	(150, 160)
Center of our plate flaw	(713, 956)

Calibration. If we have not already calibrated, we need to do that first
- 2400 25.4 [CAL]
Next we enter the coordinate menu
- [DCRD]
We enter the origin point
- 150 [ENTER] 160 [ORIG]
Now we enter the coordinates of our flaw
- 713 [ENTER] 956 [PX>DC] → 5.9584 + 8.424333i mm
Finally we convert this to Thirkell
- [MM>T] → Thirkell: 2C

9. `[QUAD]`: A Philatelic Power Tool

This is a handy tool that automates some common computations:

Compute width & height of a rectangular stamp design
Determine if two lines are parallel
Determine if four points Determine a parallelogram – i.e. are the opposite sides parallel

It is called "QUAD" because it works with four points which will form the corners of a quadrilateral – also "QUAD" avoid confusion with the built in command RECT. Below is a picture of the geometric situation.

       P1 *----------------* P2
         /                /      - Are P1-P2 & P4-P3 parallel?  i.e. is the angle between them zero?
        /                /       - Are P1-P4 & P2-P3 parallel?  i.e. is the angle between them zero?
       /                /        - What are the lengths of P1-P2 & P4-P3?
      /                /         - What are the lengths of P1-P4 & P2-P3?
     /                /          
    /                /
P4 *----------------* P3

When using the QUAD tool, the first step is to input the corner coordinates via [UL], [UR], [LR], & [LL].

In this context:

Menu	Corner	Point Number
UL	Upper Left	Point P1
UR	Upper Right	Point P2
LR	Lower Right	Point P3
LL	Lower Left	Point P4

TIP: The data entry keys ([UL], [UR], [LR], & [LL]) each require a complex number. If you provide something else they will call COMPLEX to convert the lower two stack levels into a complex number. This saves the user two key presses – i.e. you don't have to hit [SHIFT] [COMPLEX] to convert to complex before you use [ANGL].

9.1. Philatelic Application: Parallel Lines (Take 2)

For an alternative approach see: Philatelic Application: Parallel Lines (Take 1).

A typical US Washington-Franklin vertical coil has a paper width of about 21.5mm. Because of the way the stamps were cut into coils, the flat sides should be absolutely parallel.

Scenario: We have a Washington-Franklin vertical coil, and wish to verify that the flat edges are parallel. We have a 2400 DPI scan.

Our first step is to identify two points in each edge. The points should be separated as far apart as possible. Suppose this results in the following:

Corner	Coordinates
Upper left	(150, 160)
Upper right	(2182, 122)
Lower right	(2181, 2250)
Lower left	(149, 2132)

Note that we didn't try to line the points up horizontally – our upper left point is at 160 while our upper right point is at 122!

Calibration. If we have not already calibrated, we need to do that first
- 2400 25.4 [CAL]
Now we enter the corner data
- [QUAD] 150 [ENTER] 160 [UL] 2182 [ENTER] 122 [UR] 2181 [ENTER] 2250 [LR] 149 2132 [LL]
Now we can compute the LR Angle:
- [∡LR] → 0.0021 – assuming DEG angle mode

9.2. Philatelic Application: Rotary Press vs. Flat Plate (Take 2)

For an alternative approach see: Philatelic Application: Rotary Press vs. Flat Plate (Take 1)