Introduction
On June 6, 2014, I posted a revised program for the HP 15C to find the area of a polygon by given the coordinates of each vertex. You can see this post here:
http://edspi31415.blogspot.com/2014/06/hp-15c-area-of-polygon-by-vertices.html
Jason Foose, County Surveyor at Mohave County Public Works in Kingman, AZ contributed an addendum to the program: this allows you to enter curve segments and calculate the total area based on vertices and the curve segments. Jason Foose can be found on Google+ and on Linkedin.
General Instructions
The idea is to first enter all the coordinates of the vertices and calculate the area, then enter the curve segments and recalculate the area. Start at one at one point and work in either the clockwise or the counterclockwise motion.
Hence:
1. Enter initial coordinates (x0, y0): y0 ENTER x0 LBL A
2. Enter additional coordinates: y ENTER x LBL B
3. Calculate area with coordinates: LBL C
4. Enter radius and central angle, in HMS format: radius ENTER angle LBL D
5. Calculate final area: LBL E
When entering the radius and central angles, use positive values for radius for "outies", chord lines that add to the area. Use negative values for "innies", or chords that cut across the area. The 15C should be in Degrees mode.
The Expanded Program
Here is the program in full. Instructions in bold red are contributed by Jason Foose.
Memory registers used:
R0 = area
R1 = x_i
R2 = y_i
R3 = x_i+1
R4 = y_i+1
R5 = Σ (x_i * y_i+1) // ( i=1...n and cycle back to 1)
R6 = Σ (x_i+1 * y_i)
R7 = x_1
R8 = y_1
Program:
001 42, 21, 11 LBL A // enter initial vertex
002 0 0
003 44 5 STO 5
004 44 6 STO 6
005 33 R down // R↓
006 44 1 STO 1
007 44 7 STO 7
008 33 R down
009 44 2 STO 2
010 44 8 STO 8
011 43 32 RTN
012 42, 21, 12 LBL B // step 12 - add verticies
013 43 3 STO 3
014 45, 20, 2 RCL× 2
015 44, 40, 6 STO+ 6
016 33 R down
017 44 4 STO 4
018 45, 20, 1 RCL× 1
019 44, 40, 5 STO+ 5
020 45 4 RCL 4
021 44 2 STO 2
022 45 3 RCL 3
023 44 1 STO 1
024 43 32 RTN
025 42, 21, 13 LBL C // step 25 - calculate area with vertices
026 45 7 RCL 7
027 45, 20, 2 RCL× 2
028 44, 40, 6 STO+ 6
029 45 8 RCL 8
030 45, 20, 1 RCL× 1
031 44, 40, 5 STO+ 5
032 45, 5 RCL 5
033 45, 30, 6 RCL- 6
034 43 16 ABS
035 2 2
036 10 ÷
037 44 0 STO 0
Calculate the area with the segments:
Keystrokes:
Starting at Point (100, 100)
Coordinates:
100 ENTER 100 LBL A
100 ENTER 400 LBL B
200 ENTER 500 LBL B
300 ENTER 500 LBL B
300 ENTER 225 LBL B
425 ENTER 100 LBL B
LBL C \\ Area: 1.9011 acres
Add segments:
100 ENTER 90 LBL D \\ "outie" angle = 90
125 ENTER 90 CHS LBL D \\ "innie" angle = -90
LBL E \\ Area: 1.8643 acres
Special thanks to Jason Foose for the great addendum to the area by vertices program.
Eddie
On June 6, 2014, I posted a revised program for the HP 15C to find the area of a polygon by given the coordinates of each vertex. You can see this post here:
http://edspi31415.blogspot.com/2014/06/hp-15c-area-of-polygon-by-vertices.html
Jason Foose, County Surveyor at Mohave County Public Works in Kingman, AZ contributed an addendum to the program: this allows you to enter curve segments and calculate the total area based on vertices and the curve segments. Jason Foose can be found on Google+ and on Linkedin.
General Instructions
The idea is to first enter all the coordinates of the vertices and calculate the area, then enter the curve segments and recalculate the area. Start at one at one point and work in either the clockwise or the counterclockwise motion.
Hence:
1. Enter initial coordinates (x0, y0): y0 ENTER x0 LBL A
2. Enter additional coordinates: y ENTER x LBL B
3. Calculate area with coordinates: LBL C
4. Enter radius and central angle, in HMS format: radius ENTER angle LBL D
5. Calculate final area: LBL E
When entering the radius and central angles, use positive values for radius for "outies", chord lines that add to the area. Use negative values for "innies", or chords that cut across the area. The 15C should be in Degrees mode.
The Expanded Program
Here is the program in full. Instructions in bold red are contributed by Jason Foose.
Memory registers used:
R0 = area
R1 = x_i
R2 = y_i
R3 = x_i+1
R4 = y_i+1
R5 = Σ (x_i * y_i+1) // ( i=1...n and cycle back to 1)
R6 = Σ (x_i+1 * y_i)
R7 = x_1
R8 = y_1
Program:
001 42, 21, 11 LBL A // enter initial vertex
002 0 0
003 44 5 STO 5
004 44 6 STO 6
005 33 R down // R↓
006 44 1 STO 1
007 44 7 STO 7
008 33 R down
009 44 2 STO 2
010 44 8 STO 8
011 43 32 RTN
012 42, 21, 12 LBL B // step 12 - add verticies
013 43 3 STO 3
014 45, 20, 2 RCL× 2
015 44, 40, 6 STO+ 6
016 33 R down
017 44 4 STO 4
018 45, 20, 1 RCL× 1
019 44, 40, 5 STO+ 5
020 45 4 RCL 4
021 44 2 STO 2
022 45 3 RCL 3
023 44 1 STO 1
024 43 32 RTN
025 42, 21, 13 LBL C // step 25 - calculate area with vertices
026 45 7 RCL 7
027 45, 20, 2 RCL× 2
028 44, 40, 6 STO+ 6
029 45 8 RCL 8
030 45, 20, 1 RCL× 1
031 44, 40, 5 STO+ 5
032 45, 5 RCL 5
033 45, 30, 6 RCL- 6
034 43 16 ABS
035 2 2
036 10 ÷
037 44 0 STO 0
038 4 4 // where Jason's steps start
039 3 3
040 5 5
041 6 6
042 0 0
043 10 divide ÷ // convert to acres
044 43 32 RTN
045 42, 21, 14 LBL D // step 45 - segment routine
046 43 2 >HR
047 36 ENTER
048 42 3 >RAD
049 34 X<>Y
050 23 SIN
051 30 -
052 48 DECIMAL POINT (.)
053 5 5
054 20 *
055 34 X<>Y
056 43 11 XSQ (x^2)
057 20 *
058 44, 40, 0 STO+0
059 43 32 RTN
060 42, 21, 15 LBL E // step 60 - convert area to acres
061 45 0 RCL 0
062 4 4
063 3 3
064 5 5
065 6 6
066 0 0
067 10 DIVIDE ÷
068 43 32 RTN
Example (Updated 6/29/2014)
See the diagram below. The steps are included with the diagram. We are going to start at the point (100,100) and go counterclockwise. The diagram and example has been provided by Jason Foose.
Keystrokes:
Starting at Point (100, 100)
Coordinates:
100 ENTER 100 LBL A
100 ENTER 400 LBL B
200 ENTER 500 LBL B
300 ENTER 500 LBL B
300 ENTER 225 LBL B
425 ENTER 100 LBL B
LBL C \\ Area: 1.9011 acres
Add segments:
100 ENTER 90 LBL D \\ "outie" angle = 90
125 ENTER 90 CHS LBL D \\ "innie" angle = -90
LBL E \\ Area: 1.8643 acres
Special thanks to Jason Foose for the great addendum to the area by vertices program.
Eddie
