Archivo:Cardinal Spline Example.png
Cardinal_Spline_Example.png (720 × 480 píxeles; tamaño de archivo: 7 kB; tipo MIME: image/png)
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DescripciónCardinal Spline Example.png |
English: This image is a graphical representation of a Cardinal Spline. It is drawn on a 720x480 canvas and the curve has 10 control points. The tension is set to 0.1.
The red squares represent the position of the control points, and the red line represents the path of the curve. The image was created with the following w:perl script: use strict; use Image::Magick; use Math::Matrix; use Math::Gradient qw(gradient); my $rate = 500; my $tension = 0.1; my(@coords) = ( [ 23, 24], [123, 64], [167,200], [ 18,285], [293,467], [699,205], [487,181], [358,222], [262,130], [238, 24] ); my $image = Image::Magick->new; # Create new image $image ->Set(size=>'720x480'); # Set size $image ->ReadImage('xc:white'); # Make it all white foreach my $ra_coord (@coords) # For every set of coords in the list { my($x,$y) = @{$ra_coord}[0,1]; # Get the x and y $image ->Draw ( primitive => 'rectangle', points => (($x-3).','.($y-3).' '.($x+3).','.($y+3)), fill => 'red' ); # Draw a small rectangle at each coord } while (scalar(@coords) >= 4) # While there are at least 4 entries in the list { for my $u (gradient(0,1,$rate)) # iterate from 0 to 1 in 500 steps { my($x,$y) = &EvaluateCardinal2D(\@coords, $tension, $u); # Hand paramaters to formula $image ->Set("pixel\[$x,$y\]"=>'red'); # Set that pixel red } shift(@coords); # Remove the first entry of the list } $image ->Write("Cardinal_Spline_Example.png"); # Save image sub EvaluateCardinal2D { my($ra_coords,$T,$u) = @_; my $s = (1-$T)/2; my $u_matrix = new Math::Matrix # 4 x 1 ( # Matrix based off the point in the curve [($u ** 3), ($u ** 2), ($u), (1) ] ); my $cardinal_matrix = new Math::Matrix # 4 x 4 ( # Guts of the Cardinal Spline formula [(-1 * $s), (2 - $s), ($s - 2), ($s) ], [(2 * $s), ($s - 3), (3-(2 * $s)), (-1 * $s) ], [(-1 * $s), (0), ($s), (0) ], [(0), (1), (0), (0) ], ); my $x_matrix = new Math::Matrix # 1 x 4 ( # X coords for point: [${${$ra_coords}[0]}[0]], # 1 [${${$ra_coords}[1]}[0]], # 2 [${${$ra_coords}[2]}[0]], # 3 [${${$ra_coords}[3]}[0]] # 4 ); my $y_matrix = new Math::Matrix # 1 x 4 ( # Y coords for point: [${${$ra_coords}[0]}[1]], # 1 [${${$ra_coords}[1]}[1]], # 2 [${${$ra_coords}[2]}[1]], # 3 [${${$ra_coords}[3]}[1]] # 4 ); my $xt = int ($u_matrix * $cardinal_matrix * $x_matrix); # Compute for X my $yt = int ($u_matrix * $cardinal_matrix * $y_matrix); # Compute for Y return($xt,$yt); } The above source code is released under the same conditions as the image itself. (PD by owner) Missing from file history: Berland cropped the image 2007-03-05. |
Fecha | 17 October 2006 |
Fuente | Trabajo propio |
Autor | H (talk) (Uploads) |
Resumen
This image is a graphical representation of a Cardinal Spline. It is drawn on a 720x480 canvas and the curve has 10 control points. The tension is set to 0.1.
The red squares represent the position of the control points, and the red line represents the path of the curve.
The image was created with the following w:perl script:
use strict; use Image::Magick; use Math::Matrix; use Math::Gradient qw(gradient); my $rate = 500; my $tension = 0.1; my(@coords) = ( [ 23, 24], [123, 64], [167,200], [ 18,285], [293,467], [699,205], [487,181], [358,222], [262,130], [238, 24] ); my $image = Image::Magick->new; # Create new image $image ->Set(size=>'720x480'); # Set size $image ->ReadImage('xc:white'); # Make it all white foreach my $ra_coord (@coords) # For every set of coords in the list { my($x,$y) = @{$ra_coord}[0,1]; # Get the x and y $image ->Draw ( primitive => 'rectangle', points => (($x-3).','.($y-3).' '.($x+3).','.($y+3)), fill => 'red' ); # Draw a small rectangle at each coord } while (scalar(@coords) >= 4) # While there are at least 4 entries in the list { for my $u (gradient(0,1,$rate)) # iterate from 0 to 1 in 500 steps { my($x,$y) = &EvaluateCardinal2D(\@coords, $tension, $u); # Hand paramaters to formula $image ->Set("pixel\[$x,$y\]"=>'red'); # Set that pixel red } shift(@coords); # Remove the first entry of the list } $image ->Write("Cardinal_Spline_Example.png"); # Save image sub EvaluateCardinal2D { my($ra_coords,$T,$u) = @_; my $s = (1-$T)/2; my $u_matrix = new Math::Matrix # 4 x 1 ( # Matrix based off the point in the curve [($u ** 3), ($u ** 2), ($u), (1) ] ); my $cardinal_matrix = new Math::Matrix # 4 x 4 ( # Guts of the Cardinal Spline formula [(-1 * $s), (2 - $s), ($s - 2), ($s) ], [(2 * $s), ($s - 3), (3-(2 * $s)), (-1 * $s) ], [(-1 * $s), (0), ($s), (0) ], [(0), (1), (0), (0) ], ); my $x_matrix = new Math::Matrix # 1 x 4 ( # X coords for point: [${${$ra_coords}[0]}[0]], # 1 [${${$ra_coords}[1]}[0]], # 2 [${${$ra_coords}[2]}[0]], # 3 [${${$ra_coords}[3]}[0]] # 4 ); my $y_matrix = new Math::Matrix # 1 x 4 ( # Y coords for point: [${${$ra_coords}[0]}[1]], # 1 [${${$ra_coords}[1]}[1]], # 2 [${${$ra_coords}[2]}[1]], # 3 [${${$ra_coords}[3]}[1]] # 4 ); my $xt = int ($u_matrix * $cardinal_matrix * $x_matrix); # Compute for X my $yt = int ($u_matrix * $cardinal_matrix * $y_matrix); # Compute for Y return($xt,$yt); }
Licencia
Public domainPublic domainfalsefalse |
Yo, el titular de los derechos de autor de esta obra, lo libero al dominio público. Esto aplica en todo el mundo. En algunos países esto puede no ser legalmente factible; si ello ocurriese: Concedo a cualquier persona el derecho de usar este trabajo para cualquier propósito, sin ningún tipo de condición al menos que éstas sean requeridas por la ley. |
The above source code is released under the same conditions as the image itself. (PD by owner)
Missing from file history: Berland cropped the image 2007-03-05.
Elementos representados en este archivo
representa a
image/png
a8413cfb6df53fd074f9410ab6a833e8a1d50fa1
7439 byte
480 píxel
720 píxel
Historial del archivo
Haz clic sobre una fecha y hora para ver el archivo tal como apareció en ese momento.
Fecha y hora | Miniatura | Dimensiones | Usuario | Comentario | |
---|---|---|---|---|---|
actual | 00:16 19 dic 2007 | 720 × 480 (7 kB) | HighInBC | Instead of cropping an example which uses absolute coordinates, I have moved the curve closer to the edge | |
21:36 5 mar 2007 | 563 × 293 (2 kB) | Berland | |||
04:35 17 oct 2006 | 720 × 480 (6 kB) | H | == Summary == This image is a graphical representation of a ''Cardinal Spline''. It is drawn on a 720x480 canvas and the curve has 10 control points. The tension is set to ''0.1''. The red squares repesent the posistion of the control points, and the red |
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