Calculate the area enclosed by a region.
Double_Type regArea( Region_Type Region )
Double_Type regArea( Region_Type Region, Double_Type Xmin, Double_Type
Ymin, Double_Type Xmax, Double_Type Ymax, Double_Type Pixelsize )
The regArea routine returns the area inside a region. The
simple form simply takes a CIAO region variable and returns
the total area inside the region; the last 5 parameters are
omitted. However, if the region is complex and needs to be
'pixelated' to compute the area you may want to use the
second version.
For "simple" regions the area is calculated analytically.
For more-complicated regions - such as when shapes overlap -
the area is calculated numerically by counting how many pixels
fall within the region. The default values are to loop over the
bounding box of the region and consider each pixel individually.
Greater accuracy can be achieved by calling the routine with
the Pixelsize argument set to a value less than 1, although
the routine will then take longer to run.
The xmin, ymin, xmax, and ymax arguments define the region
over which the numerical calculation is performed.
When the one-argument form of regArea() is called these
limits default to the bounding box of the regions, if
one exists, otherwise the range -DBL_MAX to DBL_MAX.
An example of a region with no bounding box is
sector( 250, 400, 20, 45 )
The regExtent() routine can be used to find the bounding-box of a region.
chips> require("region")
chips> r1 = regParse("circle(10,10,4)")
chips> vmessage( "The area of the region is %f", regArea(r1) )
Here we use the simple version of the regArea() call to
calculate the area of the region
chips> shape1 = "rotbox(4096.5,4096.5,100,150,45)"
chips> shape2 = "annulus(4096.5,4096.5,40,50)"
chips> r1 = regParse(shape1)
chips> r2 = regParse(shape2)
chips> r3 = regParse(shape1 + "-" + shape2)
chips> a1 = regArea(r1)
chips> a2 = regArea(r2)
chips> a3 = regArea(r3)
chips> vmessage( "Areas = %8.2f %8.2f %8.2f", a1, a2, a3 )
Areas = 15000.00 2827.43 12190.00
Here we create three shapes: a rotated rectangle, an annulus,
and the rotated rectangle minus the annulus. The area of these
three regions is then calculated using the simple (1 argument)
version of regArea().
chips> a1c = regArea(r1,4000,4000,4200,4200,0.1)
chips> a2c = regArea(r2,4000,4000,4200,4200,0.1)
chips> a3c = regArea(r3,4000,4000,4200,4200,0.1)
chips> vmessage( "Areas = %8.2f %8.2f %8.2f", a1c, a2c, a3c )
Areas = 15000.00 2827.43 12168.19
Here we use the extended version of the regArea() call to
improve the accuracy of the calculation. It does not
make a differrence for the first two regions, but the
area of the third region has changed by
pixels, a 0.2% difference.
Note that the choice of bounding box is important for this
calculation. The range 4000-4200 for both axes was picked
since the rotated box should fit within it. The
regExtent() routine can be used to automatically calculate
the bounding box of a region, as follows:
chips> (x0,y0,x1,y1) = regExtent(r3)
chips> vmessage( "x= %.2f - %.2f y = %.2f - %.2f", x0, x1, y0, y1 )
x= 4008.11 - 4184.89 y = 4008.11 - 4184.89
If we had used a smaller
region - i.e. one smalller than the region of interest - then
regArea() would have returned the area of the region intersected
with this region. For instance:
chips> regArea(r1,4000,4000,4200,4200,0.1)
15000
chips> regArea(r1,4050,4050,4150,4150,0.1)
9109.59
chips> regArea(r1,4070,4050,4100,4150,0.1)
3010.25
The calculation of composite areas - those consisting of multiple
shapes - has been improved in this release.
The CIAO 3.2 release includes the regExtent() function, which
can be used to automatically calculate the limits used in the
six-argument form of regArea().
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