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+--- Thread: (15C) Area and Perimeter of irregular polygon (/thread-20949.html)
(15C) Area and Perimeter of irregular polygon - Marcel - 12-04-2023 06:17 PM
Hi!
I upload a document with a program for calculating the Area and the Perimeter of an irregular polygon for the HP 15C.
Have fun!
RE: (15C) Area and Perimeter of irregular polygon - Werner - 12-05-2023 12:53 PM
There's an error in the Area formula (not in the program): the first term also needs a minus sign.
If the area is all you need, you may try this small program (concocted on the fly ;-)
Enter the coefficients in any matrix, recall the matrix to the stack and (GSB) A.
33 Bytes
X Y Z T
001 LBL A
002 STO I
003 MATRIX 1
004uRCL (i)
005 RCL 0 dummy
006 0
007uRCL (i)
008 LBL 1
009 GSB 0
010uRCL (i) yj A xj xj
011 GTO 1
012 GSB 0
013 ABS
014 2
015 /
016 RTN
017 LBL 0 yi A xi
018 R^ xi yi A
019uRCL (i)
020 + xi+xj yi A A
021 X<>Y
022 LASTX
023 Rv yi xi+xj A xj
024 RCL- (i)
025 x
026 +
027 RTN
Cheers, Werner
RE: (15C) Area and Perimeter of irregular polygon - Marcel - 12-05-2023 01:50 PM
Hi Werner!
I think the formula is OK.. but a small error at the end of page 4 in the
Area = ...
I corrected the -1. It should be 1... Sorry!
I upload a new document with the correction.
I will try your program today.
Marcel
RE: (15C) Area and Perimeter of irregular polygon - Werner - 12-05-2023 02:33 PM
Hi Marcel, yes that was an error, too.
But the formula you wrote (apart from the ||):
\(
Area = \frac{(x_{1}y_{2}-x_{2}y_{1})-(x_{2}y_{3}-x_{3}y_{2})- ..-(x_{n}y_{1}-x_{1}y_{n})}{2}
\)
That first term must be negative also, or just switch them all around
\(
Area = \frac{(x_{2}y_{1}-x_{1}y_{2})+(x_{3}y_{2}-x_{2}y_{3})+ ..+(x_{1}y_{n}-x_{n}y_{1})}{2}
\)
Cheers, Werner
RE: (15C) Area and Perimeter of irregular polygon - Marcel - 12-05-2023 03:14 PM
Hi again Werner!
In english you said Shame on me! (I speak french..)
I put minus sign (-) but it is a plus sign (+).
It is corrected now...
Marcel!
RE: (15C) Area and Perimeter of irregular polygon - Marcel - 12-05-2023 05:57 PM
Hi Werner!
I try your program..Wow!
You must add to it the peremeter and upload it on the forum!
I am waiting for your version.
Marcel.
RE: (15C) Area and Perimeter of irregular polygon - John Keith - 12-05-2023 07:12 PM
Though rather long and involved, this thread may be relevant to the current discussion.
RE: (15C) Area and Perimeter of irregular polygon - Werner - 12-06-2023 09:47 AM
Area (A) (improved wrt the previous version) and perimeter (C)
(though not together; but the program can be easily changed to that extent, using a data register)
55 bytes
X Y Z T
001 LBL A
002 GSB 0
003 LBL 1 yi A - xi
004 RCLx (i) xj*yi A - xi
005 R^
006uRCL (i)
007 Rv xi xj*yi A xj
008 RCLx (i) yj*xi
009 -
010 +
011uRCL (i)
012 GTO 1
013 Rv
014 ABS
015 2
016 /
017 RTN
018 LBL C
019 GSB 0
020 LBL 2 yi P xi
021 RCL (i) xj yi P xi
022 R^
023 -
024uRCL (i)
025 Rv xj-xi yi P xj
026 X<>Y
027 RCL- (i)
028 ->P d - P xj
029 X<>Y
030 Rv
031 + P xj
032uRCL (i)
033 GTO 2
034 Rv
035 RTN
036 LBL 0
037 STO I
038 MATRIX 1
039 RCL DIM I 2 n
040 SQRT
041 RCL g(i)
042 0
043 RCL DIM I
044 RCL g(i) yn 0 xn xn
045 RTN
Cheers, Werner