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-- Simple vector plot example
-- Copyright (C) 2008, 2013 Jerry Bauck
-- This file is part of PLplot.
-- PLplot is free software; you can redistribute it and/or modify
-- it under the terms of the GNU Library General Public License as published
-- by the Free Software Foundation; either version 2 of the License, or
-- (at your option) any later version.
-- PLplot is distributed in the hope that it will be useful,
-- but WITHOUT ANY WARRANTY; without even the implied warranty of
-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-- GNU Library General Public License for more details.
-- You should have received a copy of the GNU Library General Public License
-- along with PLplot; if not, write to the Free Software
-- Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
with
System,
System.Address_To_Access_Conversions,
Ada.Numerics,
Ada.Numerics.Long_Elementary_Functions,
PLplot_Traditional,
PLplot_Auxiliary;
use
Ada.Numerics,
Ada.Numerics.Long_Elementary_Functions,
System,
PLplot_Traditional,
PLplot_Auxiliary;
procedure x22a is
-- Pairs of points making the line segments used to plot the user defined arrow
arrow_x : Real_Vector(0 .. 5) := (-0.5, 0.5, 0.3, 0.5, 0.3, 0.5);
arrow_y : Real_Vector(0 .. 5) := ( 0.0, 0.0, 0.2, 0.0, -0.2, 0.0);
arrow2_x : Real_Vector(0 .. 5) := (-0.5, 0.3, 0.3, 0.5, 0.3, 0.3);
arrow2_y : Real_Vector(0 .. 5) := ( 0.0, 0.0, 0.2, 0.0, -0.2, 0.0);
-- Vector plot of the circulation about the origin
procedure circulation is
dx, dy, x, y : Long_Float;
nx : constant Integer := 20;
ny : constant Integer := 20;
xmin, xmax, ymin, ymax : Long_Float;
u, v : Real_Matrix(0 .. nx - 1, 0 .. ny -1);
cgrid2 : aliased Transformation_Data_Type_2
(x_Last => nx - 1,
y_Last => ny - 1);
begin
dx := 1.0;
dy := 1.0;
xmin := Long_Float(-nx / 2) * dx;
xmax := Long_Float( nx / 2) * dx;
ymin := Long_Float(-ny / 2) * dy;
ymax := Long_Float( ny / 2) * dy;
-- Create data - circulation around the origin.
for i in 0 .. nx - 1 loop
x := (Long_Float(i - nx / 2) + 0.5) * dx;
for j in 0 .. ny - 1 loop
y := (Long_Float(j - ny / 2) + 0.5) * dy;
cgrid2.xg(i, j) := x;
cgrid2.yg(i, j) := y;
u(i, j) := y;
v(i, j) := -x;
end loop;
end loop;
-- Plot vectors with default arrows
plenv(xmin, xmax, ymin, ymax, 0, 0);
pllab("(x)", "(y)", "#frPLplot Example 22 - circulation");
plcol0(2);
plvect(u, v, 0.0, pltr2'access, cgrid2'Address);
plcol0(1);
end circulation;
--Vector plot of flow through a constricted pipe
procedure constriction(astyle : Integer) is
dx, dy, x, y : Long_Float;
xmin, xmax, ymin, ymax : Long_Float;
Q, b, dbdx : Long_Float;
nx : constant Integer := 20;
ny : constant Integer := 20;
u, v : Real_Matrix(0 .. nx - 1, 0 .. ny -1);
cgrid2 : aliased Transformation_Data_Type_2
(x_Last => nx - 1,
y_Last => ny - 1);
begin
dx := 1.0;
dy := 1.0;
xmin := Long_Float(-nx / 2) * dx;
xmax := Long_Float( nx / 2) * dx;
ymin := Long_Float(-ny / 2) * dy;
ymax := Long_Float( ny / 2) * dy;
Q := 2.0;
for i in 0 .. nx - 1 loop
x := (Long_Float(i - nx / 2) + 0.5) * dx;
for j in 0 .. ny - 1 loop
y := (Long_Float(j - ny / 2) + 0.5) * dy;
cgrid2.xg(i, j) := x;
cgrid2.yg(i, j) := y;
b := ymax / 4.0 * (3.0 - cos(pi * x / xmax));
if abs(y) < b then
dbdx := ymax / 4.0 * sin(pi * x / xmax) * pi / xmax * y / b;
u(i, j) := Q * ymax / b;
v(i, j) := dbdx * u(i, j);
else
u(i, j) := 0.0;
v(i, j) := 0.0;
end if;
end loop;
end loop;
plenv(xmin, xmax, ymin, ymax, 0, 0);
pllab("(x)", "(y)", "#frPLplot Example 22 - constriction (arrow style" &
Integer'image(astyle) & ")");
plcol0(2);
plvect(u, v, -1.0, pltr2'access, cgrid2'Address);
plcol0(1);
end constriction;
-- This spec is necessary in order to enforce C calling conventions, used
-- in the callback by intervening C code.
procedure transform
(x, y : Long_Float;
xt, yt : out Long_Float;
data : PLPointer);
pragma Convention(C, transform);
-- Global transform function for a constriction using data passed in
-- This is the same transformation used in constriction.
procedure transform(x, y : Long_Float; xt, yt : out Long_Float; Data : PLPointer) is
-- Convert the generic pointer represented as System.Address to a proper Ada pointer aka
-- access variable. Recall that PLpointer is a subtype of System.Address.
package Data_Address_Conversions is new System.Address_To_Access_Conversions(Long_Float);
Data_Pointer : Data_Address_Conversions.Object_Pointer; -- An Ada access variable
xmax : Long_Float;
begin
Data_Pointer := Data_Address_Conversions.To_Pointer(Data);
xmax := Data_Pointer.all;
xt := x;
yt := y / 4.0 * (3.0 - cos(Pi * x / xmax));
end transform;
-- Vector plot of flow through a constricted pipe with a coordinate transform
procedure constriction2 is
dx, dy, x, y : Long_Float;
xmin, xmax, ymin, ymax : Long_Float;
Q, b : Long_Float;
nx : constant Integer := 20;
ny : constant Integer := 20;
cgrid2 : aliased Transformation_Data_Type_2
(x_Last => nx - 1,
y_Last => ny - 1);
u, v : Real_Matrix(0 .. nx - 1, 0 .. ny - 1);
nc : constant Integer := 11;
nseg : constant Integer := 20;
clev : Real_Vector(0 .. nc - 1);
begin
dx := 1.0;
dy := 1.0;
xmin := Long_Float(-nx / 2) * dx; -- Careful; Ada / rounds, C / truncates.
xmax := Long_Float( nx / 2) * dx;
ymin := Long_Float(-ny / 2) * dy;
ymax := Long_Float( ny / 2) * dy;
plstransform(transform'Unrestricted_Access, xmax'Address);
cgrid2.nx := nx;
cgrid2.ny := ny;
Q := 2.0;
for i in 0 .. nx - 1 loop
x := (Long_Float(i - nx / 2) + 0.5) * dx;
for j in 0 .. ny - 1 loop
y := (Long_Float(j - ny / 2) + 0.5) * dy;
cgrid2.xg(i, j) := x;
cgrid2.yg(i, j) := y;
b := ymax / 4.0 * (3.0 - cos(Pi * x / xmax));
u(i, j) := Q * ymax / b;
v(i, j) := 0.0;
end loop;
end loop;
for i in 0 .. nc - 1 loop
clev(i) := Q + Long_Float(i) * Q / Long_Float(nc - 1);
end loop;
plenv(xmin, xmax, ymin, ymax, 0, 0);
pllab("(x)", "(y)", "#frPLplot Example 22 - constriction with plstransform");
plcol0(2);
plshades(u, Null,
xmin + dx / 2.0, xmax - dx / 2.0, ymin + dy / 2.0, ymax - dy / 2.0,
clev, 0.0, 1, 1.0, plfill'access, False, Null, System.Null_Address);
plvect(u, v,
-1.0, pltr2'access, cgrid2'Address);
-- Plot edges using plpath (which accounts for coordinate transformation) rather than plline
plpath(nseg, xmin, ymax, xmax, ymax);
plpath(nseg, xmin, ymin, xmax, ymin);
plcol0(1);
Clear_Custom_Coordinate_Transform;
-- or...
-- plstransform(null, System.Null_Address);
end constriction2;
-- Vector plot of the gradient of a shielded potential (see example 9)
procedure potential is
nper : constant Integer := 100;
nlevel : constant Integer := 10;
nr : constant Integer := 20;
ntheta : constant Integer := 20;
eps, q1, d1, q1i, d1i, q2, d2, q2i, d2i : Long_Float;
div1, div1i, div2, div2i : Long_Float;
r, theta, x, y, dz : Long_Float;
xmin, xmax, ymin, ymax, rmax, zmax, zmin : Long_Float;
u, v, z : Real_Matrix(0 .. nr - 1, 0 .. ntheta - 1);
px, py : Real_Vector(0 .. nper - 1);
clevel : Real_Vector(0 .. nlevel - 1);
cgrid2 : aliased Transformation_Data_Type_2
(x_Last => nr - 1,
y_Last => ntheta - 1);
function pow(x, y : Long_Float) return Long_Float is
Result : Long_Float := 1.0;
begin
for i in 1 .. Integer(y) loop
Result := Result * x;
end loop;
return Result;
end pow;
begin
-- Potential inside a conducting cylinder (or sphere) by method of images.
-- Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
-- Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
-- Also put in smoothing term at small distances.
rmax := Long_Float(nr);
eps := 2.0;
q1 := 1.0;
d1 := rmax / 4.0;
q1i := - q1 * rmax / d1;
d1i := (rmax * rmax) / d1;
q2 := -1.0;
d2 := rmax / 4.0;
q2i := - q2 * rmax / d2;
d2i := (rmax * rmax) / d2;
for i in 0 .. nr - 1 loop
r := 0.5 + Long_Float(i);
for j in 0 .. ntheta - 1 loop
theta := 2.0 * pi / Long_Float(ntheta - 1) * (0.5 + Long_Float(j));
x := r * cos(theta);
y := r * sin(theta);
cgrid2.xg(i, j) := x;
cgrid2.yg(i, j) := y;
div1 := sqrt(pow(x-d1, 2.0) + pow(y-d1, 2.0) + pow(eps, 2.0));
div1i := sqrt(pow(x-d1i, 2.0) + pow(y-d1i, 2.0) + pow(eps, 2.0));
div2 := sqrt(pow(x-d2, 2.0) + pow(y+d2, 2.0) + pow(eps, 2.0));
div2i := sqrt(pow(x-d2i, 2.0) + pow(y+d2i, 2.0) + pow(eps, 2.0));
z(i, j) := q1/div1 + q1i/div1i + q2/div2 + q2i/div2i;
u(i, j) := -q1*(x-d1)/pow(div1, 3.0) - q1i*(x-d1i)/pow(div1i, 3.00)
- q2*(x-d2)/pow(div2,3.0) - q2i*(x-d2i)/pow(div2i, 3.0);
v(i, j) := -q1*(y-d1)/pow(div1, 3.0) - q1i*(y-d1i)/pow(div1i, 3.00)
- q2*(y+d2)/pow(div2, 3.0) - q2i*(y+d2i)/pow(div2i, 3.0);
end loop;
end loop;
xmin := Matrix_Min(cgrid2.xg);
xmax := Matrix_Max(cgrid2.xg);
ymin := Matrix_Min(cgrid2.yg);
ymax := Matrix_Max(cgrid2.yg);
zmin := Matrix_Min(z);
zmax := Matrix_Max(z);
plenv(xmin, xmax, ymin, ymax, 0, 0);
pllab("(x)", "(y)", "#frPLplot Example 22 - potential gradient vector plot");
-- Plot contours of the potential
dz := (zmax - zmin) / Long_Float(nlevel);
for i in clevel'range loop
clevel(i) := zmin + (Long_Float(i) + 0.5) * dz;
end loop;
plcol0(3);
pllsty(2);
plcont(z, 1, nr, 1, ntheta, clevel, pltr2'access, cgrid2'Address);
pllsty(1);
plcol0(1);
-- Plot the vectors of the gradient of the potential
plcol0(2);
plvect(u, v, 25.0, pltr2'access, cgrid2'Address);
plcol0(1);
-- Plot the perimeter of the cylinder
for i in px'range loop
theta := (2.0 * pi / Long_Float(nper - 1)) * Long_Float(i);
px(i) := rmax * cos(theta);
py(i) := rmax * sin(theta);
end loop;
plline(px,py);
end potential;
----------------------------------------------------------------------------
-- Generates several simple vector plots.
----------------------------------------------------------------------------
begin
-- Parse and process command line arguments
plparseopts(PL_PARSE_FULL);
-- Initialize plplot
plinit;
circulation;
-- Set arrow style using arrow_x and arrow_y then plot using these arrows.
plsvect(arrow_x, arrow_y, False);
constriction(1);
-- Set arrow style using arrow2_x and arrow2_y then plot using these filled arrows.
plsvect(arrow2_x, arrow2_y, True);
constriction(2);
constriction2;
-- Reset arrow style to the default by passing two NULL arrays.
-- This line uses the awkward method of the C API to reset the default arrow style.
-- plsvect(System.Null_Address, System.Null_Address, False);
-- This method of resetting the default arrow style is a little more Ada-friendly...
plsvect;
-- ... as is this one which is identical but for name.
-- Reset_Vector_Arrow_Style;
potential;
plend;
end x22a;
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