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*DECK NXTIRA
FUNCTION NXTIRA(XYCAR ,POSPIN,VOLINT)
*
*----------
*
*Purpose:
* Compute the volume of intersection between
* a rectangular region and an annular pin.
*
*Copyright:
* Copyright (C) 2005 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
*Author(s): G. Marleau.
*
*Parameters: input
* XYCAR spatial description of the Cartesian region with:
* XYCAR(1) for left face; XYCAR(2) for right face;
* XYCAR(3) for bottom face; XYCAR(4) for top face
* positions.
* POSPIN spatial description of the annular pin region with
* POSPIN(0) the radius; POSPIN(1) the $X$ position
* of center; POSPIN(2) the $Y$ position
* of center.
*
*Parameters: output
* NXTIRA type of intersection between Cartesian region and
* annular pin or annular region and Cartesian pin, where:
* = 0 means that there is no intersection
* between the two regions;
* = 1 means that the Cartesian region
* is all located inside the annular pin;
* = 2 means that the annular pin
* is all located inside the Cartesian region;
* =-1 means that the intersection between
* the annular pin and the Cartesian region is partial.
* VOLINT 2-D volume of intersection (area) between Cartesian region
* and annular pin.
*
*Reference:
* G. Marleau,
* New Geometries Processing in DRAGON: The NXT: Module,
* Report IGE-260, Polytechnique Montreal,
* Montreal, 2005.
*
*----
*
IMPLICIT NONE
*----
* Subroutine arguments
*----
INTEGER NXTIRA
DOUBLE PRECISION XYCAR(4),POSPIN(0:2)
DOUBLE PRECISION VOLINT
*----
* Local parameters
*----
INTEGER IOUT
CHARACTER NAMSBR*6
PARAMETER (IOUT=6,NAMSBR='NXTIRA')
INTEGER IPRINT
PARAMETER (IPRINT=100)
DOUBLE PRECISION DCUTOF
PARAMETER (DCUTOF=1.0D-8)
DOUBLE PRECISION DZERO,DONE
PARAMETER (DZERO=0.0D0,DONE=1.0D0)
*----
* Functions
*----
DOUBLE PRECISION XDRCST,PI
*----
* Local variables
*----
INTEGER IFACE,ILOC(4),IDX,IDY
DOUBLE PRECISION XYFACE(4),RP2,VOLCAR,VOLPIN,FACDIR,VSUB(4),
> TRIANG,ALPHA,FACTX,FACTY,
> DIST,QUARTA,CARTV
DOUBLE PRECISION DT1,DT2,DT3
*----
* Initialize NXTIRA and VOLINT and PI
*----
IF(IPRINT .GE. 200) THEN
WRITE(IOUT,6000) NAMSBR
WRITE(IOUT,6010) (XYCAR(IFACE),IFACE=1,4)
WRITE(IOUT,6011) (POSPIN(IFACE),IFACE=0,2)
ENDIF
NXTIRA=0
VOLINT=DZERO
PI=XDRCST('Pi',' ')
*----
* Locate pin center at origin
*----
XYFACE(1)=XYCAR(1)-POSPIN(1)
XYFACE(2)=XYCAR(2)-POSPIN(1)
XYFACE(3)=XYCAR(3)-POSPIN(2)
XYFACE(4)=XYCAR(4)-POSPIN(2)
*----
* Find location of each face with respect to annular region
*----
DO 100 IFACE=1,4
IF(XYFACE(IFACE) .LE. -POSPIN(0)) THEN
*----
* Plane to the left or under
*----
ILOC(IFACE)=(-1)**IFACE
ELSE IF(XYFACE(IFACE) .GE. POSPIN(0)) THEN
*----
* Plane to the right or above
*----
ILOC(IFACE)=(-1)**(IFACE+1)
ELSE
*----
* Plane croses annular region
*----
ILOC(IFACE)=0
ENDIF
100 CONTINUE
IF(ILOC(1) .NE. 1 .AND. ILOC(2) .NE. 1 .AND.
> ILOC(3) .NE. 1 .AND. ILOC(4) .NE. 1 ) THEN
RP2=POSPIN(0)*POSPIN(0)
VOLPIN=PI*RP2
VOLCAR=(XYFACE(2)-XYFACE(1))*(XYFACE(4)-XYFACE(3))
VOLINT=VOLPIN
*----
* Find annular surface
* 1- to the left of X-
* 2- to the right of X+
* 3- below Y-
* 4- above Y+
*----
FACDIR=-DONE
DO 110 IFACE=1,4
IF(ILOC(IFACE) .EQ. -1) THEN
VSUB(IFACE)=DZERO
ELSE
TRIANG=SQRT(RP2-XYFACE(IFACE)*XYFACE(IFACE))
> *FACDIR*XYFACE(IFACE)
ALPHA=ACOS(FACDIR*XYFACE(IFACE)/POSPIN(0))
VSUB(IFACE)=RP2*ALPHA-TRIANG
VOLINT=VOLINT-VSUB(IFACE)
ENDIF
FACDIR=-FACDIR
110 CONTINUE
*----
* For the case where two faces intersect inside annular region
* compute intersections between the two surfaces VSUB
* associated with each of these faces.
*----
FACTX=DONE
DO 120 IDX=1,2
FACTY=DONE
DO 130 IDY=3,4
IF(ILOC(IDX) .EQ. 0 .AND. ILOC(IDY) .EQ. 0) THEN
DIST=XYFACE(IDX)*XYFACE(IDX)+XYFACE(IDY)*XYFACE(IDY)
IF(DIST .LT. RP2) THEN
QUARTA=0.25D0*PI*RP2
CARTV=FACTX*XYFACE(IDY)*FACTY*XYFACE(IDX)
CARTV=CARTV+0.5D0*(VSUB(IDX)+VSUB(IDY))-QUARTA
ELSE
IF(FACTX*XYFACE(IDX) .LT. DZERO) THEN
IF(FACTY*XYFACE(IDY) .LT. DZERO) THEN
CARTV=0.0
ELSE
CARTV=VSUB(IDX)
ENDIF
ELSE
IF(FACTY*XYFACE(IDY) .LT. DZERO) THEN
CARTV=VSUB(IDY)
ELSE
CARTV=-(VOLPIN-VSUB(IDX)-VSUB(IDY))
ENDIF
ENDIF
ENDIF
VOLINT=VOLINT+CARTV
ENDIF
FACTY=-FACTY
130 CONTINUE
FACTX=-FACTX
120 CONTINUE
DT1=ABS(VOLINT-VOLPIN)
DT2=ABS(VOLINT-VOLCAR)
DT3=ABS(VOLINT)
IF(DT1 .LT. DCUTOF) THEN
VOLINT=VOLPIN
NXTIRA=2
ELSE IF(DT2 .LT. DCUTOF) THEN
VOLINT=VOLCAR
NXTIRA=1
ELSE IF(DT3 .LT. DCUTOF) THEN
VOLINT=DZERO
NXTIRA=0
ELSE
NXTIRA=-1
ENDIF
ENDIF
*----
IF(IPRINT .GE. 200) THEN
WRITE(IOUT,6012) NAMSBR,NXTIRA,VOLINT
WRITE(IOUT,6001) NAMSBR
ENDIF
RETURN
*----
* Output formats
*----
6000 FORMAT('(* Output from --',A6,'-- follows ')
6001 FORMAT(' Output from --',A6,'-- completed *)')
6010 FORMAT('XYCAR ={',3(F20.10,','),F20.10,'};')
6011 FORMAT('POSPIN={',2(F20.10,','),F20.10,'};')
6012 FORMAT(A6,'={',I5,',',F20.10,'};')
END
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