R/solids.R

In tessellation: Delaunay and Voronoï Tessellations

#' @title Centric cuboctahedron
#' @description A cuboctahedron (12 vertices), with a point added at its center.
#'
#' @return A numeric matrix with 13 rows and 3 columns.
#' @export
centricCuboctahedron <- function(){
  rbind(
    c(-1, -1, 0),
    c(-1, 1, 0),
    c(1, -1, 0),
    c(1, 1, 0),
    c(-1, 0, -1),
    c(-1, 0, 1),
    c(1, 0, -1),
    c(1, 0, 1),
    c(0, -1, -1),
    c(0, -1, 1),
    c(0, 1, -1),
    c(0, 1, 1),
    c(0, 0, 0)
  )
}

#' @title Utah teapot
#' @description Vertices of the Utah teapot.
#'
#' @return A matrix with 1976 rows and 3 columns.
#' @export
teapot <- function(){
  rbind(
    c(-3, 1.64999997615814, 0),
    c(-2.98710989952087, 1.64999997615814, -0.0984380021691322),
    c(-2.98710989952087, 1.64999997615814, 0.0984380021691322),
    c(-2.98537993431091, 1.56731998920441, -0.0492190010845661),
    c(-2.98537993431091, 1.56731998920441, 0.0492190010845661),
    c(-2.9835000038147, 1.48308002948761, 0),
    c(-2.98188996315002, 1.72346997261047, -0.0492190010845661),
    c(-2.98188996315002, 1.72346997261047, 0.0492190010845661),
    c(-2.97656011581421, 1.79852998256683, 0),
    c(-2.97090005874634, 1.48620998859406, -0.0984380021691322),
    c(-2.97090005874634, 1.48620998859406, 0.0984380021691322),
    c(-2.96388006210327, 1.79533994197845, -0.0984380021691322),
    c(-2.96388006210327, 1.79533994197845, 0.0984380021691322),
    c(-2.96220993995667, 1.57017004489899, -0.133594006299973),
    c(-2.96220993995667, 1.57017004489899, 0.133594006299973),
    c(-2.95864009857178, 1.72056996822357, -0.133594006299973),
    c(-2.95864009857178, 1.72056996822357, 0.133594006299973),
    c(-2.95313000679016, 1.64999997615814, -0.168750002980232),
    c(-2.95313000679016, 1.64999997615814, 0.168750002980232),
    c(-2.95247006416321, 1.40374004840851, -0.0492190010845661),
    c(-2.95247006416321, 1.40374004840851, 0.0492190010845661),
    c(-2.93770003318787, 1.49447000026703, -0.168750002980232),
    c(-2.93770003318787, 1.49447000026703, 0.168750002980232),
    c(-2.93523001670837, 1.85214996337891, -0.0492190010845661),
    c(-2.93523001670837, 1.85214996337891, 0.0492190010845661),
    c(-2.93358993530273, 1.32011997699738, 0),
    c(-2.93044996261597, 1.78692996501923, -0.168750002980232),
    c(-2.93044996261597, 1.78692996501923, 0.168750002980232),
    c(-2.93037009239197, 1.41149997711182, -0.133594006299973),
    c(-2.93037009239197, 1.41149997711182, 0.133594006299973),
    c(-2.92188000679016, 1.32553005218506, -0.0984380021691322),
    c(-2.92188000679016, 1.32553005218506, 0.0984380021691322),
    c(-2.91278004646301, 1.84416997432709, -0.133594006299973),
    c(-2.91278004646301, 1.84416997432709, 0.133594006299973),
    c(-2.90625, 1.91015994548798, 0),
    c(-2.89422988891602, 1.90456998348236, -0.0984380021691322),
    c(-2.89422988891602, 1.90456998348236, 0.0984380021691322),
    c(-2.89138007164001, 1.57910001277924, -0.196875005960464),
    c(-2.89138007164001, 1.57910001277924, 0.196875005960464),
    c(-2.8909900188446, 1.33980000019073, -0.168750002980232),
    c(-2.8909900188446, 1.33980000019073, 0.168750002980232),
    c(-2.89065003395081, 1.71208000183105, -0.196875005960464),
    c(-2.89065003395081, 1.71208000183105, 0.196875005960464),
    c(-2.88346004486084, 1.24579000473022, -0.0483429990708828),
    c(-2.88346004486084, 1.24579000473022, 0.0483429990708828),
    c(-2.86346006393433, 1.25713002681732, -0.132717996835709),
    c(-2.86346006393433, 1.25713002681732, 0.132717996835709),
    c(-2.86265993118286, 1.43482995033264, -0.196875005960464),
    c(-2.86265993118286, 1.43482995033264, 0.196875005960464),
    c(-2.8625500202179, 1.88982999324799, -0.168750002980232),
    c(-2.8625500202179, 1.88982999324799, 0.168750002980232),
    c(-2.84999990463257, 1.64999997615814, -0.224999994039536),
    c(-2.84999990463257, 1.64999997615814, 0.224999994039536),
    c(-2.84970998764038, 1.16155004501343, 0),
    c(-2.84710001945496, 1.82081997394562, -0.196875005960464),
    c(-2.84710001945496, 1.82081997394562, 0.196875005960464),
    c(-2.84193992614746, 1.94692003726959, -0.0492190010845661),
    c(-2.84193992614746, 1.94692003726959, 0.0492190010845661),
    c(-2.8289999961853, 1.76139998435974, -0.224999994039536),
    c(-2.8289999961853, 1.76139998435974, 0.224999994039536),
    c(-2.82867002487183, 1.17597997188568, -0.0949330031871796),
    c(-2.82867002487183, 1.17597997188568, 0.0949330031871796),
    c(-2.82470011711121, 1.52193999290466, -0.224999994039536),
    c(-2.82470011711121, 1.52193999290466, 0.224999994039536),
    c(-2.82115006446838, 1.93519997596741, -0.133594006299973),
    c(-2.82115006446838, 1.93519997596741, 0.133594006299973),
    c(-2.81230998039246, 1.18719005584717, -0.168750002980232),
    c(-2.81230998039246, 1.18719005584717, 0.168750002980232),
    c(-2.80501008033752, 1.28997004032135, -0.196875005960464),
    c(-2.80501008033752, 1.28997004032135, 0.196875005960464),
    c(-2.79727005958557, 1.38311004638672, -0.224999994039536),
    c(-2.79727005958557, 1.38311004638672, 0.224999994039536),
    c(-2.78906011581421, 1.99013996124268, 0),
    c(-2.78836011886597, 1.69931995868683, -0.196875005960464),
    c(-2.78836011886597, 1.69931995868683, 0.196875005960464),
    c(-2.77820992469788, 1.98283004760742, -0.0984380021691322),
    c(-2.77820992469788, 1.98283004760742, 0.0984380021691322),
    c(-2.77442002296448, 1.52737998962402, -0.196875005960464),
    c(-2.77442002296448, 1.52737998962402, 0.196875005960464),
    c(-2.77356004714966, 1.09860002994537, -0.0843750014901161),
    c(-2.77356004714966, 1.09860002994537, 0.0843750014901161),
    c(-2.76641011238098, 1.84511995315552, -0.224999994039536),
    c(-2.76641011238098, 1.84511995315552, 0.224999994039536),
    c(-2.76033997535706, 1.90090000629425, -0.196875005960464),
    c(-2.76033997535706, 1.90090000629425, 0.196875005960464),
    c(-2.74959993362427, 1.96355998516083, -0.168750002980232),
    c(-2.74959993362427, 1.96355998516083, 0.168750002980232),
    c(-2.74831008911133, 1.78569996356964, -0.196875005960464),
    c(-2.74831008911133, 1.78569996356964, 0.196875005960464),
    c(-2.74688005447388, 1.64999997615814, -0.168750002980232),
    c(-2.74688005447388, 1.64999997615814, 0.168750002980232),
    c(-2.73125004768372, 1.00780999660492, 0),
    c(-2.72756004333496, 1.73587000370026, -0.168750002980232),
    c(-2.72756004333496, 1.73587000370026, 0.168750002980232),
    c(-2.72036004066467, 1.69082999229431, -0.133594006299973),
    c(-2.72036004066467, 1.69082999229431, 0.133594006299973),
    c(-2.71948003768921, 1.24977004528046, -0.224999994039536),
    c(-2.71948003768921, 1.24977004528046, 0.224999994039536),
    c(-2.71677994728088, 1.14468002319336, -0.196875005960464),
    c(-2.71677994728088, 1.14468002319336, 0.196875005960464),
    c(-2.71288990974426, 1.64999997615814, -0.0984380021691322),
    c(-2.71288990974426, 1.64999997615814, 0.0984380021691322),
    c(-2.7089900970459, 1.54176998138428, -0.133594006299973),
    c(-2.7089900970459, 1.54176998138428, 0.133594006299973),
    c(-2.70354008674622, 1.42640995979309, -0.168750002980232),
    c(-2.70354008674622, 1.42640995979309, 0.168750002980232),
    c(-2.70097994804382, 1.03784000873566, -0.168750002980232),
    c(-2.70097994804382, 1.03784000873566, 0.168750002980232),
    c(-2.70000004768372, 1.64999997615814, 0),
    c(-2.69965004920959, 2.0107901096344, -0.0483460016548634),
    c(-2.69965004920959, 2.0107901096344, 0.0483460016548634),
    c(-2.69711995124817, 1.68792998790741, -0.0492190010845661),
    c(-2.69711995124817, 1.68792998790741, 0.0492190010845661),
    c(-2.69412994384766, 1.72746002674103, -0.0984380021691322),
    c(-2.69412994384766, 1.72746002674103, 0.0984380021691322),
    c(-2.68661999702454, 1.54668998718262, -0.0492190010845661),
    c(-2.68661999702454, 1.54668998718262, 0.0492190010845661),
    c(-2.68263006210327, 1.76234996318817, -0.133594006299973),
    c(-2.68263006210327, 1.76234996318817, 0.133594006299973),
    c(-2.68147993087769, 1.9964599609375, -0.13272100687027),
    c(-2.68147993087769, 1.9964599609375, 0.13272100687027),
    c(-2.68144011497498, 1.72426998615265, 0),
    c(-2.67574000358582, 1.27084994316101, -0.196875005960464),
    c(-2.67574000358582, 1.27084994316101, 0.196875005960464),
    c(-2.67265009880066, 1.44068002700806, -0.0984380021691322),
    c(-2.67265009880066, 1.44068002700806, 0.0984380021691322),
    c(-2.67025995254517, 1.80040001869202, -0.168750002980232),
    c(-2.67025995254517, 1.80040001869202, 0.168750002980232),
    c(-2.667799949646, 1.84623003005981, -0.196875005960464),
    c(-2.667799949646, 1.84623003005981, 0.196875005960464),
    c(-2.66279006004333, 1.9050999879837, -0.224999994039536),
    c(-2.66279006004333, 1.9050999879837, 0.224999994039536),
    c(-2.66093993186951, 1.44608998298645, 0),
    c(-2.66018009185791, 1.75436997413635, -0.0492190010845661),
    c(-2.66018009185791, 1.75436997413635, 0.0492190010845661),
    c(-2.63858008384705, 1.78567004203796, -0.0984380021691322),
    c(-2.63858008384705, 1.78567004203796, 0.0984380021691322),
    c(-2.63438010215759, 1.10390996932983, -0.224999994039536),
    c(-2.63438010215759, 1.10390996932983, 0.224999994039536),
    c(-2.63073992729187, 1.95674002170563, -0.196875005960464),
    c(-2.63073992729187, 1.95674002170563, 0.196875005960464),
    c(-2.62655997276306, 1.78007996082306, 0),
    c(-2.625, 2.04375004768372, 0),
    c(-2.62463998794556, 1.30501997470856, -0.132813006639481),
    c(-2.62463998794556, 1.30501997470856, 0.132813006639481),
    c(-2.60642004013062, 1.31745004653931, -0.0484380014240742),
    c(-2.60642004013062, 1.31745004653931, 0.0484380014240742),
    c(-2.60631990432739, 2.02643990516663, -0.0949449986219406),
    c(-2.60631990432739, 2.02643990516663, 0.0949449986219406),
    c(-2.59179997444153, 2.01298999786377, -0.168750002980232),
    c(-2.59179997444153, 2.01298999786377, 0.168750002980232),
    c(-2.57172989845276, 1.83429002761841, -0.168750002980232),
    c(-2.57172989845276, 1.83429002761841, 0.168750002980232),
    c(-2.56777000427246, 1.16997003555298, -0.168750002980232),
    c(-2.56777000427246, 1.16997003555298, 0.168750002980232),
    c(-2.55460000038147, 1.18304002285004, -0.0953150019049644),
    c(-2.55460000038147, 1.18304002285004, 0.0953150019049644),
    c(-2.54975008964539, 1.89058995246887, -0.196875005960464),
    c(-2.54975008964539, 1.89058995246887, 0.196875005960464),
    c(-2.5495400428772, 0.878983974456787, -0.0843750014901161),
    c(-2.5495400428772, 0.878983974456787, 0.0843750014901161),
    c(-2.5464301109314, 1.83196997642517, -0.13272100687027),
    c(-2.5464301109314, 1.83196997642517, 0.13272100687027),
    c(-2.53749990463257, 1.20000004768372, 0),
    c(-2.52720999717712, 1.81920003890991, -0.0483460016548634),
    c(-2.52720999717712, 1.81920003890991, 0.0483460016548634),
    c(-2.51874995231628, 1.94530999660492, -0.224999994039536),
    c(-2.51874995231628, 1.94530999660492, 0.224999994039536),
    c(-2.51682996749878, 0.932671010494232, -0.196875005960464),
    c(-2.51682996749878, 0.932671010494232, 0.196875005960464),
    c(-2.47183990478516, 1.00648999214172, -0.196875005960464),
    c(-2.47183990478516, 1.00648999214172, 0.196875005960464),
    c(-2.44569993019104, 1.87764000892639, -0.168750002980232),
    c(-2.44569993019104, 1.87764000892639, 0.168750002980232),
    c(-2.43913006782532, 1.06017994880676, -0.0843750014901161),
    c(-2.43913006782532, 1.06017994880676, 0.0843750014901161),
    c(-2.43118000030518, 1.86417996883392, -0.0949449986219406),
    c(-2.43118000030518, 1.86417996883392, 0.0949449986219406),
    c(-2.41249990463257, 1.84686994552612, 0),
    c(-2.38827991485596, 0.716602027416229, 0),
    c(-2.3822500705719, 0.737662971019745, -0.0958539992570877),
    c(-2.3822500705719, 0.737662971019745, 0.0958539992570877),
    c(-2.37883996963501, 2.05202007293701, -0.0843750014901161),
    c(-2.37883996963501, 2.05202007293701, 0.0843750014901161),
    c(-2.37766003608704, 0.753679990768433, -0.168750002980232),
    c(-2.37766003608704, 0.753679990768433, 0.168750002980232),
    c(-2.36474990844727, 0.798761010169983, -0.199836000800133),
    c(-2.36474990844727, 0.798761010169983, 0.199836000800133),
    c(-2.35430002212524, 0.835254013538361, -0.224999994039536),
    c(-2.35430002212524, 0.835254013538361, 0.224999994039536),
    c(-2.34383988380432, 0.871747016906738, -0.199836000800133),
    c(-2.34383988380432, 0.871747016906738, 0.199836000800133),
    c(-2.3411500453949, 1.99971997737885, -0.196875005960464),
    c(-2.3411500453949, 1.99971997737885, 0.196875005960464),
    c(-2.33092999458313, 0.916827023029327, -0.168750002980232),
    c(-2.33092999458313, 0.916827023029327, 0.168750002980232),
    c(-2.32031011581421, 0.953905999660492, 0),
    c(-2.28931999206543, 1.9278199672699, -0.196875005960464),
    c(-2.28931999206543, 1.9278199672699, 0.196875005960464),
    c(-2.251620054245, 1.87551999092102, -0.0843750014901161),
    c(-2.251620054245, 1.87551999092102, 0.0843750014901161),
    c(-2.24741005897522, 0.882284998893738, -0.0843750014901161),
    c(-2.24741005897522, 0.882284998893738, 0.0843750014901161),
    c(-2.17362999916077, 0.844043016433716, 0),
    c(-2.16852998733521, 0.826951026916504, -0.0971840023994446),
    c(-2.16852998733521, 0.826951026916504, 0.0971840023994446),
    c(-2.16476988792419, 0.814364016056061, -0.168750002980232),
    c(-2.16476988792419, 0.814364016056061, 0.168750002980232),
    c(-2.15687990188599, 0.78669399023056, -0.187068000435829),
    c(-2.15687990188599, 0.78669399023056, 0.187068000435829),
    c(-2.15625, 2.09296989440918, 0),
    c(-2.15411996841431, 0.740520000457764, -0.215193003416061),
    c(-2.15411996841431, 0.740520000457764, 0.215193003416061),
    c(-2.15017008781433, 0.69473397731781, -0.215193003416061),
    c(-2.15017008781433, 0.69473397731781, 0.215193003416061),
    c(-2.14741992950439, 0.648559987545013, -0.187068000435829),
    c(-2.14741992950439, 0.648559987545013, 0.187068000435829),
    c(-2.14495992660522, 0.6127769947052, -0.132947996258736),
    c(-2.14495992660522, 0.6127769947052, 0.132947996258736),
    c(-2.143709897995, 0.59178900718689, -0.0485729984939098),
    c(-2.143709897995, 0.59178900718689, 0.0485729984939098),
    c(-2.14232993125916, 2.05836009979248, -0.168750002980232),
    c(-2.14232993125916, 2.05836009979248, 0.168750002980232),
    c(-2.11172008514404, 1.98222994804382, -0.224999994039536),
    c(-2.11172008514404, 1.98222994804382, 0.224999994039536),
    c(-2.08447003364563, 0.789525985717773, -0.0489050000905991),
    c(-2.08447003364563, 0.789525985717773, 0.0489050000905991),
    c(-2.08109998703003, 1.90609002113342, -0.168750002980232),
    c(-2.08109998703003, 1.90609002113342, 0.168750002980232),
    c(-2.07834005355835, 0.77038699388504, -0.133279994130135),
    c(-2.07834005355835, 0.77038699388504, 0.133279994130135),
    c(-2.06718993186951, 1.87147998809814, 0),
    c(-2, 0.75, 0),
    c(-1.99570000171661, 0.737109005451202, -0.0984380021691322),
    c(-1.99570000171661, 0.737109005451202, 0.0984380021691322),
    c(-1.98438000679016, 0.703125, -0.168750002980232),
    c(-1.98438000679016, 0.703125, 0.168750002980232),
    c(-1.97852003574371, 0.591650009155273, 0),
    c(-1.96937000751495, 0.670825004577637, -0.202656000852585),
    c(-1.96937000751495, 0.670825004577637, 0.202656000852585),
    c(-1.96835994720459, 0.655077993869781, -0.210938006639481),
    c(-1.96835994720459, 0.655077993869781, 0.210938006639481),
    c(-1.96000003814697, 0.75, -0.407499998807907),
    c(-1.96000003814697, 0.75, 0.407499998807907),
    c(-1.9587299823761, 0.925194978713989, -0.201561003923416),
    c(-1.9587299823761, 0.925194978713989, 0.201561003923416),
    c(-1.9570300579071, 1.10038995742798, 0),
    c(-1.95000004768372, 0.600000023841858, -0.224999994039536),
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