File:Tesseract tetrahedron shadow with alternating vertex colors.png
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Captions
Summary
[edit]DescriptionTesseract tetrahedron shadow with alternating vertex colors.png |
The central projection of the tesseract from a vertex gives a 3-dimensional shadow with a tetrahedral convex hull. This file was created to match File:Concertina tesseract with blue faces.png. This image was created with POV-Ray. |
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Source | Own work | ||
Author |
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Licensing
[edit]Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
POV-Ray source
[edit]#version 3.6;
global_settings { assumed_gamma 1.0 }
#default{ finish{ ambient 0.1 diffuse 0.9 conserve_energy}}
#include "colors.inc"
///////////////////////////// camera and light
#declare Camera_Position = <10, 16, -50>;
camera{
location Camera_Position
right x*image_width/image_height
angle 11.3
look_at <.7, 1.1, 0>
}
light_source{ <-400, 500, -300> color White*0.9 shadowless}
light_source{ <400, 200, 100> color White*0.4 shadowless}
light_source{ Camera_Position color rgb<0.9,0.9,1>*0.2 shadowless}
sky_sphere{ pigment{ White } }
/////////////////////////////////////////////////////////////////////////////////////////////////
#declare Factor = 7;
#declare VertexPoints = array[15]{ <-0.7071067811865475, -0.408248290463863, -0.28867513459481287>, <0.0, 0.0, 0.8660254037844386>, <-0.35355339059327373, -0.2041241452319315, 0.28867513459481287>, <0.0, 0.816496580927726, -0.28867513459481287>, <-0.35355339059327373, 0.2041241452319315, -0.28867513459481287>, <0.0, 0.408248290463863, 0.28867513459481287>, <-0.2357022603955158, 0.13608276348795434, 0.09622504486493762>, <0.7071067811865475, -0.408248290463863, -0.28867513459481287>, <0.0, -0.408248290463863, -0.28867513459481287>, <0.35355339059327373, -0.2041241452319315, 0.28867513459481287>, <0.0, -0.2721655269759087, 0.09622504486493762>, <0.35355339059327373, 0.2041241452319315, -0.28867513459481287>, <0.0, 0.0, -0.28867513459481287>, <0.2357022603955158, 0.13608276348795434, 0.09622504486493762>, <0.0, 0.0, 0.0> }
#declare VertexRanks = array[15]{ 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 }
#declare FakeRanks = array[5]{0, 1, 3, 6, 10};
#declare VertexRankParities = array[15]{ 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0 }
#declare Edges = array[28]{ array[2]{2, 3}, array[2]{4, 5}, array[2]{6, 7}, array[2]{8, 9}, array[2]{10, 11}, array[2]{12, 13}, array[2]{14, 15}, array[2]{1, 3}, array[2]{4, 6}, array[2]{5, 7}, array[2]{8, 10}, array[2]{9, 11}, array[2]{12, 14}, array[2]{13, 15}, array[2]{1, 5}, array[2]{2, 6}, array[2]{3, 7}, array[2]{8, 12}, array[2]{9, 13}, array[2]{10, 14}, array[2]{11, 15}, array[2]{1, 9}, array[2]{2, 10}, array[2]{3, 11}, array[2]{4, 12}, array[2]{5, 13}, array[2]{6, 14}, array[2]{7, 15} }
#declare Faces = array[18]{ array[4]{5, 1, 3, 7}, array[4]{6, 2, 3, 7}, array[4]{6, 4, 5, 7}, array[4]{10, 8, 9, 11}, array[4]{9, 1, 3, 11}, array[4]{10, 2, 3, 11}, array[4]{12, 4, 5, 13}, array[4]{12, 8, 9, 13}, array[4]{9, 1, 5, 13}, array[4]{12, 4, 6, 14}, array[4]{12, 8, 10, 14}, array[4]{10, 2, 6, 14}, array[4]{11, 3, 7, 15}, array[4]{14, 6, 7, 15}, array[4]{14, 10, 11, 15}, array[4]{13, 9, 11, 15}, array[4]{14, 12, 13, 15}, array[4]{13, 5, 7, 15} }
/////////////////////////////////////////////////////////////////////////////////////////////////
union{
// VERTICES
union{
#for( i, 0, dimension_size(VertexPoints, 1)-1 )
#local Rank = VertexRanks[i];
#local FakeRank = FakeRanks[Rank];
#local Rad = .05 + pow(10-FakeRank, 2) / 600;
sphere{ VertexPoints[i]*Factor, Rad
#if(VertexRankParities[i])
pigment{color rgb<1,0.8,0.65>*.2}
#else
pigment{color rgb<1,0.8,0.65>*.5}
#end
}
#end
}
// EDGES
union{
#for( i, 0, dimension_size(Edges, 1)-1 )
#local Edge = Edges[i];
#local Index1 = Edge[0] - 1;
#local Index2 = Edge[1] - 1;
#local Point1 = VertexPoints[Index1]*Factor;
#local Point2 = VertexPoints[Index2]*Factor;
#local Rank1 = VertexRanks[Index1];
#local Rank2 = VertexRanks[Index2];
#local FakeRank1 = FakeRanks[Rank1];
#local FakeRank2 = FakeRanks[Rank2];
#local Rad1 = (.05 + pow(10-FakeRank1, 2) / 600) / 3.5;
#local Rad2 = (.05 + pow(10-FakeRank2, 2) / 600) / 3.5;
cone{ Point1, Rad1, Point2, Rad2 }
#end
pigment{color rgb .5}
}
// FACES
union{
#for( i, 0, dimension_size(Faces, 1)-1 )
#local FaceArray = Faces[i];
#local LenOfFaceArray = dimension_size(FaceArray, 1);
polygon{ LenOfFaceArray,
#for(VertexIndexInFace, 0, LenOfFaceArray-1)
#local VertexIndexInPolytope = FaceArray[VertexIndexInFace] - 1;
VertexPoints[VertexIndexInPolytope]*Factor
#end
}
#end
pigment{color rgbt<0, 0, 1, .8>}
}
rotate -90*x
rotate 4*y
rotate 4*z
}
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:26, 31 March 2018 | 3,624 × 3,990 (922 KB) | Watchduck (talk | contribs) |
You cannot overwrite this file.
File usage on Commons
The following 10 pages use this file:
- User talk:Watchduck
- File:Concertina tesseract with blue faces.png
- File:Concertina tesseract with gray cells.png
- File:Tesseract Schlegel.png
- File:Tesseract tetrahedron shadow.png
- File:Tesseract tetrahedron shadow rgby.png
- File:Tesseract tetrahedron shadow with alternating vertex colors, lower cube.png
- File:Tesseract tetrahedron shadow with alternating vertex colors, upper cube.png
- Category:Hypercubes (blue alt)
- Category:Tesseract Schlegel shadow (blue alt)
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
PNG file comment |
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Horizontal resolution | 28.35 dpc |
Vertical resolution | 28.35 dpc |
File change date and time | 15:44, 31 March 2018 |