CLS
PRINT "GEOMETRIC PROPERTIES OF AN"
PRINT "ARBITRARY PLANE DOMAIN"
PRINT
REM DATA INPUT MODULE
PRINT "(R)EAD FROM DATA OR (I)NPUT DATA?";
INPUT " ";IN$
AF=0

IF IN$="r" OR IN$="R" THEN AF=1 
PRINT
IF AF=0 THEN
INPUT "TOTAL NUMBER OF CONTOURS? ";N3
ELSE IF
READ N3
END IF

N3=N3-1

IF AF=0 THEN
PRINT
PRINT "FOR EACH CONTOUR"
PRINT "VERTICES MUST BE NUMBERED CONSECUTIVELY"
PRINT "STARTING WITH 1"
PRINT
PRINT "DEFINITION OF EXTERIOR CONTOUR"
PRINT
INPUT "NUMBER OF VERTICES? "; N1
PRINT
ELSE IF
READ N1
END IF

N = N1
REM ==COMPUTE ELEMENT PROPERTIES FOR EXTERIOR CONTOUR==
GOSUB [ONZETHZE]
REM ==CHECK FOR AREA SIGN==
I0 = 1
IF S0 >0 THEN [TWFOZE]
I0 = -1
REM ==SIMPLIFY CONNECTED DOMAIN PROPERTIES==
[TWFOZE]
A = I0 * S0
Q1 = I0 * M1
Q2 = I0 * M2
I1 =ABS(R1)
I2 =ABS(R2)
I3 =I0 * R3
REM ==CHECK FOR MULTIPLE CONNECTIVITY==
IF N3 = 0 THEN [FIZEZE]
REM ==INTERIOR DOMAINS==
J = 0
[THTWZE]
J = J + 1

IF AF=0 THEN
PRINT
PRINT "DEFINITION OFINTERIOR CONTOUR"; J
PRINT
INPUT "NUMBER OF VERTICES? ";N2
ELSE IF
READ N2
END IF

N = N2
REM ==COMPUTE INTERIOR ELEMENT PROPERTIES==
GOSUB [ONZETHZE]
REM ==CHECK FOR AREA SIGN==
I0 = 1
IF S0 > 0 THEN [FOTHZE]
I0 =-1
REM ==UPDATE PROPERTIES==
[FOTHZE]
A = A -I0 * S0
Q1 = Q1 -I0 * M1
Q2 = Q2 -I0 * M2
I1 = I1 -ABS(R1)
I2 =I2 -ABS(R2)
I3 = I3 -I0 * R3
REM ==CHECK FOR CONNECTIVITY ORDER==
IF J < N3 THEN [THTWZE]
REM ==CENTROID COORDINATES==
[FIZEZE]
X = Q2 / A
Y = Q1 / A
PRINT
PRINT
PRINT "GEOMETRIC PROPERTIES"
PRINT "WITH RESPECT TO GIVEN AXES"
PRINT
PRINT"AREA=";A
PRINT
PRINT"COORDINATES OF CENTROID"
PRINT"XG=";X
PRINT"YG=";Y
PRINT
PRINT "MOMENTS OF INERTIA"
PRINT "IXX ="; I1
PRINT "IYY ="; I2
PRINT "IXY="; I3
PRINT
PRINT "STATIC MOMENTS"
PRINT "MXX=";Q1
PRINT "MYY ="; Q2
PRINT
PRINT "PRESS RETURN TO CONTINUE"
INPUT W$
REM ==CENTROIDAL PROPERTIES WITH RESPECT TO PARALLEL AXES==
J1 = I1 -A * Y * Y
J2 = I2 -A * X * X
J3 = I3 -A * X * Y
C1 = (J1 + J2) / 2
C2 = (J2 -J1) / 2
C3 = (C2 * C2 + J3 * J3)^.5
REM ==PRINCIPAL PROPERTIES==
P1 = C1 + C3
P2 = C1 -C3
P0 = 3.141592653589
REM ==COMPUTE ORIENTATIONOFPRINCIPAL AXES==
T = P0 / 4
IF ( ABS(C2) < .00001) THEN [EISIZE]
T = ATN(J3 / C2) / 2
[EISIZE]
T = T * 180 / P0
PRINT
PRINT
PRINT "INERTIA TENSOR WITH RESPECT"
PRINT "TO PARALLEL AXES THRU CENTROID"
PRINT
PRINT "IXXG =";J1
PRINT "IYYG="; J2
PRINT "IXYG=";J3
PRINT
PRINT
PRINT "PRINCIPAL AXES AND MOMENTS OF INERTIA"
PRINT
PRINT "ANGLE =";T
PRINT "IMAX = "; P1
PRINT "IMIN ="; P2
GOTO [ONFOZEZE]
REM ==INITIALIZE ELEMENT VARIABLES==
[ONZETHZE]
S0 = 0
M1 = 0
M2 = 0
R1 = 0
R2 = 0
R3 = 0
REM ==INPUT COORDINATES==
IF AF=0 THEN
PRINT
PRINT "ENTER VERTEX COORDINATES (X,Y)"
PRINT "VERTEX 1 X,Y?"
INPUT "X= ";X1
INPUT "Y= ";Y1
PRINT
ELSE IF
READ X1
READ Y1
END IF

X0 = X1
Y0 = Y1
I = 2
[ONONFIZE]

IF AF=0 THEN
PRINT "VERTEX ";I;" X,Y?"
INPUT "X= ";X2
INPUT "Y= ";Y2
ELSE IF
READ X2
READ Y2
END IF

REM ==ELEMENT AREA==
[ONONSEZE]
S= (X1 *Y2-X2*Y1) /2
REM ==ELEMENT CENTROID==
Z1 =(X1 +X2)/3
Z2 = (Y1 + Y2) / 3
REM ==FIRST MOMENTS==
M1 = M1 +S *(Z2)
M2 =M2+S * (Z1)
REM ==INERTIA MOMENTS==
R1 = R1 + S * (Y1 * Y1 + Y2 * Y2 + Y1 * Y2) / 6
R2 = R2 + S * (X1 * X1 + X2 * X2 + X1 * X2) / 6
R3 = R3 + S * (X1 * Y1 + X2 * Y2 +(X1 * Y2 +X2 * Y1)/2)/6
REM ==UPDATE AREA==
S0 = S0 + S
X1 = X2
Y1 = Y2
I = I + 1
REM ==CHECK FOR  LAST VERTEX==
IF I< N + 1 THEN [ONONFIZE]
IF I>(N+1) THEN [ONTHFOZE]
REM ==LAST ELEMENT==
X2 = X0
Y2 = Y0
GOTO [ONONSEZE]
[ONTHFOZE]
RETURN
[ONFOZEZE]
END
DATA 4
DATA 8,7.5,3,18.5,3,21,13,23,13,23,15,3,15,3,13,5,13
DATA 4,8,4,10,4,10,13,6,13
DATA 4,11,13,15,13,15,4,11,4
DATA 4,20,13,16,13,16,4,18,4