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SUBROUTINE CONCAL (XD,YD,ZD,NT,IPT,NL,IPL,PDD,ITI,XII,YII,ZII,
1 ITPV)
C
C +-----------------------------------------------------------------+
C | |
C | Copyright (C) 1986 by UCAR |
C | University Corporation for Atmospheric Research |
C | All Rights Reserved |
C | |
C | NCARGRAPHICS Version 1.00 |
C | |
C +-----------------------------------------------------------------+
C
C
C
C THIS SUBROUTINE PERFORMS PUNCTUAL INTERPOLATION OR EXTRAPO-
C LATION, I.E., DETERMINES THE Z VALUE AT A POINT.
C THE INPUT PARAMETERS ARE
C
C XD,YD,ZD = ARRAYS CONTAINING THE X, Y, AND Z
C COORDINATES OF DATA POINTS,
C NT = NUMBER OF TRIANGLES,
C IPT = INTEGER ARRAY CONTAINING THE POINT NUMBERS OF
C THE VERTEXES OF THE TRIANGLES,
C NL = NUMBER OF BORDER LINE SEGMENTS,
C IPL = INTEGER ARRAY CONTAINING THE POINT NUMBERS OF
C THE END POINTS OF THE BORDER LINE SEGMENTS AND
C THEIR RESPECTIVE TRIANGLE NUMBERS,
C PDD = ARRAY CONTAINING THE PARTIAL DERIVATIVES AT
C THE DATA POINTS,
C ITI = TRIANGLE NUMBER OF THE TRIANGLE IN WHICH LIES
C THE POINT FOR WHICH INTERPOLATION IS TO BE
C PERFORMED,
C XII,YII = X AND Y COORDINATES OF THE POINT FOR WHICH
C INTERPOLATION IS TO BE PERFORMED.
C THE OUTPUT PARAMETER IS
C
C ZII = INTERPOLATED Z VALUE.
C
C DECLARATION STATEMENTS
C
C
DIMENSION XD(1) ,YD(1) ,ZD(1) ,IPT(1) ,
1 IPL(1) ,PDD(1)
DIMENSION X(3) ,Y(3) ,Z(3) ,PD(15) ,
1 ZU(3) ,ZV(3) ,ZUU(3) ,ZUV(3) ,
2 ZVV(3)
REAL LU ,LV
EQUIVALENCE (P5,P50)
C
SAVE
C
C PRELIMINARY PROCESSING
C
IT0 = ITI
NTL = NT+NL
IF (IT0 .LE. NTL) GO TO 100
IL1 = IT0/NTL
IL2 = IT0-IL1*NTL
IF (IL1 .EQ. IL2) GO TO 150
GO TO 200
C
C CALCULATION OF ZII BY INTERPOLATION.
C CHECKS IF THE NECESSARY COEFFICIENTS HAVE BEEN CALCULATED.
C
100 IF (IT0 .EQ. ITPV) GO TO 140
C
C LOADS COORDINATE AND PARTIAL DERIVATIVE VALUES AT THE
C IPI 102 VERTEXES.
C IPI 103
C
JIPT = 3*(IT0-1)
JPD = 0
DO 120 I=1,3
JIPT = JIPT+1
IDP = IPT(JIPT)
X(I) = XD(IDP)
Y(I) = YD(IDP)
Z(I) = ZD(IDP)
JPDD = 5*(IDP-1)
DO 110 KPD=1,5
JPD = JPD+1
JPDD = JPDD+1
PD(JPD) = PDD(JPDD)
110 CONTINUE
120 CONTINUE
C
C DETERMINES THE COEFFICIENTS FOR THE COORDINATE SYSTEM
C TRANSFORMATION FROM THE X-Y SYSTEM TO THE U-V SYSTEM
C AND VICE VERSA.
C
X0 = X(1)
Y0 = Y(1)
A = X(2)-X0
B = X(3)-X0
C = Y(2)-Y0
D = Y(3)-Y0
AD = A*D
BC = B*C
DLT = AD-BC
AP = D/DLT
BP = -B/DLT
CP = -C/DLT
DP = A/DLT
C
C CONVERTS THE PARTIAL DERIVATIVES AT THE VERTEXES OF THE
C TRIANGLE FOR THE U-V COORDINATE SYSTEM.
C
AA = A*A
ACT2 = 2.0*A*C
CC = C*C
AB = A*B
ADBC = AD+BC
CD = C*D
BB = B*B
BDT2 = 2.0*B*D
DD = D*D
DO 130 I=1,3
JPD = 5*I
ZU(I) = A*PD(JPD-4)+C*PD(JPD-3)
ZV(I) = B*PD(JPD-4)+D*PD(JPD-3)
ZUU(I) = AA*PD(JPD-2)+ACT2*PD(JPD-1)+CC*PD(JPD)
ZUV(I) = AB*PD(JPD-2)+ADBC*PD(JPD-1)+CD*PD(JPD)
ZVV(I) = BB*PD(JPD-2)+BDT2*PD(JPD-1)+DD*PD(JPD)
130 CONTINUE
C
C CALCULATES THE COEFFICIENTS OF THE POLYNOMIAL.
C
P00 = Z(1)
P10 = ZU(1)
P01 = ZV(1)
P20 = 0.5*ZUU(1)
P11 = ZUV(1)
P02 = 0.5*ZVV(1)
H1 = Z(2)-P00-P10-P20
H2 = ZU(2)-P10-ZUU(1)
H3 = ZUU(2)-ZUU(1)
P30 = 10.0*H1-4.0*H2+0.5*H3
P40 = -15.0*H1+7.0*H2-H3
P50 = 6.0*H1-3.0*H2+0.5*H3
H1 = Z(3)-P00-P01-P02
H2 = ZV(3)-P01-ZVV(1)
H3 = ZVV(3)-ZVV(1)
P03 = 10.0*H1-4.0*H2+0.5*H3
P04 = -15.0*H1+7.0*H2-H3
P05 = 6.0*H1-3.0*H2+0.5*H3
LU = SQRT(AA+CC)
LV = SQRT(BB+DD)
THXU = ATAN2(C,A)
THUV = ATAN2(D,B)-THXU
CSUV = COS(THUV)
P41 = 5.0*LV*CSUV/LU*P50
P14 = 5.0*LU*CSUV/LV*P05
H1 = ZV(2)-P01-P11-P41
H2 = ZUV(2)-P11-4.0*P41
P21 = 3.0*H1-H2
P31 = -2.0*H1+H2
H1 = ZU(3)-P10-P11-P14
H2 = ZUV(3)-P11-4.0*P14
P12 = 3.0*H1-H2
P13 = -2.0*H1+H2
THUS = ATAN2(D-C,B-A)-THXU
THSV = THUV-THUS
AA = SIN(THSV)/LU
BB = -COS(THSV)/LU
CC = SIN(THUS)/LV
DD = COS(THUS)/LV
AC = AA*CC
AD = AA*DD
BC = BB*CC
G1 = AA*AC*(3.0*BC+2.0*AD)
G2 = CC*AC*(3.0*AD+2.0*BC)
H1 = -AA*AA*AA*(5.0*AA*BB*P50+(4.0*BC+AD)*P41)-
1 CC*CC*CC*(5.0*CC*DD*P05+(4.0*AD+BC)*P14)
H2 = 0.5*ZVV(2)-P02-P12
H3 = 0.5*ZUU(3)-P20-P21
P22 = (G1*H2+G2*H3-H1)/(G1+G2)
P32 = H2-P22
P23 = H3-P22
ITPV = IT0
C
C CONVERTS XII AND YII TO U-V SYSTEM.
C
140 DX = XII-X0
DY = YII-Y0
U = AP*DX+BP*DY
V = CP*DX+DP*DY
C
C EVALUATES THE POLYNOMIAL.
C
P0 = P00+V*(P01+V*(P02+V*(P03+V*(P04+V*P05))))
P1 = P10+V*(P11+V*(P12+V*(P13+V*P14)))
P2 = P20+V*(P21+V*(P22+V*P23))
P3 = P30+V*(P31+V*P32)
P4 = P40+V*P41
ZII = P0+U*(P1+U*(P2+U*(P3+U*(P4+U*P5))))
RETURN
C
C CALCULATION OF ZII BY EXTRATERPOLATION IN THE RECTANGLE.
C CHECKS IF THE NECESSARY COEFFICIENTS HAVE BEEN CALCULATED.
C
150 IF (IT0 .EQ. ITPV) GO TO 190
C
C LOADS COORDINATE AND PARTIAL DERIVATIVE VALUES AT THE END
C POINTS OF THE BORDER LINE SEGMENT.
C
JIPL = 3*(IL1-1)
JPD = 0
DO 170 I=1,2
JIPL = JIPL+1
IDP = IPL(JIPL)
X(I) = XD(IDP)
Y(I) = YD(IDP)
Z(I) = ZD(IDP)
JPDD = 5*(IDP-1)
DO 160 KPD=1,5
JPD = JPD+1
JPDD = JPDD+1
PD(JPD) = PDD(JPDD)
160 CONTINUE
170 CONTINUE
C
C DETERMINES THE COEFFICIENTS FOR THE COORDINATE SYSTEM
C TRANSFORMATION FROM THE X-Y SYSTEM TO THE U-V SYSTEM
C AND VICE VERSA.
C
X0 = X(1)
Y0 = Y(1)
A = Y(2)-Y(1)
B = X(2)-X(1)
C = -B
D = A
AD = A*D
BC = B*C
DLT = AD-BC
AP = D/DLT
BP = -B/DLT
CP = -BP
DP = AP
C
C CONVERTS THE PARTIAL DERIVATIVES AT THE END POINTS OF THE
C BORDER LINE SEGMENT FOR THE U-V COORDINATE SYSTEM.
C
AA = A*A
ACT2 = 2.0*A*C
CC = C*C
AB = A*B
ADBC = AD+BC
CD = C*D
BB = B*B
BDT2 = 2.0*B*D
DD = D*D
DO 180 I=1,2
JPD = 5*I
ZU(I) = A*PD(JPD-4)+C*PD(JPD-3)
ZV(I) = B*PD(JPD-4)+D*PD(JPD-3)
ZUU(I) = AA*PD(JPD-2)+ACT2*PD(JPD-1)+CC*PD(JPD)
ZUV(I) = AB*PD(JPD-2)+ADBC*PD(JPD-1)+CD*PD(JPD)
ZVV(I) = BB*PD(JPD-2)+BDT2*PD(JPD-1)+DD*PD(JPD)
180 CONTINUE
C
C CALCULATES THE COEFFICIENTS OF THE POLYNOMIAL.
C
P00 = Z(1)
P10 = ZU(1)
P01 = ZV(1)
P20 = 0.5*ZUU(1)
P11 = ZUV(1)
P02 = 0.5*ZVV(1)
H1 = Z(2)-P00-P01-P02
H2 = ZV(2)-P01-ZVV(1)
H3 = ZVV(2)-ZVV(1)
P03 = 10.0*H1-4.0*H2+0.5*H3
P04 = -15.0*H1+7.0*H2-H3
P05 = 6.0*H1-3.0*H2+0.5*H3
H1 = ZU(2)-P10-P11
H2 = ZUV(2)-P11
P12 = 3.0*H1-H2
P13 = -2.0*H1+H2
P21 = 0.0
P23 = -ZUU(2)+ZUU(1)
P22 = -1.5*P23
ITPV = IT0
C
C CONVERTS XII AND YII TO U-V SYSTEM.
C
190 DX = XII-X0
DY = YII-Y0
U = AP*DX+BP*DY
V = CP*DX+DP*DY
C
C EVALUATES THE POLYNOMIAL.
C
P0 = P00+V*(P01+V*(P02+V*(P03+V*(P04+V*P05))))
P1 = P10+V*(P11+V*(P12+V*P13))
P2 = P20+V*(P21+V*(P22+V*P23))
ZII = P0+U*(P1+U*P2)
RETURN
C
C CALCULATION OF ZII BY EXTRATERPOLATION IN THE TRIANGLE.
C CHECKS IF THE NECESSARY COEFFICIENTS HAVE BEEN CALCULATED.
C
200 IF (IT0 .EQ. ITPV) GO TO 220
C
C LOADS COORDINATE AND PARTIAL DERIVATIVE VALUES AT THE VERTEX
C OF THE TRIANGLE.
C
JIPL = 3*IL2-2
IDP = IPL(JIPL)
X(1) = XD(IDP)
Y(1) = YD(IDP)
Z(1) = ZD(IDP)
JPDD = 5*(IDP-1)
DO 210 KPD=1,5
JPDD = JPDD+1
PD(KPD) = PDD(JPDD)
210 CONTINUE
C
C CALCULATES THE COEFFICIENTS OF THE POLYNOMIAL.
C
P00 = Z(1)
P10 = PD(1)
P01 = PD(2)
P20 = 0.5*PD(3)
P11 = PD(4)
P02 = 0.5*PD(5)
ITPV = IT0
C
C CONVERTS XII AND YII TO U-V SYSTEM.
C
220 U = XII-X(1)
V = YII-Y(1)
C
C EVALUATES THE POLYNOMIAL.
C
P0 = P00+V*(P01+V*P02)
P1 = P10+V*P11
ZII = P0+U*(P1+U*P20)
RETURN
END
|
