CIRCLE_SEGMENT
Area, Height, Angle, Sampling and Quadrature
CIRCLE_SEGMENT
is a C library which
carries out various computations associated with a circle segment,
using gnuplot to illustrate some of the computations.
Begin with a circle of radius R. Choose two points P1 and P2 on the
circle, and draw the chord P1:P2. This chord divides the circle
into two pieces, each of which is called a circle segment.
Consider one of the pieces. The "angle" THETA of this segment is the
angle P1:C:P2, where C is the center of the circle. Let Q be the point
on the chord P1:P2 which is closest to C. The "height" H of the segment
is the distance from Q to the perimeter of the circle.
This library considers various computations, including:
Determine the angle THETA, given R and H.
Determine the height H, given R and THETA.
Determine the height H, given R and AREA.
Determine the width W, given R and H.
Determine the area, given R and H.
Determine the centroid, given R and H.
Select points uniformly at random from a segment, given R and H.
Determine a cumulative density function (CDF) for the height H2
of a circle segment defined by a point selected at random from
a circle segment of height H.
Determine a quadrature rule that can be used to estimate integrals
of functions f(x,y) over the segment.
CIRCLE_SEGMENT creates some graphics plots using gnuplot.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
CIRCLE_SEGMENT is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
CIRCLE_RULE,
a C library which
computes quadrature rules for the unit circle in 2D, that is,
the circumference of the circle of radius 1 and center (0,0).
GEOMETRY,
a C library which
performs geometric calculations in 2, 3 and M dimensional space,
including the computation of angles, areas, containment, distances,
intersections, lengths, and volumes.
GNUPLOT,
C programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
STROUD,
a C library which
defines quadrature rules for a variety of M-dimensional regions,
including the interior of the square, cube and hypercube, the pyramid,
cone and ellipse, the hexagon, the M-dimensional octahedron,
the circle, sphere and hypersphere, the triangle, tetrahedron and simplex,
and the surface of the circle, sphere and hypersphere.
Source Code:
Examples and Tests:
Test number 6 creates some samples of points in circle segments, and
writes out data files and gnuplot command files to create graphics:
-
sample01_boundary.txt,
data defining the boundary of the circle segment.
-
sample01_commands.txt,
commands to gnuplot to create a plot.
-
sample01_data.txt,
the sample data.
-
sample01.png,
the plot
-
sample02_boundary.txt,
data defining the boundary of the circle segment.
-
sample02_commands.txt,
commands to gnuplot to create a plot.
-
sample02_data.txt,
the sample data.
-
sample02.png,
the plot
-
sample03_boundary.txt,
data defining the boundary of the circle segment.
-
sample03_commands.txt,
commands to gnuplot to create a plot.
-
sample03_data.txt,
the sample data.
-
sample03.png,
the plot
-
sample04_boundary.txt,
data defining the boundary of the circle segment.
-
sample04_commands.txt,
commands to gnuplot to create a plot.
-
sample04_data.txt,
the sample data.
-
sample04.png,
the plot
List of Routines:
-
CIRCLE_SEGMENT_ANGLE_FROM_CHORD computes the angle of a circle segment.
-
CIRCLE_SEGMENT_ANGLE_FROM_CHORD_ANGLES computes angle of a circle segment.
-
CIRCLE_SEGMENT_ANGLE_FROM_HEIGHT computes the angle of a circle segment.
-
CIRCLE_SEGMENT_AREA_FROM_ANGLE computes the area of a circle segment.
-
CIRCLE_SEGMENT_AREA_FROM_CHORD computes the area of a circle segment.
-
CIRCLE_SEGMENT_AREA_FROM_HEIGHT computes the area of a circle segment.
-
CIRCLE_SEGMENT_AREA_FROM_SAMPLE computes the area of a circle segment.
-
CIRCLE_SEGMENT_CDF computes a CDF related to a circle segment.
-
CIRCLE_SEGMENT_CENTROID_FROM_CHORD computes the centroid of a circle segment.
-
CIRCLE_SEGMENT_CENTROID_FROM_HEIGHT computes centroid of a circle segment.
-
CIRCLE_SEGMENT_CENTROID_FROM_SAMPLE estimates a circle segment centroid.
-
CIRCLE_SEGMENT_CONTAINS_POINT reports whether a point is in a circle segment.
-
CIRCLE_SEGMENT_HEIGHT_FROM_ANGLE: height of a circle segment from angle.
-
CIRCLE_SEGMENT_HEIGHT_FROM_AREA: height of a circle segment from area.
-
CIRCLE_SEGMENT_HEIGHT_FROM_CHORD: height of a circle segment from chord.
-
CIRCLE_SEGMENT_SAMPLE_FROM_CHORD samples points from a circle segment.
-
CIRCLE_SEGMENT_SAMPLE_FROM_HEIGHT samples points from a circle segment.
-
CIRCLE_SEGMENT_WIDTH_FROM_HEIGHT computes the width of a circle segment.
-
FILENAME_INC increments a partially numeric file name.
-
R8_ACOS computes the arc cosine function, with argument truncation.
-
R8_ASIN computes the arc sine function, with argument truncation.
-
R8_ATAN computes the inverse tangent of the ratio Y / X.
-
R8_EPSILON returns the R8 round off unit.
-
R8_MAX returns the maximum of two R8's.
-
R8_MIN returns the minimum of two R8's.
-
R8_UNIFORM_01 returns a pseudorandom R8 scaled to [0,1].
-
R8MAT_UNIFORM_01_NEW fills an R8MAT with pseudorandom values scaled to [0,1].
-
R8VEC_LINSPACE_NEW creates a vector of linearly spaced values.
-
R8VEC_SUM returns the sum of an R8VEC.
-
R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.
-
TIMESTAMP prints the current YMDHMS date as a time stamp.
-
TRIDISOLVE solves a tridiagonal system of linear equations.
You can go up one level to
the C source codes.
Last revised on 06 July 2013.