File:Tesseract tetrahedron shadow with alternating vertex colors, lower cube.png

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Description

Lower cube in

One vertex in the preimage of this cube is the projection center, and this vertex is therefore not shown in the image.

Compare upper cube:

This image was created with POV-Ray.

Source

Own work

Author

Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Licensing edit

I, the copyright holder of this work, hereby publish it under the following licenses:

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.

This file is licensed under the Creative Commons Attribution 4.0 International license.

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.

You may select the license of your choice.

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 EdgeColor = <.5, .5, .5, 0>;
#declare TransparentEdgeColor = <.5, .5, .5, .95>;

#declare LightVertexColor = <.5, .8*.5, .65*.5, 0>;
#declare DarkVertexColor  = <.2, .8*.2, .65*.2, 0>;
#declare TransparentLightVertexColor = <.5, .8*.5, .65*.5, .95>;
#declare TransparentDarkVertexColor  = <.2, .8*.2, .65*.2, .95>;

#declare RedFaceColor  = <1, 0, 0, .18>;


/////////////////////////////////////////////////////////////////////////////////////////////////


#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 TransparentVertices = array[8]{ 2, 3, 6, 10, 7, 11, 14, 15 };

#declare SolidVertices = array[7]{ 1, 4, 8, 5, 9, 12, 13 };


#declare TransparentEdges = array[19]{ 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]{2, 3}, array[2]{2, 6}, array[2]{2, 10}, array[2]{3, 7}, array[2]{3, 11}, array[2]{6, 7}, array[2]{6, 14}, array[2]{10, 11}, array[2]{10, 14}, array[2]{7, 15}, array[2]{11, 15}, array[2]{14, 15} }

#declare SolidEdges = array[9]{ array[2]{1, 9}, array[2]{1, 5}, array[2]{8, 9}, array[2]{8, 12}, array[2]{4, 5}, array[2]{4, 12}, array[2]{5, 13}, array[2]{9, 13}, array[2]{12, 13} }


#declare Faces = array[3]{ array[4]{9, 1, 5, 13}, array[4]{12, 4, 5, 13}, array[4]{12, 8, 9, 13} }


/////////////////////////////////////////////////////////////////////////////////////////////////


union{

    // TRANSPARENT VERTICES AND EDGES
    merge{
        union{
            #for( i, 0, dimension_size(TransparentVertices, 1)-1 )
                #local VertexIndex = TransparentVertices[i] - 1;
                #local Rank = VertexRanks[VertexIndex];
                #local FakeRank = FakeRanks[Rank];
                #local Rad = .05 + pow(10-FakeRank, 2) / 600;
                sphere{ VertexPoints[VertexIndex]*Factor, Rad 
                    #if(VertexRankParities[VertexIndex])
                        pigment{color rgbt TransparentDarkVertexColor}
                    #else
                        pigment{color rgbt TransparentLightVertexColor}
                    #end
                }
            #end
        }
        union{
            #for( i, 0, dimension_size(TransparentEdges, 1)-1 )
                #local Edge = TransparentEdges[i];
                #local VertexIndex1 = Edge[0] - 1;
                #local VertexIndex2 = Edge[1] - 1;
                #local Point1 = VertexPoints[VertexIndex1]*Factor;
                #local Point2 = VertexPoints[VertexIndex2]*Factor;
                #local Rank1 = VertexRanks[VertexIndex1];
                #local Rank2 = VertexRanks[VertexIndex2];
                #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 rgbt TransparentEdgeColor}
        }
    }

    // SOLID VERTICES
    union{
        #for( i, 0, dimension_size(SolidVertices, 1)-1 )
            #local VertexIndex = SolidVertices[i] - 1;
            #local Rank = VertexRanks[VertexIndex];
            #local FakeRank = FakeRanks[Rank];
            #local Rad = .05 + pow(10-FakeRank, 2) / 600;
            sphere{ VertexPoints[VertexIndex]*Factor, Rad 
                #if(VertexRankParities[VertexIndex])
                    pigment{color rgbt DarkVertexColor}
                #else
                    pigment{color rgbt LightVertexColor}
                #end
            }
        #end
    }

    // SOLID EDGES
    union{
        #for( i, 0, dimension_size(SolidEdges, 1)-1 )
            #local Edge = SolidEdges[i];
            #local VertexIndex1 = Edge[0] - 1;
            #local VertexIndex2 = Edge[1] - 1;
            #local Point1 = VertexPoints[VertexIndex1]*Factor;
            #local Point2 = VertexPoints[VertexIndex2]*Factor;
            #local Rank1 = VertexRanks[VertexIndex1];
            #local Rank2 = VertexRanks[VertexIndex2];
            #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 rgbt EdgeColor}
    }

    // 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 RedFaceColor}
    }
    
    rotate -90*x
    rotate 4*y
    rotate 4*z
}

File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	20:26, 31 March 2018		3,624 × 3,990 (829 KB)	Watchduck (talk \| contribs)

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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	Render Date: 2018-03-31 14:58:39Z Platform: x86_64-pc-linux-gnu Compiler: g++ 5.2.1
Horizontal resolution	28.35 dpc
Vertical resolution	28.35 dpc
File change date and time	15:38, 31 March 2018

File:Tesseract tetrahedron shadow with alternating vertex colors, lower cube.png

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