File:Blowup.png

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Original file(1,024 × 1,024 pixels, file size: 182 KB, MIME type: image/png)

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Summary

Description
English: An affine chart of the blowing-up of the affine plane at the origin. The exceptional curve is marked in red, the strict transforms of some lines through the origin are marked in gray.
Date
Source Own work
Author Robx

Generated using surf, with the following script.

width = 1024;
height = 1024;

scale_x = 0.2;
//scale_y = 2;
rot_y = -0.4;
rot_x = 0.05;

second = scale;
third = rotate;

//clip = 3;

// affine plane has coordinates z,y
surface = x*z-y;
//surface = x;
draw_surface;

curve_width = 1;
curve_red = 100;
curve_blue = 100;
curve_green = 100;

double pi = 2*arcsin(1);
int steps = 12;
int stepsdrawn = 9;
int i = -stepsdrawn;
double angle = 0;
loop:
	alpha = i*pi/(2*steps);
	//plane = cos(alpha)*y + sin(alpha)*z;
	plane = x - tan(alpha);
	cut_with_plane;
	i = i + 1;
	if (i < stepsdrawn) goto loop;

// E
curve_red = 200;
curve_blue = 30;
curve_green = 30;
plane = z-0;
cut_with_plane;

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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depicts

11 July 2008

image/png

06ff3aca9451a9508dabec7824dbdebb43999b4f

185,890 byte

1,024 pixel

1,024 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current13:01, 11 July 2008Thumbnail for version as of 13:01, 11 July 20081,024 × 1,024 (182 KB)wikimediacommons>Robx{{Information |Description={{en|1=an affine chart of the blowing-up of the affine plane at the origin}} |Source=Own work by uploader |Author=Robx |Date=20080711 |Permission= |other_versions= }} {{ImageUpload|full}} Category:Surfaces

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