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# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
include <mach.h>
include "im2interpdef.h"
include <math/iminterp.h>
# MSIGRL -- Procedure to integrate the 2D interpolant over a specified area.
# The x and y arrays are assumed to describe a polygon which is the domain over
# which the integration is to be performed. The x and y must describe a closed
# curve and npts must be >= 4 with the last vertex equal to the first vertex.
# The routine uses the technique of separation of variables. The restriction on
# the polygon is that horizontal lines have at most one segment in common with
# the domain of integration. Polygons which do not fit this restriction can be
# split into one or more polygons before calling msigrl and the results can
# then be summed.
real procedure msigrl (msi, x, y, npts)
pointer msi # pointer to the interpolant descriptor structure
real x[npts] # array of x values
real y[npts] # array of y values
int npts # number of points which describe the boundary
int i, interp_type, nylmin, nylmax, offset
pointer x1lim, x2lim, xintegrl, ptr
real xmin, xmax, ymin, ymax, accum
real ii_1dinteg()
begin
# set up 1D interpolant type
switch (MSI_TYPE(msi)) {
case II_BINEAREST:
interp_type = II_NEAREST
case II_BILINEAR:
interp_type = II_LINEAR
case II_BIDRIZZLE:
interp_type = II_DRIZZLE
case II_BIPOLY3:
interp_type = II_POLY3
case II_BIPOLY5:
interp_type = II_POLY5
case II_BISPLINE3:
interp_type = II_SPLINE3
case II_BISINC:
interp_type = II_SINC
case II_BILSINC:
interp_type = II_LSINC
}
# set up temporary storage for x limits and the x integrals
call calloc (x1lim, MSI_NYCOEFF(msi), TY_REAL)
call calloc (x2lim, MSI_NYCOEFF(msi), TY_REAL)
call calloc (xintegrl, MSI_NYCOEFF(msi), TY_REAL)
# offset of first data point from edge of coefficient array
offset = mod (MSI_FSTPNT(msi), MSI_NXCOEFF(msi))
# convert the (x,y) points which describe the polygon into
# two arrays of x limits x1lim and x2lim and two y limits ymin and ymax
call ii_find_limits (x, y, npts, 0, 0, MSI_NYCOEFF(msi),
Memr[x1lim+offset], Memr[x2lim+offset], ymin, ymax, nylmin, nylmax)
nylmin = nylmin + offset
nylmax = nylmax + offset
# integrate in x
ptr = MSI_COEFF(msi) + offset + (nylmin - 1) * MSI_NXCOEFF(msi)
do i = nylmin, nylmax {
xmin = min (Memr[x1lim+i-1], Memr[x2lim+i-1])
xmax = max (Memr[x1lim+i-1], Memr[x2lim+i-1])
Memr[xintegrl+i-1] = ii_1dinteg (COEFF(ptr), MSI_NXCOEFF(msi),
xmin, xmax, interp_type, MSI_NSINC(msi), DX, MSI_XPIXFRAC(msi))
ptr = ptr + MSI_NXCOEFF(msi)
}
# integrate in y
if (interp_type == II_SPLINE3) {
call amulkr (Memr[xintegrl], 6.0, Memr[xintegrl], MSI_NYCOEFF(msi))
accum = ii_1dinteg (Memr[xintegrl+offset], MSI_NYCOEFF(msi), ymin,
ymax, II_NEAREST, MSI_NSINC(msi), DY, MSI_YPIXFRAC(msi))
} else {
accum = ii_1dinteg (Memr[xintegrl+offset], MSI_NYCOEFF(msi), ymin,
ymax, II_NEAREST, MSI_NSINC(msi), DY, MSI_YPIXFRAC(msi))
}
# free space
call mfree (xintegrl, TY_REAL)
call mfree (x1lim, TY_REAL)
call mfree (x2lim, TY_REAL)
return (accum)
end
# II_FIND_LIMITS -- Procedure to transform a set of (x,y)'s describing a
# polygon into a set of limits.
procedure ii_find_limits (x, y, npts, xboff, xeoff, max_nylines, x1lim, x2lim,
ymin, ymax, nylmin, nylmax)
real x[npts] # array of x values
real y[npts] # array of y values
int npts # number of data points
int xboff, xeoff # boundary extension limits
int max_nylines # max number of lines to integrate
real x1lim[ARB] # array of x1 limits
real x2lim[ARB] # array of x2 limits
real ymin # minimum y value for integration
real ymax # maximum y value for integration
int nylmin # minimum line number for x integration
int nylmax # maximum line number for x integration
int i, ninter
pointer sp, xintr, yintr
real xmin, xmax, lx, ld
int ii_pyclip()
begin
call smark (sp)
call salloc (xintr, npts, TY_REAL)
call salloc (yintr, npts, TY_REAL)
# find x and y limits and their indicess
call alimr (x, npts, xmin, xmax)
call alimr (y, npts, ymin, ymax)
# calculate the line limits for integration
nylmin = max (1, min (int (ymin + 0.5) - xboff, max_nylines))
nylmax = min (max_nylines, max (1, int (ymax + 0.5) + xeoff))
# initialize
lx = xmax - xmin
# calculate the limits
for (i = nylmin; i <= nylmax; i = i + 1) {
if (ymin > i)
ld = min (i + 0.5, ymax) * lx
else if (ymax < i)
ld = max (i - 0.5, ymin) * lx
else
ld = i * lx
ninter = ii_pyclip (x, y, Memr[xintr], Memr[yintr], npts, lx, ld)
if (ninter <= 0) {
x1lim[i] = xmin
x2lim[i] = xmin
} else {
x1lim[i] = min (Memr[xintr], Memr[xintr+1])
x2lim[i] = max (Memr[xintr], Memr[xintr+1])
}
}
call sfree (sp)
end
# II_YCLIP -- Procedure to determine the intersection points of a
# horizontal image line with an arbitrary polygon.
int procedure ii_pyclip (xver, yver, xintr, yintr, nver, lx, ld)
real xver[ARB] # x vertex coords
real yver[ARB] # y vertex coords
real xintr[ARB] # x intersection coords
real yintr[ARB] # y intersection coords
int nver # number of vertices
real lx, ld # equation of image line
int i, nintr
real u1, u2, u1u2, dx, dy, dd, xa, ya, wa
begin
nintr = 0
u1 = - lx * yver[1] + ld
do i = 2, nver {
u2 = - lx * yver[i] + ld
u1u2 = u1 * u2
# Test whether polygon line segment intersects image line or not.
if (u1u2 <= 0.0) {
# Compute the intersection coords.
if (u1 != 0.0 && u2 != 0.0) {
dy = yver[i-1] - yver[i]
dx = xver[i-1] - xver[i]
dd = xver[i-1] * yver[i] - yver[i-1] * xver[i]
xa = (dx * ld - lx * dd)
ya = dy * ld
wa = dy * lx
nintr = nintr + 1
xintr[nintr] = xa / wa
yintr[nintr] = ya / wa
# Test for collinearity.
} else if (u1 == 0.0 && u2 == 0.0) {
nintr = nintr + 1
xintr[nintr] = xver[i-1]
yintr[nintr] = yver[i-1]
nintr = nintr + 1
xintr[nintr] = xver[i]
yintr[nintr] = yver[i]
} else if (u1 != 0.0) {
if (i == 1) {
dy = (yver[2] - yver[1])
dd = (yver[nver-1] - yver[1])
} else if (i == nver) {
dy = (yver[2] - yver[nver])
dd = dy * (yver[nver-1] - yver[nver])
} else {
dy = (yver[i+1] - yver[i])
dd = dy * (yver[i-1] - yver[i])
}
if (dy != 0.0) {
nintr = nintr + 1
xintr[nintr] = xver[i]
yintr[nintr] = yver[i]
}
if (dd > 0.0) {
nintr = nintr + 1
xintr[nintr] = xver[i]
yintr[nintr] = yver[i]
}
}
}
u1 = u2
}
return (nintr)
end
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