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CONOSCERE LASCENSIONE GLOBALE
E parteciparvi nel migliore dei modi
Parte 2 di 2
Documento offerto gratuitamente da Master
http://web.tiscalinet.it/master2000/spiritual.htm
Messaggio da Master:
Queste informazioni, raccolte da Franco, sono state prese dal sito
http://www.freeweb.org/newage/franco2000
Grazie Franco!
Io conoscevo Franco di persona, ma purtroppo ora ci ha lasciato per andare in qualche altradimensione, devo dire che era una persona stupenda e piena d'amore, nel suo sito ho trovato
moltissime notizie per me vere. Leggetele con amore ed in sintonia con il DIO che voi siete, e
scoprirete che la verit in voi.
Amore e Luce per tutti.
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SOMMARIO
IL LINGUAGGIO DI LUCE TONI DOPPI .....................................................................................3
COME UTILIZZARE IL LINGUAGGIO DI LUCE PER FACILITARE L'ASCENSIONE ...........8
WHY WE SEE THREE-DIMENSIONAL OBJECTS: ANOTHER APPROACH............................ 11
ABSTRACT...................................................................................................................................................11
Keywords.............................................................................................................................................11
Introduction.........................................................................................................................................11Theory..................................................................................................................................................12
M.S.D.A. Experimental Setup..............................................................................................................12
Failures of M.S.D.A.............................................................................................................................12
M.S.D.S.M. Experimental Setup..........................................................................................................14M.S.D.S.M. Algorithm Behavior..........................................................................................................14Result Comparison..............................................................................................................................15
Discussion............................................................................................................................................16
Future Work.........................................................................................................................................16Conclusion...........................................................................................................................................16
REFERENCES................................................................................................................................................16
APPENDIX I: SHAPE LINE DRAWINGS..............................................................................................................17
APPENDIX II: SHAPE DEFINITIONS..................................................................................................................18
* * *
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#1
Perdono
#48
DioDea/
TuttoCi
CheE'
#49 PERDONO INCONDIZIONATO
Natura: Integrativo
#1 Perdono e #48 DioDeaTuttoCiCheE'diventa #49 PERDONO INCONDIZIONATO
Il Perdono Incondizionato produce l'essenza di DioDeaTuttoCiCheE', ed
in relazione allo stato di accettazione. La capacit di accettare tutto
quello che si espande dentro se stesso, diventa parte intrinseca del proprio
modello energetico. Cessa il bisogno di manipolare, aderire o essere
contrari, consentendo semplicemente lespansione dellesistenza.
#4
Compas-
sione
#48
DioDea/
TuttoCi
CheE'
#50 COMPASSIONE INCONDIZIONATA
Natura: Completamento
#4 Compassione e #48 DioDeaTuttoCiCheE'
diventa: #50 COMPASSIONE INCONDIZIONATAE' un tono di completamento che unifica i toni 40-49 in una vibrazione
singola di Compassione Incondizionata che un aspetto di
DioDeaTuttoCiCheE' che fornisce chiarimento e apertura per la
creazione. E' la capacit di entrare in pieno contatto o lavorare con le
vibrazioni della creazione in espansione e non opporre pi resistenza al
desiderio infinito di creare, espandere ed evolvere.
#6 AmoreIncondi-
zionato
#48DioDea/
TuttoCi
CheE'
#51 AMORE ONNIPRESENTE
Natura: Attivo
#6 Amore Incondizionato e #48 DioDeaTuttoCiCheE'
diventa: AMORE ONNIPRESENTE
LAmore Onnipresente cerca di espandersi in nuove direzioni,combinandosi con gli altri toni di creazione, spingendosi aldil del
conosciuto. Espande la grandezza degli altri toni facendoli diventare
come fuochi di espressione: chiarire, purificare, transizione e
trasmutazione. Ogni espressione combinata con l'Amore Onnipresente
non ha punti fissi di paragone, ma solamente direzioni senza
impedimenti.
#11
Giurisdi-
zione
#48
DioDea/
TuttoCi
CheE'
#52 GIURISDIZIONE ONNIPRESENTE
Natura: Passivo
#11 Giurisdizione e #48 DioDeaTuttoCiCheE'
diventa: #52 GIURISDIZIONE ONNIPRESENTEE' il tono guida della creazione che forma e contiene un'espressione della
sua magnificenza nel fondersi con gli altri toni di creazione. Direzione,
programma e dispensazione dell'evoluzione del piano divino sono aspetti
della Giurisdizione Onnipresente, che orchestra l'evoluzione elargendo
(quando necessario) il modellamento o le vibrazioni adatte che consentono
un'ordinata espansione della creazione.
#20Clande-
stinit
#48DioDea/
TuttoCi
#53 CLANDESTINITA' INCONDIZIONATA
Natura: Integrativo
#20 Clandestinit e #48 DioDeaTuttoCiCheE'
diventa: #53 CLANDESTIINTA' INCONDIZIONATA
E' la forza e il vigore che c dietro ogni creazione, che considera lunit
d'intento e direzione, in tutte le aree di unione tra i creatori. Il tono
integrativo, unendo gli scopi comuni, non determinati dalla dimensione,
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CheE' ma dalla grandezza degli intenti. Lunit di coscienza determinata dalla
vibrazione di Onore, che alla base della clandestinit in relazione a tutti
gli aspetti dell'atto di creazione.
#29
Inte-
grit
#48
DioDea/
TuttoCi
CheE'
#54 INTEGRITA' INCONDIZIONATA
Natura: Activa
#29 Integrit e #48 DioDeaTuttoCiCheE'
diventa: #54 INTEGRITA' INCONDIZIONATA
Permette lintegrit in tutti gli atti di creazione. E un ingrediente che
riflette e sostiene l'onore di tutte le relazioni. L'integrit porta oneste
comunicazioni in tutte le interazioni. L'onest sostiene l'onore, che fa
vedere tutti gli aspetti dell'espressione senza veli o cose nascoste,
allineandosi agli scopi dell'evoluzione.
#3
Potere
#48
DioDea/
TuttoCi
CheE'
#55 FORZA VITALE INCONDIZIONATA
Natura: Passivo
#3 Potere e #48 DioDeaTuttoCiCheE'
diventa: #55 FORZA VITALE INCONDIZIONATAAlimenta gli aspetti creativi che sono visti come uguali e quindi
meritevoli del sostegno delle forze creative necessarie a sostenere,
permettere l'evoluzione e la continua ascensione di tutte le forme di vita,
o per sostenere la manifestazione di una nuova creazione.
#16
Grandez-
za
#48
DioDea/
TuttoCi
CheE'
#56 GRANDEZZA INCONDIZIONATA
Natura: Integrativo
#16 Grandezza e #48 DioDeaTuttoCiCheE'
diventa: #56 GRANDEZZA INCONDIZIONATA
E' il tono che consente l'unione dei toni di clandestinit, integrit e
forza vitale per produrre la Grandezza di una creazione. La grandezza
sinonimo di magnificienza, che sperimentata quando tutti gli aspetti
creativi sono portati in assoluto allineamento con il piano divino di
TuttoCiCheE', con lo scopo comune di ascensione.
#8
Unione
Divina
#15
Prospe-
rit
#57 MUNIFICIENZA
Natura: Attivo
#8 Unione Divina e #15 Prosperit
diventa: #57 MUNIFICIENZA
La munificienza incondizionata l'abbondanza presente in ogni creazione.
La munificienza viene da tutti gli aspetti di una creazione, che riceve cura,
nutrimento, attenzione, amore ed energia, per poter evolvere e finalmente
ascendere. Assicura che tuttie le sostanze nutrienti siano disponibili perl'evoluzione di segmenti e per l'evoluzione globale.
#31
Onore
#42
Comuni-
cazione
#58 SERVIZIO
Natura: Passivo
#31 Onore e #42 Comunicazione
diventa: #58 SERVIZIO
E' la comprensione che tutti gli aspetti creativi sono al servizio della
complessit della creazione. Ogni parte contribuisce con i suoi doni e
talenti al grande bene dell'insieme. Il Servizio implica che ogni aspetto
si doni completamente, senza limitazioni e misure, dove ogni
segmento contribuisce in modo illimitato, ad assicurare ilmantenimento e l'evoluzione dell'insieme.
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#4
Compas-sione
#38
Comu-nione
#59 UNIONE INCONDIZIONATA
Natura: Integrativo
#4 Compassione e #38 Comunione
diventa: #59 UNIONE INCONDIZIONATA
Sostiene l'unione e la costante comunicazione creatore/creazione in un
costante di scambio di energie. L'unione incondizionata amplifical'energie, che sostengono e alimentano l'ulteriore evoluzione e
ascensione.
#9
Unit di
Coscienza
#40
Com-
unit
#60 COMUNITA' INCONDIZIONATA
Natura: Completamento
#9 Unita di Coscienza e #40 Comunit
diventa: #60 COMUNITA' INCONDIZIONATA
E' il tono di completamento che unifica i toni 50-59 nel tono della
Comunit Incondizionata. Permette l'unione incondizionata delle creazione
multiple. Consente ai creatori e le creazioni di agire sotto l'ombrello di una
comune evoluzione.
#5 Respiro
di vita
#34
Passione
#61 FERMEZZA
Natura: Attivo
#5 Respiro di Vita e #34 Passione
diventa: #61 FERMEZZA
Amplifica la verit, l'unit e la perseveranza in modo da aumentare
l'energia e la spinta evolutiva, per creare evoluzione e ascensione sia
individuale che di gruppo.
#4
Compas-
sione
#25
Verit
#62 UNITA'-VERITA' FONDAMENTALE
Natura: Passivo
#4 Compassione e #25 Verit
diventa: #62 UNITA'-VERITA' FONDAMENTALE
Definisce i confini della verit fondamentale in ogni creazione data. La
verit come un segmento di vibrazioni che porta una esperienza
particolare. Questo tono prevede solo vibrazioni di verit risonanti per
scopi e progetti comuni con ogni creazione.
#5 Respiro
di Vita
#25 Verit
#63 EVOLUZIONE
Natura: Integrativo
#5 Respiro di Vita e #25 Verit
diventa: #63 EVOLUZIONE
E' la spinta verso il sentiero di ascensione. Provocher l'abbandono di modi
di vita superati. In un gruppo, questo tono potrebbe provocare l'uscita diqualche membro che mantiene basse le vibrazioni, impedendo l'aumento di
vibrazioni del gruppo come insieme.
#32 Sogno #3
Potere
#64 ZONA DI SOVRANITA'
Natura: Attivo
#32 Sogno e #3 Potere
diventa: #64 ZONA DI SOVRANITA'
Contiene i principi di Fermezza, Unit-Verit fondamentale e Evoluzione.
Nell'evoluzione, le creazioni sono continuamente modellate per produrre
salti di vibrazione, producendo fasi di dinamiche energetiche individuali e
di gruppo, creando un dominio nel quale sono contenuti ogni membro delgruppo o anima.
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#24
Unicit
#7
Libert
#65 ESISTENZA o IO SONO CIO' CHE SONO
Natura: Passivo
#24 Unit e #7 Libert
diventa: #65 ESISTENZA o IO SONO CIO' CHE SONO
Consente l'esistenza di una data creazione cos com', insieme con la
creazione intera. E' attraverso l'accoglimento che si compie l'abbandono,che l'atto di rinunciare al proprio ego, basato sui desideri, consegnandolo
agli scopi dell'anima. Stati sempre pi profondi di abbandono avvengono
un poco alla volta nel processo evolutivo individuale o di gruppo. Pi
profondo la resa all'anima, pi profondamente ci si muove in uno stato di
totale abbandono o accettazione di TuttoCiCheE'..
#23
Este-
riorit
#2
Struttura
#66 UNITA'-RELAZIONI BASE
Natura: Integrativo
#23 Esteriorit e #2 Struttura
diventa: #66 UNITA'-RELAZIONI BASE
E' il tono che permette di accettare individui e gruppi. Accettando leespressioni, le esperienze, le interazioni degli altri, si sostiene l'unit.
Richiede di incorporare il tono IO SONO CIO' CHE SONO in modo da
accettare totalmente gli altri. Si padroneggia l'unit delle relazioni solo
nella totale accettazione e accoglimento di tutte le esperienze altrui.
#18
Funzione
#17
Intuizione
#67 CAMMINO
Natura: Attivo
#18 Funzione e #17 Intuizione
diventa: #67 CAMMINO
Rappresenta la propria particolare verit che si deciso di sperimentare.
Ogni verit un raggio individuale necessario che, insieme formano una
ruota. Si richiede a tutti i raggi di comporre l'intera ruota, per sostenerel'insieme. Ogni verit crea un'unica esperienza evolutiva che contribuisce
al cammino complessivo di tutti.
#2
Struttura
#25
Verit
#68 MAPPA o SENTIERO PER L'EVOLUZIONE
Natura: Passivo
#2 Struttura e #25 Verit
diventa: #68 MAPPA o SENTIERO PER L'EVOLUZIONE
E' il tono che allinea costantemente il proprio cammino sulla Terra ad una
particolare verit. Ci sono molti sentieri che si possono prendere e non tutti
sono allineati con la propria verit.
#35
Creativit
#19
Perse-
veranza
#69 ILLUMINAZIONENatura: Integrativo
#35 Creativit e #19 Perseveranza
diventa: #69 ILLUMINAZIONE
Questo tono porta una continua illuminazione, o aumento di vibrazioni
sia in un individuo che in gruppo. Il tono invoca la liberazione di tutte le
vibrazioni pi dense che si incorporano. E' come spogliarsi di un abito
invernale quando si avvicina la primavera.
#24 #25
#70 ASCENSIONE
Natura: Completamento
#24 Unit e #25 Veritdiventa: #70 ASCENSIONE
E' il tono di completamento che combina i toni 61-70 nel singolo tono di
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Unit Verit Ascensione. Stabilizza sia i gruppi che gli individui nel dominio nella
successiva alta vibrazione raggiunta. E' il momento del completamento di
ogni segmento di iniziazioni. Si nel respiro ritmico della creazione. E' il
momento della stabilizzazione, prima di procedere nei passi successivi
dell'evoluzione..
COME UTILIZZARE IL LINGUAGGIO DI LUCE PER FACILITARE L'ASCENSIONE
Lady Gaia tramite Karen Danrich, Mila Sinoski
6 Aprile, 2000
Il Linguaggio di Luce, canalizzato in 48 simboli, alla fine del 1999, una rappresentazione di toni e
vibrazioni di una nuova forma pensiero, che collega l'attuale sistema di credenza basato sulla
polarit in una nuova forma pensiero di unit e non-polarit. I toni del Linguaggio di Luce possono
essere paragonati ai toni della creazione (conosciuti come Bija Mantras) che sono i toni necessari a
sostenere la vita nella terza dimensione. La Terra e tutte le cose viventi, inclusa l'umanit, stanno
transitando dalla terza alla quinta dimensione o, in altri termini, stanno ascendendo. Per raggiungere
questo scopo, stato costruito un collegamento di toni che crea un sentiero dalla terza alla quinta
dimensione, attraverso il Linguaggio di Luce.
Dalla fine del 1998 fino alla fine del 1999, alla SSOA venne dato il progetto di costruire una mappa
per il sentiero di ascensione per la specie umana, per le iniziazioni superiori alla 1024. Il gruppo cheha aderito, nel corso di 15 mesi, attraverso un'iniziazione di gruppo, ha creato un po' alla volta
questa mappa. Questi toni consentono anche a piccoli gruppi di individui, di elevarsi da 1024 a
5024 strati di DNA, o conseguire lo stato di Bodhisattva, nella loro realt fisica ed ascensione
personale.
L'ascensione un'impresa biologica nella quale la forma fisica aumenta gradualmente di vibrazione,
entrando in un'altra dimensione, dove svaniranno le forme-pensiero che sono state prevalenti ed
importanti finora. Pi aumentano le vibrazioni, pi le vecchie forme-pensiero basate sulla paura,
non troveranno pi posto nella vostra vita e saranno sostituite con un nuovo paradigma di unit di
coscienza. Le informazioni genetiche per conseguire lo stato di Bodhisattva, sono state
recentemente rese disponibili per tutti quelli che hanno scelto di ascendere. I simboli sonodisponibili sul sito web nella linkLinguaggio di Luce, oppure in forma di tarocchi in file formato
PDF che pu essere stampato direttamente a colori, con il significato di ogni simbolo.
Vogliamo condividere con ognuno di voi alcuni modi in cui il Linguaggio di Luce pu essere
incorporato nella vostra vita, per alimentare l'ascensione personale. Molti della SSOA hanno
cominciato ad applicarli nei loro compiti quotidiani di guarigione e ne traggono beneficio, perch
lavorando giornalmente con le vibrazioni di ascensione, non si pu fare a meno di aumentare le
proprie vibrazioni. Il Linguaggio di Luce pu effettivamente portarci alla dimensione successiva, a
trascendere tutti i vecchi modelli di attaccamento e di possesso, perch questi impediscono
l'elevazione e bloccano le vibrazioni. Gli attaccamenti, o legami, possono essere visti come
minuscole corde di energia collegate alle persone, agli animali, alle piante o agli oggetti che si
possiedono. Questi attaccamenti devono essere sciolti, perch creano un buco nel campo aurico,
attraverso il quale si perde energia. Nell'ascensione, c' una continua liberazione di questi legami
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karmici e si sigilla il proprio campo aurico sempre di pi, per poter mantenere sempre pi stabile
l'energia. Ogni cambiamento eterico porta un relativo cambiamento biologico, che permette alla
forma fisica di mantenere un'alta vibrazione molecolare e cellulare.
Per sintonizzarsi sul Linguaggio di Luce si devono semplicemente visualizzare i simboli nella
propria vita quotidiana e focalizzarsi su di essi, portandoli gradualmente in sequenza nel vostrocampo aurico. I toni in se stessi sono proprio come una scala. Il tono numero 1 la vibrazione pi
bassa, che quella del "Perdono". Questa vibrazione porta un certo segmento di ascensione
biologica, insieme ai cambiamenti eterici e dei corpi sottili, che circondano la forma fisica. Il tono
numero due, una vibrazione un po' pi alta, che la "Struttura". Di nuovo, appena incorporato,
porta il successivo segmento di ascensione biologica. Ogni tono contiene in s tutte le informazioni
necessarie per ascendere direttamente nella fase successiva.
Bisogna prima raggiungere l'iniziazione 1024, o diventare cristallini, prima di poter iniziare la fase
successiva di ascensione allo stato di Bodhisattva e incorporare il Linguaggio di Luce. Ci sono
ulteriori dettagli contenuti nelle Note ai nostri affiliati. Queste note sono state canalizzate agli
affiliati del gruppo di iniziazione della SSOA, cominciato nel gennaio 1999. Nei prossimi mesisaranno disponibili queste informazioni, che potranno essere utili ad altri che incorporano l'unit di
coscienza nella loro personale esperienza di ascensione.
La scuola spirituale ha effettivamente incorporato l'ultimo simbolo del Linguaggio di Luce (#48)
come gruppo, nel dicembre del 1999. Il gruppo continua a crescere di vibrazioni. A seguito dei
simboli ci sono i "Doppi Toni" Linguaggio di Luce - Doppi Toniche si combinano insieme per
creare una nuova e pi alta vibrazione, con un nuovo significato. Il 1 giugno 2000, il primo gruppo
di Toni Doppi stato aggiunto alla sezione "Linguaggio di Luce" del nostro sito. La SSOA rende
disponibili queste informazioni solamente dopo averle conseguite nel processo di iniziazione di
gruppo. La SSOA incorporer gli ultimi due toni (#96) durante l'evento annuale "Conclave dei
Maestri" a settembre 2000. Anticipiamo che tutti i 96 Doppi Toni saranno aggiunti al sito web alla
fine dell'anno 2000.
Lady Gaia, la coscienza di Madre Terra, sta soprintendendo l'evento del "Conclave dei Maestri" che
unisce un piccolo gruppo di individui (200-300) che aiuteranno Lady Gaia in questo segmento
principale del suo processo di iniziazione globale. Lady Gaia in procinto di incorporare
l'Iniziazione Globale 1024. Questo consentir anche a molti iniziati intorno al mondo, di conseguire
simultaneamente maggiori settori di "completamento" nella loro ascensione personale, contribuendo
con la loro energia a fornire la spinta necessaria alla Terra per ascendere.
Incorporando i Doppi Toni nella vostra personale ascensione, cominciate il processo di ascensionedallo stato di Bodhisattva a quello di Mahavishnu (o incorporare 15.000 strati di DNA). Il livello
Mahavishnu incorpora un'ottava pi alta di quella di Bodhisattva. Il materiale genetico Mahavishnu
ancora in fase di mappatura ma anticipiamo che sar fornito all'umanit a gennaio 2001.
La Terra sta aumentando rapidamente le sue vibrazioni. Se l'umanit non vorr rimanere indietro,
dovr fare rapidamente un salto in avanti. Vi invitiamo ad utilizzare il Linguaggio di Luce per dare
carburante alla vostra personale ascensione. Per quelli a cui il concetto di ascensione nuovo, vi
invitiamo ad affermare quotidianamente, verbalmente, in ogni momento, l'"intenzione di
ascendere", perch attraverso l'intento cosciente che l'ascensione pu avvenire, per chi sceglie
questo sentiero in questi tempi della storia umana. L'ascensione in quinta dimensione significa
porre fine per sempre alle esperienze di morte fisica, e vivrete per vedere una nuova era di pace, digioia, di unit e d'amore, nascere nell'esperienza umana sulla Terra.
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Alla prossima volta, molte benedizioni sul vostro viaggio. Namaste.
Copyright 19982000 Karen Danrich. All Rights Reserved.
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Why We See Three-Dimensional Objects: Another Approach
Eric W. Brown, M.S.
Patrick S. P. Wang, [email protected]
Abstract
This paper considers the work done by Thomas Marill in a series of papers on the recognition of
two-dimensional wire-frame figures as three-dimensional objects without the use of models. Marill
discovered that if one minimizes the standard deviation of the angles found at each vertex of the
figure, the likelihood of the computer interpretation of the figure matching the human interpretation
is much higher than might be expected a priori. Here it is observed that the human mind's tendency
to simplify inputs and find patterns even where there are none might be at least partly responsible
for the observed phenomenon. It is conjectured that if this is indeed the case, it should be possible
to get similar behavior from minimizing the standard deviation of other features. In particular,
segment length presents itself as being an excellent choice of a test feature -- it is very different
from angles and is less computationally intensive. Thus another approach is considered: minimum
standard deviation of segment magnitudes is explored in lieu of minimum standard deviation of
angles.
Marill's original experiment is then carefully repeated with several additional figures that were
deliberately chosen not to have all equal angles. The experiment is described in detail, and all the
failures of Marill's algorithm are carefully studied and explained. The problem of straight angles is
touched upon and the difficulties of solving it as a special case are briefly discussed.
A new program is then written to minimize the standard deviation of segment magnitudes instead ofminimizing the standard deviation of angles. This program is run on the same test figures as the
original algorithm. Its successes and failures are noted and explained, and its behaviors are studied.
The results of the two algorithms are then compared and the differences noted. It is of particular
interest that the two algorithms have different areas of failure, suggesting that a combined algorithm
should be able to produce better results than either one alone. This and some other avenues of future
work are suggested.
Finally, some comments about the basic behaviors of both algorithms are made.
Keywords
object recognition and interpretation, 3D pattern recovery from 2D images, MinimumStandard Deviation of Angles (MSDA), Minimum Standard Deviation of SegmentMagnitudes (MSDSM)
Introduction
The interpretation of two-dimensional wire-frame diagrams as three-dimensional objects in a
human manner is a topic that has received much attention and study. Restricting the domain of the
problem to wire-frame pictures simplifies the matter enough to be explored in a solid manner while
still maintaining enough generality to provide insight into the greater problem of interpreting the
full set of two-dimensional pictures as three-dimensional objects. Many methods of interpretation
utilized models and thus were restricted to only identifying a fixed number of different objects.Thomas Marill pioneered a novel approach that does not require models1; rather it simply tries to
return the three-dimensional object that minimizes the standard deviation of its angles (M.S.D.A.).
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He experimented with this method in several papers1,2,3and other authors followed suit4,5,6. He
hypothesized3 that this algorithm worked because the human mind has an in-built compression
system of sorts; it will always store the data in a minimal fashion.
Theory
It seems reasonable to assume that while this is possible, it is not the only explanation. Another
possibility is that the human mind attempts to simplify all of its inputs, building patterns even where
there are none. If Marill's minimization of standard deviation of angles approach works because of
this tendency, there is a likelihood that other similar approaches would also work. In particular the
minimization of standard deviation of segment magnitudes (M.S.D.S.M.) suggests itself as a lesscomputationally intensive alternative.
M.S.D.A. Experimental Setup
In principle it is not too hard to test this theory. In practice, a few real-world problems (such as
differences between independent computer platforms) presented themselves. The program writtenby Baird & Wang for their paper5 seemed nearly ideal as a cornerstone upon which to build a test
program, but it was written for the Macintosh platform. With some effort, the program was
converted to compile and build using standard X-Windows and GNU's gcc and could then be built
and run on virtually any UNIX box. The program was additionally tested after being built with
Sun's acc compiler, and it was carefully linted and made clean. The program was enhanced to take
advantage of some of the features of its new environment and to provide more user feedback and
current result information, and to read its shape information at run-time so that new shapes could be
added without requiring a rebuild. This exercise unearthed a heretofore unmentioned behavior of
the Marill algorithm: it is very sensitive to initial conditions. It is somewhat chaotic: tiny
differences in its initial input (such as the ones resulting from the use of two different random seeds
or the random number generators on two different platforms) can mean the difference between a
successful run and an unsuccessful one. The sensitivity of the assorted figures to these tiny
differences of initial conditions seemed to vary from figure to figure; no detailed analysis was done
on this behavior but it may be an interesting avenue for future work. Certainly it is advisable that
future Marill-type algorithms make hidden initial conditions (such as the ones resulting from
different random seeds) explicit.
Failures of M.S.D.A.
In the cases where Marill's algorithm failed, the results were still easily explained. There were two
primary causes of failure: the gradient descent bottomed out in a local minima rather than the globalone, or the M.S.D.A. for the figure actually produced false results.
A failure in the gradient descent resulted in a tangled figure that often contained obvoluted, non-
planar faces (see Figure 1, "Examples of Tangles"). This was by far the most common problem with
the test set of figures, and this was what was most sensitive to initial conditions. The difference of a
random seed or an internal step size or method of gradient descent had large impact on the results; a
particular implementation on a particular machine could very easily be tweaked to give excellent
results for a specific test set while still having only mediocre results on a more general test set.
While tangles were responsible for many failures, they are really not a serious problem.
Expectations are that the additional psychological assumptions suggested by Leclerc & Fischler4
will virtually eliminate tangles as these obvolutions seem to universally result from solutions
involving non-planar faces and the like.While it is true that the set of gradient descent failures is potentially much larger than the set of
tangles, no such occurrences were ever seen during the full course of this experiment. If this sort of
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failure ever does become more troublesome, undoubtedly standard methods for minimizing local
minima difficulties could be employed with typical amounts of success. Certainly the creation of an
algorithm that combines the ideas of Marill, Leclerc & Fischler, and this paper will help clarify the
extent of the problem posed by general gradient descent failure and even perhaps pave the way for
the application of other techniques (included but not limited to the family of simulated annealing
algorithms).
Figure 1: Examples of Tangles
The second cause of failure is more fundamental and thus more problematical. It is the case where
using the correct M.S.D.A. still produces incorrect results. This type of error is due to a real
limitation with the algorithm; it cannot be fully eliminated with Leclerc & Fischler's additions.
There were not too many examples in Marill's original test data set that had this problem. Most
simple wire-frame images do not, and it requires a little deliberate thought to create such examples.
Shapes such as prisms and pyramids often have multiple dominant angles and thus were potential
troublemakers for the straight Marill algorithm. Irregular shapes often have no real dominant angle
and can wreak equal havoc. A few such shapes were added to the test set. Although these shapes did
seem to cause difficulties for the algorithm, it was typically tough to see the errors caused byinappropriate M.S.D.A.'s through the tangles. Figure 2, "Examples of Bad M.S.D.A.'s" shows a
couple of cases where the fact that the calculated M.S.D.A. really did not reflect the real shape was
a little more apparent than average.
Figure 2: Examples of Bad M.S.D.A.'s
A special case of inappropriate M.S.D.A.'s occurs in wire-frames that contain 180 angles. These
straight angles seem to universally confuse the pure form of Marill's algorithm. Figure 3, "Examples
of Straight Angle Confusions," shows two of these cases. While at first blush it might seem to be a
relatively simple fix to make the algorithm recognize this special case, it turns out not to be so.
Simply removing all straight angles from the M.S.D.A. calculations does not work. In addition to
introducing a new threshold in the definition of a straight angle (is a 177 angle straight or not?) it is
important to remember that a given point is usually involved in other angles besides the straight one
of interest. The consequences of the other modifications affecting that point can still nullify any
advantages gained by eliminating the straight angle from the M.S.D.A. calculation. Straight angleelimination was incorporated into a version of Marill's algorithm anyway; no improvements were
noted. While it is possible that careful tweaks to the algorithm could have some positive impact, it
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is not clear that this path would be fruitful enough to justify any effort; at best it could only improve
the performance for one small special case of a much larger general problem.
Figure 3: Examples of Straight Angle Confusions
M.S.D.S.M. Experimental Setup
Finally, after this converted program had been tested and verified, it was used as the basis for a
program that worked with the standard deviation of segment lengths rather than the standard
deviation of angles. Such a program was written. It took a straightforward approach very similar to
Marill's original one1: new objects were generated by adding or subtracting a small amount fromeach z-coordinate in the original figure. The standard deviation of segment lengths was calculated
for each and the minimum picked. The cycle was then repeated endlessly until the image settled.
The gradient descent method used by Baird & Wang5 is clearly superior to this method, but for
initial testing of the theory this method was far more direct. Additionally, since the calculation of
segment lengths is simpler than the calculation of angles, it turned out that the overall speed of even
the simplistic version of this algorithm was comparable to the speed of the M.S.D.A. algorithm with
Baird & Wang's improvements. It is expected that further speed improvements could be made to
this algorithm using an approach analogous to that used by Baird & Wang.
M.S.D.S.M. Algorithm Behavior
Expectations were that if the initial assumption of the human mind naturally trying to build patterns
was the underlying reason the M.S.D.A. approach worked was in fact correct, then the minimum
standard deviation of segment magnitudes approach should also work for certain cases with similar
(albeit hopefully different) strengths and weaknesses. Initial experimentation showed that this was
indeed the case. Just as with M.S.D.A., the biggest problem M.S.D.S.M. faced (in terms of number
of failures) was wire-frames getting tangled. Not only was the percentage of tangled cases similar,
the actual resulting tangled images themselves were indistinguishable from the tangled images
produced by the M.S.D.A. algorithm. Once again, please refer to Figure 1, "Examples of Tangles,"
to see some examples of tangled images. As with M.S.D.A., it is expected that the addition of the
conditions suggested by Leclerc & Fischler could virtually eliminate this particular type of failurefrom the algorithm.
Also, just as it was possible for the M.S.D.A. algorithm to fail in cases where the M.S.D.A. simply
was not adequate to represent the intended image, it was expected that the M.S.D.S.M. algorithm
would fail in some cases where the M.S.D.S.M. was not adequate. The obvious place to look for
such failures was in wire-frame objects built from segments of varying lengths, and upon searching
such failures were indeed found (see Figure 4, "Examples of Bad M.S.D.S.M.'s"). There is really no
natural analog to M.S.D.A.'s special case problem of straight angles in the M.S.D.S.M. domain; the
closest is perhaps segments of zero length. This seemed to be such an odd case that it was ignored.
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Figure 3: Examples of Bad M.S.D.S.M.'s
One somewhat unexpected difference between the two algorithms was their sensitivity to small
changes in initial conditions. While slightly different inputs often resulted in vastly different outputs
for the M.S.D.A. algorithm, equivalent differences input to the M.S.D.S.M. algorithm rarely
resulted in noticeable outputs at all. It is hypothesized that this is somehow related to the nature of
the calculations required for determining angles, but it could also be somehow related to the
different types of gradient descent algorithms employed.
Result Comparison
The two algorithms were then run side by side for five trials on each object in the test data set (see
"Appendix I: Shape Line Drawings"). A random seed of 1.0 was used in every case. Neither
program was restarted after individual trials, and the settling time given for each trial was three
minutes. While it is of course true that some randomness in running time will inevitably be present
in every multi-tasking system, all attempts were made to minimize such effects (only one user was
allowed on the system while the test program was running, no additional user programs were
running, etc.). Table 1, "Test Results" below summarizes these results.
Shape Name Results of M.S.D.A. Algorithm Results of M.S.D.S.M. Algorithm
Special Shape 0% 0%Cube 40% 0%
Stairs 80% 0%
Uneven Stairs 0% 0%
Table 20% 0%
Symphony Hall 0% 0%
Triangular Prism 60% 100%
Tetrahedron 100% 100%
Simple Fridge (HL) 40% 0%
Fridge 0% 0%
Symphony Hall (HL) 0% 0%
Open Fridge (HL) 0% 0%
Pyramid 0% 100%
Octahedron 0% 100%
Pentagonal Prism 0% 80%
Tetrahedron 2 100% 100%
Pyramid 2 0% 100%
Truncated Pyramid 0% 0%
Table 1: Test Results
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Note that the abbreviation HL (both here and elsewhere) indicates that the wire-frame diagram
contained hidden lines. The percentage numbers indicate the percentage of successful trials out of
the five. Thus, a 10% indicates that in only one trial of five did the algorithm produce correct
results. Note also that the rigor used in allowing a certain amount of settling time might not be fully
necessary. On no occasion was it observed that an image started to obvolute and then correct itself.
Every such occurrence ended in a tangled image.
Discussion
Several observations may be made from these results. The first is that both algorithms were able to
correctly interpret the same number of images (seven) correctly some of the time. The other images
they completely failed to interpret properly every time. The second is that while the M.S.D.S.M.
seemed to score better on this data set, the difference was not a huge one particularly when the first
observation is taken into account and it is remembered that some cases that were expected to be
hard for M.S.D.A. were deliberately added to the data set. The third is that there were some images
that were easy for both algorithms (such as the tetrahedrons), some images that were hard for both
algorithms (such as irregular shapes like the special shape and mixed shapes like the truncatedpyramid), some images that were hard for M.S.D.A. but easy for M.S.D.S.M. (such as the pyramid),
and some images that were easy for M.S.D.A. and hard for M.S.D.S.M. (such as the stairs). Other
observations about algorithm behaviors (such as sensitivity to initial conditions) have already been
mentioned and need not be repeated here.
Future Work
These results suggest many avenues for future work. Since the sets of cases that each algorithm is
good at are not identical, it seems extremely reasonable to assume that improved overall results
could be obtained by combining the two. If an algorithm were devised to implement both the
M.S.D.A. and M.S.D.S.M. approaches along with the conditions suggested by Leclerc & Fischler,
expectations are that results would be dramatically improved. Irregular shapes would probably still
be problematical, but possibly the forced balance between the different algorithms would help in
this regard, or at least provide more insight into new directions for even further research.
It is also clear that there may be other features that could be exploited in much the way that angles
and segment magnitudes are to produce even further dramatic improvements.
Conclusion
The results clearly indicate that the M.S.D.S.M. approach has some merit. They would also argue
against the use of either pure M.S.D.S.M. or pure M.S.D.A. algorithms as the only means of objectreconstruction in a serious project. While both provide some ability to recognize objects, neither
provides enough alone to be generally reliable. The results also reinforce the initial theory of this
paper -- that Marill's approach works because of the nature of the human mind.
On a final note, it may appear that this paper is treating Marill's M.S.D.A. algorithm somewhat
harshly. It should be clearly stated that this is not the intent. While it is true that the M.S.D.A.
algorithm by itself cannot completely deal with the problem of interpreting wire-frame diagrams as
three-dimensional objects in a human-like manner, it is true that Marill's experiment has introduced
a wonderful new technique to the world that is capable of much expansion and enhancement. The
advantages of a non-model based approach to the problem should be so obvious as to not require
comment.
References
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1
Thomas Marill, "Recognizing Three-Dimensional Objects Without the Use of Models", A. I.
Memo #1157 of the MIT Artificial Intelligence Laboratory, 1-13, September 1989
2
Thomas Marill, "Emulating the Human Interpretation of Line-Drawings as Three-
Dimensional Objects", International Journal of Computer Vision, Iss. 6:2, 147-161, 1991,Kluwer Academic Publishers, The Netherlands
3
Thomas Marill, "Why Do We See Three-Dimensional Objects?", A. I. Memo #1366 of the
MIT Artificial Intelligence Laboratory, 1-22, June 1992
4
Yvan G. Leclerc & Martin A. Fischler, "An Optimization-Based Approach to the
Interpretation of Single Line Drawings as 3-D Wire Frames", International Journal of
Computer Vision, 1-14, 1992, The Netherlands
5
Leemon Baird & Patrick Wang, "3D Object Recognition Using Gradient Descent and the
Universal 3-D Array Grammar", SPIE, Vol. 1607, 711-716, 19916
Leemon Baird & Patrick Wang, "3D Object Perception Using Gradient Descent", Int.
Journal of Mathematical Imaging and Vision (IJMIV), 5, 111-117, 1995
Appendix I: Shape Line Drawings
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Appendix II: Shape Definitions
# The wire-frame data file for the xmar program
#
# Format Description:
#
# Recognized fields include: Name, Random Seed, Random Range
# Step Size, Step Decrement, Scale, Points List, and Lines List.
# The octothorpe `#' character is used at the beginning of a line to
# indicate a comment.
# All the fields (except for the two list types) should be followed by
# a colon `:' and two spaces before the argument is given. All of# these fields expect a floating point argument with the exception
# of Name. Name expects a string.
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# The two list types should sit on a line by themselves followed by
# a colon. The following lines contain the actual point or line data.
# Point data is contained in ordered triples of floating point
# numbers delineated by parentheses and separated by commas.
# Line data is contained in ordered pairs of floating point numbers
# delineated by braces and separated by commas.#
# Each defined shape should have a Name and Point & Lines lists.
# Other fields are optional.
#
Name: Special Shape
Random Seed: 1.000
Points List:
( 0.000, 0.000,0.0), ( 3.460, 0.000,0.0), ( 5.430, -0.700,0.0),
( 16.290, -2.100,0.0), ( 19.750, -2.100,0.0), ( 21.720, -2.800,0.0),
( 21.370, -6.740,0.0), ( 17.910, -6.740,0.0), ( 17.560,-10.680,0.0),( 14.100,-10.680,0.0), ( 13.750,-14.620,0.0), ( 6.830,-14.620,0.0),
( -1.050,-11.820,0.0), ( 19.400, -6.040,0.0), ( 15.940, -6.040,0.0),
( 15.590, -9.980,0.0), ( 12.130, -9.980,0.0), ( 11.780,-13.920,0.0),
( 8.320,-13.920,0.0), ( 2.410,-11.820,0.0), ( 8.670, -9.980,0.0)
Lines List:
{ 0, 1}, { 0,12}, { 1,19}, {12,19}, { 2,20},
{20, 3}, { 3, 2}, { 1, 2}, {20,18}, { 3, 4},
{17,10}, {16, 9}, {15, 8}, {14, 7}, {13, 6},
{ 4, 5}, {12,11}, {11,10}, {10, 9}, { 9, 8},
{ 8, 7}, { 7, 6}, { 6, 5}, { 4,13}, {13,14},
{14,15}, {16,17}, {17,18}, {18,19}, {15,16}
Name: Cube
Random Seed: 1.000
Points List:
( -2.890, -1.620,0.0), ( 0.570, -1.620,0.0), ( 0.920, 2.320,0.0),
( -2.540, 2.320,0.0), ( -0.920, -2.320,0.0), ( 2.540, -2.320,0.0),
( 2.890, 1.620,0.0), ( -0.570, 1.620,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 0, 3}, { 4, 5},
{ 5, 6}, { 6, 7}, { 4, 7}, { 0, 4}, { 1, 5},{ 2, 6}, { 3, 7}
Name: Stairs
Random Seed: 1.000
Points List:
( -2.400, -1.450,0.0), ( 0.140, 2.070,0.0), ( -0.710, 1.710,0.0),
( -0.710, 0.900,0.0), ( -1.560, 0.540,0.0), ( -1.560, -0.280,0.0),
( -2.400, -0.630,0.0), ( 0.780, -2.790,0.0), ( 3.320, -1.720,0.0),
( 3.320, 0.730,0.0), ( 2.470, 0.370,0.0), ( 2.470, -0.450,0.0),
( 1.630, -0.800,0.0), ( 1.630, -1.620,0.0), ( 0.780, -1.980,0.0)
Lines List:{ 1, 2}, { 2, 3}, { 3, 4}, { 4, 5}, { 5, 6},
{ 6, 0}, { 7, 8}, { 8, 9}, { 9,10}, {10,11},
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{11,12}, {12,13}, {13,14}, {14, 7}, { 0, 7},
{ 1, 9}, { 2,10}, { 3,11}, { 4,12}, { 5,13},
{ 6,14}
Name: Uneven Stairs
Random Seed: 1.000Points List:
(-15.510, 12.740,0.0), (-13.760, 14.990,0.0), (-14.080, 14.780,0.0),
(-14.020, 14.450,0.0), (-14.340, 14.240,0.0), (-14.280, 13.990,0.0),
(-15.570, 13.070,0.0), (-14.110, 12.410,0.0), (-12.180, 13.660,0.0),
(-12.350, 14.670,0.0), (-12.680, 14.460,0.0), (-12.620, 14.130,0.0),
(-12.940, 13.920,0.0), (-12.880, 13.670,0.0), (-14.170, 12.750,0.0)
Lines List:
{ 1, 2}, { 2, 3}, { 3, 4}, { 4, 5}, { 5, 6},
{ 6, 0}, { 7, 8}, { 8, 9}, { 9,10}, {10,11},
{11,12}, {12,13}, {13,14}, {14, 7}, { 0, 7},
{ 1, 9}, { 2,10}, { 3,11}, { 4,12}, { 5,13},{ 6,14}
Name: Table
Random Seed: 1.000
Points List:
( -0.670, 1.500,0.0), ( 3.670, 1.070,0.0), ( 1.670, 0.470,0.0),
( -2.670, 0.900,0.0), ( -0.670, -0.470,0.0), ( 3.670, -0.900,0.0),
( 1.670, -1.500,0.0), ( -2.670, -1.070,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 3, 0}, { 0, 4},
{ 1, 5}, { 2, 6}, { 3, 7}
Name: Syphony Hall
Random Seed: 1.000
Points List:
( 0.000, 15.000,0.0), ( 8.000, 17.000,0.0), ( 26.000, 11.000,0.0),
( 26.000, 5.000,0.0), ( 18.000, 3.000,0.0), ( 17.000, 2.000,0.0),
( 9.000, 0.000,0.0), ( 6.000, 5.000,0.0), ( 6.000, 7.000,0.0),
( 0.000, 9.000,0.0), ( 8.000, 11.000,0.0), ( 14.000, 9.000,0.0),
( 14.000, 7.000,0.0), ( 20.000, 5.000,0.0), ( 20.000, 7.000,0.0),
( 18.000, 9.000,0.0), ( 12.000, 3.000,0.0), ( 12.000, 5.000,0.0)Lines List:
{ 0, 1}, { 0, 9}, { 9,10}, { 1,10}, { 9, 8},
{10,11}, { 1, 2}, { 2, 3}, { 3, 4}, { 3,14},
{ 8,11}, {11,14}, { 7, 8}, {11,12}, {13,14},
{ 7,12}, {12,13}, { 6, 7}, { 5,12}, { 5, 6},
{ 5,13}, { 0,15}, { 2,15}, { 4,15}, { 8,17},
{14,17}, {16,17}, { 4,17}, { 6,16}, { 7,16},
{13,16}
Name: Triangular Prism
Random Seed: 1.000Points List:
( 17.000, 2.000,0.0), ( 9.000, 0.000,0.0), ( 6.000, 5.000,0.0),
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( 14.000, 7.000,0.0), ( 15.000, 2.000,0.0), ( 7.000, 0.000,0.0)
Lines List:
{ 2, 3}, { 3, 4}, { 1, 2}, { 0, 3}, { 0, 1},
{ 0, 4}, { 1, 5}, { 2, 5}, { 4, 5}
Name: TetrahedronRandom Seed: 1.000
Points List:
( 17.000, 2.000,0.0), ( 14.000, 7.000,0.0), ( 20.000, 5.000,0.0),
( 19.000, 3.000,0.0)
Lines List:
{ 0, 1}, { 0, 2}, { 0, 3}, { 1, 2}, { 1, 3},
{ 2, 3}
Name: Simple Fridge (HL)
Random Seed: 1.000
Points List:( 13.000, 11.000,0.0), ( 13.000, 6.000,0.0), ( 13.000, 6.000,0.0),
( 13.000, 3.000,0.0), ( 8.000, 1.000,0.0), ( 5.000, 0.000,0.0),
( 0.000, 2.000,0.0), ( 0.000, 10.000,0.0), ( 3.000, 11.000,0.0),
( 8.000, 9.000,0.0), ( 8.000, 4.000,0.0), ( 3.000, 3.000,0.0)
Lines List:
{ 4, 5}, { 4, 9}, { 4,11}, { 5, 6}, { 6, 7},
{ 6,11}, { 7, 8}, { 8, 9}, { 8,11}
Name: Fridge
Random Seed: 1.000
Points List:
( 13.000, 11.000,0.0), ( 13.000, 6.000,0.0), ( 13.000, 6.000,0.0),
( 13.000, 3.000,0.0), ( 8.000, 1.000,0.0), ( 5.000, 0.000,0.0),
( 0.000, 2.000,0.0), ( 0.000, 5.000,0.0), ( 0.000, 10.000,0.0),
( 3.000, 11.000,0.0), ( 8.000, 9.000,0.0), ( 8.000, 4.000,0.0),
( 3.000, 3.000,0.0), ( 3.000, 6.000,0.0), ( 5.000, 3.000,0.0),
( 5.000, 8.000,0.0)
Lines List:
{ 4, 5}, { 4,11}, { 4,12}, { 5, 6}, { 6, 7},
{ 6,12}, { 7, 8}, { 7,13}, { 8, 9}, { 9,10},
{ 9,13}, {10,11}, {11,13}, {12,13}, { 5,14},{ 7,14}, { 8,15}, {10,15}, {14,15}, {11,14}
Name: Symphony Hall (HL)
Random Seed: 1.000
Points List:
( 0.000, 15.000,0.0), ( 8.000, 17.000,0.0), ( 26.000, 11.000,0.0),
( 26.000, 5.000,0.0), ( 18.000, 3.000,0.0), ( 17.000, 2.000,0.0),
( 9.000, 0.000,0.0), ( 6.000, 5.000,0.0), ( 6.000, 7.000,0.0),
( 0.000, 9.000,0.0), ( 8.000, 11.000,0.0), ( 14.000, 9.000,0.0),
( 14.000, 7.000,0.0), ( 20.000, 5.000,0.0), ( 20.000, 7.000,0.0)
Lines List:{ 0, 1}, { 0, 9}, { 9,10}, { 1,10}, { 9, 8},
{10,11}, { 1, 2}, { 2, 3}, { 3, 4}, { 3,14},
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{ 8,11}, {11,14}, { 7, 8}, {11,12}, {13,14},
{ 7,12}, {12,13}, { 6, 7}, { 5,12}, { 5, 6},
{ 5,13}
Name: Open Fridge (HL)
Random Seed: 1.000Points List:
( 13.000, 11.000,0.0), ( 13.000, 6.000,0.0), ( 13.000, 6.000,0.0),
( 13.000, 3.000,0.0), ( 8.000, 1.000,0.0), ( 5.000, 0.000,0.0),
( 0.000, 2.000,0.0), ( 0.000, 5.000,0.0), ( 0.000, 10.000,0.0),
( 3.000, 11.000,0.0), ( 8.000, 9.000,0.0), ( 8.000, 4.000,0.0),
( 3.000, 3.000,0.0), ( 3.000, 6.000,0.0)
Lines List:
{ 0, 1}, { 0,10}, { 1,11}, { 2, 3}, { 2,11},
{ 3, 4}, { 4, 5}, { 4,11}, { 4,12}, { 5, 6},
{ 6, 7}, { 6,12}, { 7, 8}, { 7,13}, { 8, 9},
{ 9,10}, { 9,13}, {10,11}, {11,13}, {12,13}
Name: Pyramid
Random Seed: 1.000
Points List:
( 0.920, 2.320,0.0), ( -2.540, 2.320,0.0), ( -0.570, 1.620,0.0),
( 2.890, 1.620,0.0), ( 0.180, -1.270,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 0, 3}, { 0, 4},
{ 1, 4}, { 2, 4}, { 3, 4}
Name: Octahedron
Random Seed: 1.000
Points List:
( 0.920, 2.310,0.0), ( -2.540, 2.310,0.0), ( -0.570, 1.610,0.0),
( 2.890, 1.610,0.0), ( 0.180, -1.280,0.0), ( 0.180, 5.200,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 0, 3}, { 0, 4},
{ 1, 4}, { 2, 4}, { 3, 4}, { 0, 5}, { 1, 5},
{ 2, 5}, { 3, 5}
Name: Pentagonal PrismRandom Seed: 1.000
Points List:
( 0.000, 0.000,0.0), ( 3.460, 0.000,0.0), ( 4.530, 3.290,0.0),
( 1.730, 5.320,0.0), ( -1.070, 3.290,0.0), ( 1.970, 0.700,0.0),
( 5.430, 0.700,0.0), ( 6.500, 3.990,0.0), ( 3.700, 6.020,0.0),
( 0.900, 3.990,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 3, 4}, { 0, 4},
{ 5, 6}, { 6, 7}, { 7, 8}, { 8, 9}, { 9, 5},
{ 0, 5}, { 1, 6}, { 2, 7}, { 3, 8}, { 4, 9}
Name: Tetrahedron 2
Random Seed: 1.000
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Points List:
( 0.000, 0.000,0.0), ( 1.000, 0.000,0.0), ( 0.500, 0.866,0.0),
( 0.500, 0.288,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 0, 2}, { 0, 3},
{ 1, 3}
Name: Pyramid 2
Random Seed: 1.000
Points List:
( 0.000, 0.000,0.0), ( 1.000, 0.000,0.0), ( 1.000, 1.000,0.0),
( 0.000, 1.000,0.0), ( 0.500, 0.500,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 0, 3}, { 0, 4},
{ 1, 4}, { 2, 4}, { 3, 4}
Name: Truncated PyramidRandom Seed: 1.000
Points List:
( 0.000, 0.000,0.0), ( 3.000, 0.000,0.0), ( 3.000, 3.000,0.0),
( 0.000, 3.000,0.0), ( 1.000, 1.000,0.0), ( 2.000, 1.000,0.0),
( 2.000, 2.000,0.0), ( 1.000, 2.000,0.0)
Lines List:
{ 0, 1}, { 1, 2}, { 2, 3}, { 0, 3}, { 4, 5},
{ 5, 6}, { 6, 7}, { 4, 7}, { 0, 4}, { 1, 5},
{ 2, 6}, { 3, 7}
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