generate_cartesian_mesh.m File Reference

Functions
	Map (i, j) to vertex number vertex_count=0
	x (i)
	y (j)]
	vertex_map (i, j)
end end Generate	cells (quadrilaterals) cells
id	cells ()
end Write vertices section	fprintf (fid, 'Vertices\n')
	fprintf (fid, '%8d\n', size(vertices, 1))
end Write cells section	fprintf (fid, 'cells\n')
	fprintf (fid, '%8d\n', size(cells, 1))
end Write centers section	fprintf (fid, 'centers\n')
end	fclose (fid)
end Plot vertices as red dots	plot (vertices(:, 1), vertices(:, 2), 'ro', 'MarkerSize', 4, 'MarkerFaceColor', 'red')
Plot cell centers as blue dots	plot (cell_centers(:, 1), cell_centers(:, 2), 'bo', 'MarkerSize', 3, 'MarkerFaceColor', 'blue')
	xlabel ('X')
	ylabel ('Y')
	title (sprintf('Cartesian Mesh %dx%d on Domain[%.2f,%.2f] x[%.2f,%.2f]',... N, M, xmin, xmax, ymin, ymax))
	legend ('Mesh lines', 'Vertices', 'Cell centers', 'Location', 'best')
	xlim ([xmin - margin_x, xmax+margin_x])
	ylim ([ymin - margin_y, ymax+margin_y])
	fprintf ('Mesh successfully generated and saved as %s\n', filename)
	fprintf ('Number of vertices:%d\n', size(vertices, 1))
	fprintf ('Number of cells:%d\n', size(cells, 1))
end Example Unit mesh	generate_cartesian_mesh ([0, 2, 0, 1], 10, 5)
Rectangle[0, 2] mesh	generate_cartesian_mesh ([-1, 1, -1, 1], 4, 4)

Variables
function generate_cartesian_mesh(domain, N, M) % GENERATE_CARTESIAN_MESH - Generate cartesian mesh for rectangular domain % % INPUTS	xmax = domain(2)
	ymin = domain(3)
	ymax = domain(4)
Create grid points	x = linspace(xmin, xmax, N+1)
	y = linspace(ymin, ymax, M+1)
Generate vertices	vertices = []
	vertex_map = zeros(N+1, M+1)
for	j
	cell_centers = []
	v1
	v2
	v3
	v4
Cell center	center_x = (x(i) + x(i+1)) / 2
	center_y = (y(j) + y(j+1)) / 2
end end Create filename	filename = sprintf('cart%dx%d.typ2', N, M)
Write to typ2 file	fid = fopen(filename, 'w')
for	i
Plot the mesh	figure
hold	on
Set axis properties axis	equal
Set axis limits with small margin	margin_x = (xmax - xmin) * 0.05
	margin_y = (ymax - ymin) * 0.05
hold	off
end Example	usage
end Example Unit	square

Function Documentation

cells() [1/2]

id cells ( )

virtual

cells() [2/2]

end end Generate cells

(

quadrilaterals

)

fclose()

end fclose

(

fid

)

fprintf() [1/8]

fprintf	(	'Mesh successfully generated and saved as %s\n'	,
		filename
	)

fprintf() [2/8]

fprintf	(	'Number of cells:%d\n'	,
		size(cells, 1)
	)

fprintf() [3/8]

fprintf	(	'Number of vertices:%d\n'	,
		size(vertices, 1)
	)

fprintf() [4/8]

fprintf	(	fid	,
		'%8d\n'	,
		size(cells, 1)
	)

fprintf() [5/8]

fprintf	(	fid	,
		'%8d\n'	,
		size(vertices, 1)
	)

fprintf() [6/8]

end Write cells section fprintf	(	fid	,
		'cells\n'
	)

fprintf() [7/8]

end Write centers section fprintf	(	fid	,
		'centers\n'
	)

fprintf() [8/8]

end Write vertices section fprintf	(	fid	,
		'Vertices\n'
	)

generate_cartesian_mesh() [1/2]

Rectangle[0, 2] mesh generate_cartesian_mesh	(	4	,
		4
	)

generate_cartesian_mesh() [2/2]

end Example Unit mesh generate_cartesian_mesh	(	10	,
		5
	)

legend()

legend	(	'Mesh lines'	,
		'Vertices'	,
		'Cell centers'	,
		'Location'	,
		'best'
	)

Map()

Map ( i  , j    )

pure virtual

plot() [1/2]

Plot cell centers as blue dots plot	(	cell_centers(:, 1)	,
		cell_centers(:, 2)	,
		'bo'	,
		'MarkerSize'	,
		3	,
		'MarkerFaceColor'	,
		'blue'
	)

plot() [2/2]

end Plot vertices as red dots plot	(	vertices(:, 1)	,
		vertices(:, 2)	,
		'ro'	,
		'MarkerSize'	,
		4	,
		'MarkerFaceColor'	,
		'red'
	)

title()

title

(

sprintf( 'Cartesian Mesh %dx%d on Domain[%.2f,%.2f] x[%.2f,%.2f]',... N, M, xmin, xmax, ymin, ymax)

)

vertex_map()

vertex_map	(	i	,
		j
	)

x()

x

(

i

)

xlabel()

xlabel

(

'X'

)

xlim()

xlim

(

)

y()

y

(

j

)

ylabel()

ylabel

(

'Y'

)

ylim()

ylim

(

)

Variable Documentation

cell_centers

cell_centers = []

center_x

center_x = (x(i) + x(i+1)) / 2

center_y

center_y = (y(j) + y(j+1)) / 2

equal

Set axis properties axis equal

fid

if fid = fopen(filename, 'w')

figure

Plot the mesh figure

filename

end end Create filename filename = sprintf('cart%dx%d.typ2', N, M)

i

Plot mesh lines for i

Initial value:

= 1:size(vertices, 1)
        fprintf(fid, '%20.16f %20.16f     \n', vertices(i, 1), vertices(i, 2))

j

end for j

Initial value:

= 1:M+1
        for i = 1:N+1
            vertex_count = vertex_count + 1

margin_x

Set axis limits with small margin margin_x = (xmax - xmin) * 0.05

margin_y

margin_y = (ymax - ymin) * 0.05

off

hold off

on

grid on

square

end Example Unit square

usage

end Example usage

v1

v1

v2

v2

v3

v3

v4

v4

vertex_map

i j vertex_map = zeros(N+1, M+1)

vertices

vertices = []

x

Square [-1,1] x[-1, 1] = linspace(xmin, xmax, N+1)

xmax

function generate_cartesian_mesh (domain, N, M) % GENERATE_CARTESIAN_MESH - Generate cartesian mesh for rectangular domain % % INPUTS xmax = domain(2)

y

y = linspace(ymin, ymax, M+1)

ymax

ymax = domain(4)

ymin

ymin = domain(3)