Area Calculation from points

I am measuring a feature that is somewhat round but has lot of jagged edges. I want to use all of the areas to calculate the area. I am measuring this using hundreds of points. Anyone have any ideas ? I have searched for answers but can't seem to come up with any.

Parents

AndersI over 6 years ago

Would it be possible (maybe even slightly easier) to adapt the Shoelace Formula ( https://en.wikipedia.org/wiki/Shoelace_formula) to this?

Thanks for this link! The Shoelace Formula was an interesting read. I tested a bit, and got this generalized version:

PNT_A1     =FEAT/POINT,CARTESIAN,NO
            THEO/<4,10,0>,<0,0,1>
            ACTL/<4,10,0>,<0,0,1>
            CONSTR/POINT,CAST,PNT_A
SCN1       =FEAT/SET,CARTESIAN
            THEO/<6,6.2,0>,<0,0,1>
            ACTL/<6,6.2,0>,<0,0,1>
            CONSTR/SET,BASIC,PNT_A,PNT_B,PNT_C,PNT_D,PNT_A1,,
            ASSIGN/N=SCN1.NUMHITS-1
            ASSIGN/VX=SCN1.HIT[1..SCN1.NUMHITS].X
            ASSIGN/VY=SCN1.HIT[1..SCN1.NUMHITS].Y
            ASSIGN/AREA=0
            ASSIGN/I=1
            WHILE/I<=N
              ASSIGN/XY=VX[I]*VY[I+1]
              ASSIGN/YX=VY[I]*VX[I+1]
              ASSIGN/AREA=AREA+(XY-YX)
              ASSIGN/I=I+1
            END_WHILE/
            ASSIGN/AREA=ABS(AREA/2)
            COMMENT/OPER,NO,FULL SCREEN=NO,AUTO-CONTINUE=NO,
            "area = "+AREA

The only trick is in duplicating the first point PNT_A into PNT_A1 and creating a set of all points (A, B, C, D, A in this example). Then looping from 1 to N and accumulating the AREA, finally taking ABS() and dividing by 2.

I wrote every step as a separate command, but it can of course be much more crammed together, but will be more difficult to understand:

            ASSIGN/AREA=0
I          =LOOP/START,ID=NO,NUMBER=N,START=1,SKIP=,
              OFFSET:XAXIS=0,YAXIS=0,ZAXIS=0,ANGLE=0
              ASSIGN/AREA=AREA+(SCN1.HIT[I].X*SCN1.HIT[I+1].Y-SCN1.HIT[I].Y*SCN1.HIT[I+1].X)
            LOOP/END
            ASSIGN/AREA=ABS(AREA/2)
            COMMENT/OPER,NO,FULL SCREEN=NO,AUTO-CONTINUE=NO,
            AREA

Edit: OK, now I've done code in the ' JEFMAN spirit' too - no loops, totally undecipherable :-)) and fast!

            CONSTR/SET,BASIC,PNT_A,PNT_B,PNT_C,PNT_D,PNT_A1,,
            ASSIGN/N=SCN1.NUMHITS-1
            ASSIGN/AR=SCN1.HIT[1..N].X*SCN1.HIT[2..N+1].Y-SCN1.HIT[1..N].Y*SCN1.HIT[2..N+1].X
            ASSIGN/AR[N+1]=0
            ASSIGN/AREA=ABS(SUM(AR))/2
            COMMENT/OPER,NO,FULL SCREEN=NO,AUTO-CONTINUE=NO,
            AREA

Reply

AndersI over 6 years ago

Would it be possible (maybe even slightly easier) to adapt the Shoelace Formula ( https://en.wikipedia.org/wiki/Shoelace_formula) to this?

Thanks for this link! The Shoelace Formula was an interesting read. I tested a bit, and got this generalized version:

PNT_A1     =FEAT/POINT,CARTESIAN,NO
            THEO/<4,10,0>,<0,0,1>
            ACTL/<4,10,0>,<0,0,1>
            CONSTR/POINT,CAST,PNT_A
SCN1       =FEAT/SET,CARTESIAN
            THEO/<6,6.2,0>,<0,0,1>
            ACTL/<6,6.2,0>,<0,0,1>
            CONSTR/SET,BASIC,PNT_A,PNT_B,PNT_C,PNT_D,PNT_A1,,
            ASSIGN/N=SCN1.NUMHITS-1
            ASSIGN/VX=SCN1.HIT[1..SCN1.NUMHITS].X
            ASSIGN/VY=SCN1.HIT[1..SCN1.NUMHITS].Y
            ASSIGN/AREA=0
            ASSIGN/I=1
            WHILE/I<=N
              ASSIGN/XY=VX[I]*VY[I+1]
              ASSIGN/YX=VY[I]*VX[I+1]
              ASSIGN/AREA=AREA+(XY-YX)
              ASSIGN/I=I+1
            END_WHILE/
            ASSIGN/AREA=ABS(AREA/2)
            COMMENT/OPER,NO,FULL SCREEN=NO,AUTO-CONTINUE=NO,
            "area = "+AREA

            ASSIGN/AREA=0
I          =LOOP/START,ID=NO,NUMBER=N,START=1,SKIP=,
              OFFSET:XAXIS=0,YAXIS=0,ZAXIS=0,ANGLE=0
              ASSIGN/AREA=AREA+(SCN1.HIT[I].X*SCN1.HIT[I+1].Y-SCN1.HIT[I].Y*SCN1.HIT[I+1].X)
            LOOP/END
            ASSIGN/AREA=ABS(AREA/2)
            COMMENT/OPER,NO,FULL SCREEN=NO,AUTO-CONTINUE=NO,
            AREA

Edit: OK, now I've done code in the ' JEFMAN spirit' too - no loops, totally undecipherable :-)) and fast!

            CONSTR/SET,BASIC,PNT_A,PNT_B,PNT_C,PNT_D,PNT_A1,,
            ASSIGN/N=SCN1.NUMHITS-1
            ASSIGN/AR=SCN1.HIT[1..N].X*SCN1.HIT[2..N+1].Y-SCN1.HIT[1..N].Y*SCN1.HIT[2..N+1].X
            ASSIGN/AR[N+1]=0
            ASSIGN/AREA=ABS(SUM(AR))/2
            COMMENT/OPER,NO,FULL SCREEN=NO,AUTO-CONTINUE=NO,
            AREA

Children

VinniUSMC over 6 years ago in reply to AndersI

Coding this stuff is way above my head, but I love the math behind it, and I thought there had to be a way to calculate a triangle's area with the 3 points making its vertices as the known variables. I found something else before finding this, but the Shoelace formula is the underlying math behind it, and JEFMAN's elegant (but roundabout) solution.
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