function p = points_ball(d,n)

% This function returns a set of interpolation points for total degree
% interpolation of degree n in the unit ball in d dimensions. The
% cardinality of the set of points is N, the dimension of the space of
% polynomials in d variables with total degree less than or equal to n.

% The set of points is given in the format of one vector of length N times
% d, with the first d entries of the vector containing the d coordinates of
% the first point, and so on.

% The set is unisolvent, and has a very low Lebesgue constant.

% Sets are available for the following choices:
% d=2: n=1,...,10
% d=3: n=1,...,5


% Inputs: dimension d, degree n.
% Outputs: interpolation points p.

%==============

if d > 3
    error('Dimension d must be between 2 or 3')
end

switch d
    
    case 2
        
        if n > 10
            error('Degree n must be between 1 and 10 for d=2')
        end
        
        switch n
            
            case 1
                p=[
                    -0.276417739221336
                    -0.961037960169225
                    -0.694074166069382
                    0.719903501863559
                    0.970491941326819
                    0.241134142453327
                    ];
                
            case 2
                p=[
                    0.109371258266216
                    0.994001145050096
                    0.979150664955998
                    0.203135381730427
                    -0.158093770125050
                    0.099360070999387
                    -0.672799306036877
                    -0.739825565935603
                    0.495842795487006
                    -0.868412820529591
                    -0.911557530718660
                    0.411172497911128
                    ];
            case 3
                p=[
                    -0.032425582106145
                    0.473741467107587
                    0.941285296811318
                    0.307573092487865
                    0.804691473705096
                    -0.593692954438870
                    -0.797136155448618
                    -0.603799593971248
                    0.425306690191829
                    -0.198383122576090
                    -0.470388263271783
                    0.882459044377483
                    -0.948616877880466
                    0.301245966169203
                    0.004968037648618
                    -0.991209881471940
                    -0.388116642426785
                    -0.268349617563658
                    0.488968677882346
                    0.872301391882184
                    ];
            case 4
                p=[
                    0.817644522746324
                    0.537894666979774
                    0.675797200026546
                    0.044092327720293
                    0.990290563363634
                    -0.130675163398707
                    -0.486177893236526
                    -0.521929467948250
                    -0.625473942243124
                    -0.780680384704868
                    0.049513249466270
                    -0.970062759680942
                    0.342428848464597
                    -0.565737209549743
                    -0.592431538502041
                    0.304928739008462
                    -0.366714811940018
                    0.881057434853120
                    -0.938250266731437
                    -0.214224229131164
                    -0.891581314630993
                    0.481345234177947
                    0.267209537269399
                    0.977484985446555
                    0.680560765580493
                    -0.737428729316808
                    -0.034757754247310
                    0.021847959663947
                    0.149949728887174
                    0.687661092503759
                    ];
            case 5
                p=[
                    -0.539991341162190
                    -0.520174942598338
                    -0.268118120098466
                    0.180541025577454
                    0.725188779553972
                    0.285705580209535
                    0.175875362200483
                    0.726760291612535
                    0.688053689592183
                    -0.718887582927370
                    0.289916352840459
                    0.127787406786535
                    -0.468156639905914
                    0.883647227655595
                    0.651552554818049
                    -0.381587367048610
                    0.936525314382631
                    0.350596655318831
                    0.944209145074299
                    -0.232762107547637
                    -0.790541731415990
                    -0.612409744227945
                    0.197333885991648
                    -0.980337279811814
                    -0.845898170862363
                    0.474116315341630
                    -0.998726785606508
                    -0.050439630472852
                    0.134899594422263
                    -0.770188656285048
                    -0.752795827423451
                    0.015918386478850
                    0.584190448342899
                    0.770553627414739
                    0.098597373393363
                    0.995128087967277
                    -0.353080390704015
                    -0.899492575680477
                    -0.418083141998450
                    0.655935491309331
                    -0.036155948943497
                    -0.320897843895220
                    ];
            case 6
                p=[
                    0.479632404233057
                    0.877469570919426
                    -0.946140752476985
                    -0.288325174840606
                    0.969050109285293
                    0.066570504005482
                    0.049922151391748
                    0.969298542913733
                    -0.082333378524596
                    -0.766857709056736
                    -0.787963821223072
                    0.615721541686561
                    -0.392663143502308
                    0.919682377130399
                    -0.760627541093294
                    -0.098211680138967
                    0.504411131687206
                    -0.682171512936309
                    -0.584652638052536
                    -0.599511989115378
                    -0.326679459360019
                    -0.344793717660044
                    0.727633676662472
                    0.374804964597607
                    0.924670734755692
                    -0.380767739229208
                    0.758017976217097
                    -0.214541185749720
                    -0.438135210618740
                    0.242374254581027
                    0.170420259011426
                    -0.960307488740029
                    0.350604428965908
                    0.736009368096123
                    0.260722121924715
                    -0.422561848960410
                    0.103813667018566
                    0.462960998943731
                    0.866171381422173
                    0.499747133258728
                    -0.249124726912410
                    0.751075214897889
                    -0.258760783894678
                    -0.954116115889332
                    -0.692137255788926
                    0.477952858624561
                    -0.693058400876197
                    -0.720881458630393
                    0.015615795214370
                    0.007186071312251
                    0.627913563153839
                    -0.778283055679570
                    0.467525580341588
                    0.129096292461293
                    -0.966239164744131
                    0.148588570341508
                    ];
            case 7
                p=[
                    -0.663663990248067
                    0.520771738562224
                    0.969942826018790
                    -0.100572953075104
                    0.812344770072609
                    0.210874841128208
                    -0.869221741600593
                    -0.494422454922800
                    0.374286871547207
                    0.911453579707516
                    -0.505439484138538
                    0.262399039552622
                    -0.145804552716331
                    0.561983754018173
                    -0.409403307257853
                    -0.723022163486972
                    -0.254611570130751
                    -0.059281673022002
                    -0.991422019394833
                    -0.056988104968709
                    0.067199611335137
                    -0.831480345711198
                    -0.778425812206037
                    -0.417768701879332
                    0.396781608349764
                    0.449331262853573
                    0.535147650840596
                    -0.705743930830857
                    -0.577700514674065
                    -0.816248746566702
                    0.886354066347137
                    -0.462917684217582
                    -0.125764487339321
                    -0.583313490368210
                    -0.810403386289148
                    0.042776447705428
                    0.202188496124212
                    -0.979345048933431
                    0.957115757914065
                    0.289705857472042
                    -0.931769830205322
                    0.290570244884397
                    0.152289127665710
                    0.781426744183739
                    -0.762763713731405
                    0.646677262065489
                    -0.306267405958292
                    0.794940650396556
                    -0.392892297326615
                    0.919584496217537
                    0.773957679030907
                    -0.294645446808967
                    0.372085908332845
                    -0.478819816510866
                    0.026211095848314
                    0.982295730372278
                    0.086511320495389
                    0.256005692057906
                    0.732537894176747
                    0.680726141764852
                    0.164893324108756
                    -0.176865482429273
                    0.601781850826884
                    -0.798660403649645
                    -0.549368883380743
                    -0.277054067471410
                    -0.196440218710983
                    -0.958967364104633
                    0.603285630927412
                    0.623101917290759
                    0.576695604688527
                    -0.011453644322414
                    ];
            case 8
                p=[
                    -0.961680842581191
                    -0.232245907819851
                    -0.989215266936207
                    0.146504941612686
                    0.154017751393326
                    -0.977854723879610
                    -0.579861034556425
                    -0.660505959068001
                    -0.088245263514073
                    -0.345029250843604
                    0.033168757312546
                    0.985183386476072
                    0.938096776613438
                    -0.346373289306410
                    -0.070141571114384
                    0.107929286806232
                    0.331275501315206
                    -0.136356803160627
                    -0.862953138487334
                    0.503116271131710
                    -0.834886002475096
                    -0.517637517350131
                    0.836391620258390
                    -0.327618108651866
                    0.902129749447446
                    0.400233596889745
                    -0.616345400991360
                    0.760710617480847
                    0.722151943687154
                    0.670674833424480
                    0.295455924127788
                    -0.509819872854796
                    0.741755093247007
                    -0.661859035341614
                    -0.349960830816731
                    0.936774135223256
                    0.634723939303702
                    -0.257644273636764
                    -0.373315536904184
                    0.652883736348714
                    0.408825352342560
                    0.912607311167419
                    0.553514451028472
                    -0.639219132259293
                    0.619965702144976
                    0.202727038893610
                    0.457893104112862
                    -0.869260994948491
                    0.341759021618132
                    0.592228351284270
                    -0.219226663975887
                    -0.975674065169962
                    -0.471908367800630
                    -0.073732213117723
                    -0.441451317200302
                    0.340769483290578
                    -0.697946804881385
                    0.501270597526196
                    -0.780791606446297
                    -0.289119374866164
                    -0.201384075978218
                    -0.875713932821315
                    0.999186162312819
                    0.040206269847486
                    0.393580079486343
                    0.814770567340034
                    -0.703147848471645
                    0.079013336611565
                    -0.144123688141072
                    -0.680767022398374
                    -0.351760446313603
                    0.852055655759084
                    -0.065856401407705
                    0.497208760614551
                    -0.504187798089057
                    -0.440955173821812
                    0.030827588912025
                    0.818294128208073
                    0.854920240370826
                    0.091797804131448
                    0.711965406935308
                    0.467424090619654
                    -0.909078183907480
                    0.114531890526859
                    0.201175735898973
                    -0.814970102164513
                    -0.612693120140192
                    -0.790330421614143
                    0.295517756028860
                    0.282159707729213
                    ];
            case 9
                p=[
                    -0.117620808130490
                    0.170312901811960
                    -0.554453569346585
                    0.832222607979139
                    -0.796059511625607
                    0.592275812760243
                    -0.736920305180140
                    -0.227510094803049
                    -0.939581871462691
                    -0.342343214166260
                    0.253274962570643
                    0.871636760366145
                    -0.466099278336753
                    -0.009769670531152
                    -0.141123910511403
                    0.855099741184506
                    -0.927851478452082
                    0.328324672612577
                    -0.461514479942737
                    0.373059906015866
                    -0.515674278067280
                    -0.856789583856963
                    -0.512602627853493
                    0.775931265019569
                    -0.163290140194554
                    0.569160433658868
                    0.321871721829169
                    -0.861101656407022
                    0.920742049290706
                    0.101704414345308
                    -0.999363114899795
                    0.035892573728402
                    0.119073840211295
                    0.724752207228676
                    -0.762825011705693
                    -0.626118353411829
                    0.509994350948239
                    0.211234749304825
                    0.882892189838960
                    -0.446157953729199
                    -0.729896397159091
                    0.469786639936000
                    0.772128081417087
                    0.011686215641588
                    0.680120675646195
                    0.733109337587078
                    0.870593656642708
                    0.464219613416148
                    0.704912577610344
                    -0.709301976416324
                    -0.646104640536056
                    -0.543240261092351
                    -0.452672534423291
                    -0.809924552652483
                    0.988508801501834
                    0.151188658566202
                    0.200163596386095
                    0.010424866212665
                    0.063639509071928
                    -0.989897533851875
                    0.647262129634964
                    -0.641591938688935
                    -0.904843873979842
                    0.108148708721700
                    0.366960845264315
                    -0.930240185970090
                    -0.089098980152593
                    -0.186113509016041
                    -0.039332911408122
                    -0.859774849100059
                    0.622401097434820
                    0.681751490900522
                    0.969039916427191
                    -0.180314877135513
                    -0.318227606926579
                    -0.704832603587288
                    0.188572987452724
                    0.425089916235074
                    -0.872031331912101
                    -0.308159076992361
                    -0.235341959614621
                    0.963845379333465
                    0.355887390725609
                    0.934533339811925
                    -0.392342962206938
                    -0.386901614481248
                    0.271710392178931
                    -0.395967476835268
                    0.248794138780446
                    -0.726929140456870
                    0.493828468415066
                    0.586547943189333
                    0.754472701302652
                    0.377942072430174
                    -0.049002208224257
                    -0.580197978493670
                    -0.424598779226019
                    0.641024394274964
                    -0.220569306966978
                    -0.959455852186705
                    0.813207498298128
                    -0.304278312692523
                    0.567107132971002
                    -0.499529607339655
                    0.559167760989193
                    -0.175827245177469
                    0.058203042986783
                    0.982605328253936
                    -0.717743980715636
                    0.172911792393983
                    ];
            case 10
                p=[
                    -0.902191750736140
                    0.242782222768782
                    0.800794799531725
                    0.175861251422481
                    -0.405473559088817
                    0.356742535244240
                    -0.424139020421383
                    -0.810476920533605
                    -0.710499018651892
                    -0.284573722803117
                    0.373918446509245
                    0.671594720376077
                    -0.809276200334024
                    -0.587433748038917
                    0.599406288491127
                    -0.690808220017409
                    -0.075931894282623
                    0.799907146930509
                    -0.968889172726741
                    0.247500615645427
                    0.262042479873646
                    -0.871588347591724
                    -0.519755689175693
                    0.563430893178414
                    -0.425882322709220
                    0.776888462784491
                    -0.565737393833747
                    0.028403013860298
                    0.964620576760595
                    0.196280602418541
                    0.252544978789350
                    -0.967585443251810
                    -0.418850760875549
                    -0.297386496132018
                    -0.337630886552898
                    -0.925688975597347
                    -0.400583352729598
                    0.911706565499115
                    0.922843113175235
                    -0.051727751493417
                    0.076279485699771
                    0.631820613055863
                    -0.960471171638122
                    -0.278388466388984
                    0.678231104631314
                    0.734844866317126
                    -0.718449138066592
                    -0.575968860749581
                    0.205800918074666
                    0.228548210181716
                    -0.820814022416497
                    0.571191154099259
                    -0.112543925448702
                    0.936503235825005
                    -0.114420006743949
                    0.993432466792348
                    0.532611243638416
                    -0.829961727050906
                    0.087807209056612
                    -0.711413633994770
                    0.458772776409201
                    0.871204726714700
                    0.590417335128247
                    0.719681445287745
                    0.231993085185771
                    -0.462600843938235
                    -0.038190893046680
                    -0.999273189361226
                    0.917358436483177
                    -0.398068855868895
                    0.519995261600093
                    0.131037416564664
                    0.723863926759064
                    -0.679088154631375
                    0.997932920564231
                    -0.064264242941713
                    -0.896978393274667
                    -0.267880350449809
                    0.231078057121485
                    0.859560983075582
                    -0.010893726939675
                    0.042158078364656
                    0.494553707041220
                    -0.234655074729752
                    0.891965117204766
                    0.452112179275996
                    0.620858433135150
                    -0.413583249444483
                    -0.496891905336298
                    -0.549081583351117
                    0.833292060330369
                    0.418675338413661
                    0.276351712688868
                    -0.135454228582568
                    0.743313890493637
                    -0.123530704679187
                    0.387211081288681
                    -0.629959107286739
                    0.839395907805918
                    -0.395647865690767
                    0.200569207915133
                    0.976532336739003
                    0.338564001924249
                    0.440751612720931
                    -0.231425323329250
                    0.634949674135666
                    -0.078352451935500
                    -0.274343510637114
                    -0.065171630737711
                    0.334371407716046
                    -0.560209929187584
                    -0.819219468543540
                    0.640314252743097
                    0.428647678646576
                    -0.049947651978853
                    -0.911543205262983
                    -0.147615198544920
                    -0.521327060601384
                    -0.726099465653169
                    0.579767407478938
                    -0.834528997671085
                    0.004465809651682
                    -0.984551007371396
                    -0.015478139809029
                    -0.719170998561632
                    0.279999859330559
                    -0.300550330435487
                    0.011068913420045
                    -0.208153985035811
                    -0.728607110907132
                    -0.630583576715921
                    0.757824129987491
                    ];
        end
        
    case 3
        
        if n > 5
            error('Degree n must be between 1 and 5 for d=3')
        end
        
        switch n
            
            case 1
                p=[
                    -0.752254320629631
                    0.377860681343186
                    -0.539754235657313
                    0.498276237568739
                    -0.677281762357833
                    -0.541295840930239
                    0.621306229321957
                    0.738655896589525
                    0.261470270556302
                    -0.367289960832324
                    -0.439330010184887
                    0.819807210082037
                    ];
            case 2
                p=[
                    0.975208514398215
                    0.062106943926737
                    0.212394604206083
                    -0.050254106316277
                    0.199260760780612
                    -0.480866141009837
                    0.146812008654699
                    -0.412472015754604
                    0.899062636683842
                    -0.099412103894589
                    0.714888876003532
                    0.692135621318271
                    0.344090666814528
                    0.853868174036239
                    -0.390525823476870
                    -0.885054332351410
                    -0.318769322795248
                    0.339212824857013
                    -0.537194140694450
                    -0.304759190235631
                    -0.786476299180641
                    0.190059226833717
                    -0.972256101960613
                    -0.136364570510294
                    0.505610890906734
                    -0.091973876668172
                    -0.857845651193585
                    -0.699319260021511
                    0.639962054507340
                    -0.318435744995357
                    ];
            case 3
                p=[
                    0.861003675557623
                    0.328358089178440
                    0.388399495173997
                    -0.815577907989743
                    -0.578621826463220
                    0.005470565533496
                    -0.393914432920116
                    -0.315003602818576
                    0.863484035182899
                    -0.000019538176369
                    0.586896733790919
                    0.809661874587375
                    -0.860923243332717
                    0.329037240520607
                    0.388002760615654
                    0.857256244824903
                    0.326446732413809
                    -0.398176731801198
                    0.432426672706843
                    0.331806058286728
                    -0.020497075533667
                    -0.465817041863138
                    0.884850609593738
                    -0.007365426122141
                    0.000801850673615
                    -0.887369654384284
                    -0.461058303743866
                    -0.000673780452553
                    -0.877550153521682
                    0.479484270958408
                    0.392859372816384
                    -0.336651234996987
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                    -0.855770704825208
                    0.393970942674937
                    -0.315201470910764
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                    ];
            case 4
                p=[
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                    -0.566879882916435
                    -0.221367681757297
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                    0.157588289826702
                    -0.964008869632613
                    ];
            case 5
                p=[
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                    0.871733355853107
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                    -0.130978496831080
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                    -0.106169153666495
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                    ];
                
        end
        
end

end