New Drawings of the Alhambra: Deformations of Muqarnas in the Pendentives of the Sala de la Barca - MDPI
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sustainability
Article
New Drawings of the Alhambra: Deformations of
Muqarnas in the Pendentives of the Sala de la Barca
Ignacio Ferrer-Pérez-Blanco 1 , Antonio Gámiz-Gordo 2 and
Juan Francisco Reinoso-Gordo 3, *
1 Laboratory of Digital Culture for Architectural Projects, École Polytechnique Fédérale de Lausanne,
Lausanne CH-1015, Switzerland; ignacio.ferrer@epfl.ch
2 Architectural Graphic Expression, University of Sevilla, Sevilla 41012, Spain; antoniogg@us.es
3 Architectural and Engineering Graphic Expression, University of Granada, Granada 18071, Spain
* Correspondence: jreinoso@ugr.es; Tel.: +34-958249485
Received: 27 November 2018; Accepted: 27 December 2018; Published: 9 January 2019
Abstract: Architectural heritage preservation and sustainability need advanced graphic techniques
in order to document and understand the disposition/composition of plaster muqarnas, a fragile
construction element. The muqarnas are key elements in the Nasrid architecture developed during
the 14th century in the Alhambra complex, nowadays part of World Heritage. As a case study,
this analysis focuses on the muqarnas pendentives of the Sala de la Barca in the Comares Palace.
After examining both explanations and drawings published by architects Jones and Goury from
1842 to 1845, our research provides new drawings (plans and elevations) derived from laser scanner
technology. Theoretically, though muqarnas are composed of simple geometrical shapes, these new
drawings unveil important deformations hitherto unknown, and which have not been studied yet by
other bibliographic references. Finally, we provide some considerations about the causes of these
deformations and the monument sustainability across the time and the images’ capacity to show the
muqarnas complex shapes in a reliable way.
Keywords: muqarnas; Alhambra; deformation; geometry; stereotomy; plaster; conservation;
architecture; heritage
1. Introduction
Drawing is an element essential to attain the preservation and sustainability of architectural
heritage. In the restoration and preservation of any historic building, it is crucial to rely on updated,
accurate graphic documentation [1]. A monument that is accurately documented will have a greater
chance to survive across time, even after adverse and disastrous events. Even when fatal destruction
happens, the building’s intangible value remain safe thanks to graphic documentation, as these
documents will eventually facilitate virtual or real reconstruction of the monument.
Muqarnas are one of the most admired elements in the 14th century Nasrid architecture found in
the Alhambra. Despite their frailty, the muqarnas produce complex arrays of amazing visual effects.
Muqarnas exist in very different architectonic elements like friezes, capitals, complex domes, arcs,
and pendentives, and their abundant variety of shapes was developed under the reign of Muhammad
V [2–4]. Even today, little is known of the muqarnas complex process of 3-D geometrical construction,
starting from very simple pieces, since only simple shapes were available.
For all these reasons, the main goal of this research is to provide a new and accurate graphic
documentation concerning some of these fragile architectonic elements in order to facilitate a better
understanding and sustainability of the muqarnas. This work has used, for the first time, 21st century
graphical techniques for their representation, specifically a 3-D laser scanner. It should be highlighted
Sustainability 2019, 11, 316; doi:10.3390/su11020316 www.mdpi.com/journal/sustainability
Sustainability 2019, 11, 316 2 of 16
the Alhambra
SustainabilityNasrid Palaces. Moreover, only a few authors have depicted the muqarnas
2019, 11, 316 using
2 of 15
traditional drawings, and only a few examples are included in 19th century plans, just as the ones by
Jones and Goury commented here.
that nowadays there are no digital drawings representing the muqarnas complex shapes existing in the
Different muqarnas groups in the monumental complex could be scanned thanks to the precious
Alhambra Nasrid Palaces. Moreover, only a few authors have depicted the muqarnas using traditional
collaboration
drawings, of and
the only
Council
a fewPatronato
examples are deincluded
la Alhambra
in 19thycentury
Generalife
plans, and the
just as thependentives
ones by Jonesfrom and the
Sala deGoury
la Barca locatedhere.
commented in the Comares palace were finally selected for this paper. This hall is a
prominent Different
rectangular roomgroups
muqarnas used as a precedent
in the monumental space to the
complex Salón
could de Embajadores
be scanned thanks to the (throne
precious room)
collaboration
and supports of the Council
a splendid Patronato de la Alhambra y Generalife and the pendentives from the Sala
lattice dome.
In our study, the 3-D muqarnas palace
de la Barca located in the Comares were finally
construction selected for
comprises this paper.
a difficult This hall issolution
geometric a prominentbecause
rectangular room used as a precedent space to the Salón de Embajadores
the muqarnas elevate from two allegedly orthogonal plans up to the arc of the circle supporting the (throne room) and supports
a splendid lattice dome.
upper dome. There are remarkable graphic references documenting this case: the drawings published
In our study, the 3-D muqarnas construction comprises a difficult geometric solution because
in 1842–1845 by architects Owen Jones and Jules Goury, along with a text explaining the principles
the muqarnas elevate from two allegedly orthogonal plans up to the arc of the circle supporting the
for grouping geometrically
upper dome. the muqarnas.
There are remarkable graphic references documenting this case: the drawings published
Among the bibliographical
in 1842–1845 by architects Owen references
Jones and onJules
the muqarnas,
Goury, alongtwo withmanuscripts on carpentry
a text explaining the principlesfromfor 17th
centurygrouping
should geometrically
be mentioned: thethe ones by Fray Andrés de San Miguel [5] and Diego López de Arenas
muqarnas.
Among the bibliographical
[6]. These authors explain how to geometrically references on build
the muqarnas,
the plantwofrom manuscripts on carpentry
three geometrically from
flat shapes
(Figure17th
1); acentury
rectangleshould withbe ratio
mentioned:
5 to 7 the ones by to
(rounded Fray Andrés
5 root de an
of 2), Sanisosceles
Miguel [5]right
and Diego
triangleLópez de
composed
of two Arenas
cathetus [6]. These authors explain how to geometrically build the plan from three geometrically flat
of 5, and a hypotenuse of 7 (also rounded) and an isosceles triangle with 45° angle
shapes (Figure 1); a rectangle with ratio 5 to 7 (rounded to 5 root of 2), an isosceles right triangle
and longer sides of 5, making possible to combine the last one with an identical symmetrical triangle
composed of two cathetus of 5, and a hypotenuse of 7 (also rounded) and an isosceles triangle with
pivoting on the shortest side. Theoretically, the layout of the muqarnas’ inner angles are reduced to
45◦ angle and longer sides of 5, making possible to combine the last one with an identical symmetrical
four: 45°, 67.5°,pivoting
triangle 90°, and on 135°. Takingside.
the shortest intoTheoretically,
account thatthe muqarnas follow
layout of the the patterns
muqarnas’ produced
inner angles are by
those angles,
reducedittoisfour: possible◦ to identify
45 , 67.5 ◦ , 90 , andwhether
◦ ◦ if they
135 . Taking intoare deformed
account with respect
that muqarnas followto thetheir original
patterns
shape. produced by those angles, it is possible to identify whether if they are deformed with respect to their
original shape.
Figure 1. Proportions and angles of the three basic plan shapes of the muqarnas described by Fray
Andrés de San Miguel and Diego López de Arenas.
Figure 1. Proportions and angles of the three basic plan shapes of the muqarnas described by Fray
AndrésAlong
de Sanwith
Miguel and Diego López de
the above-mentioned Arenas.studies about muqarnas, it should be highlighted
historical
the research works from the architect Enrique Nuere (late 20th century), who graphically analyzed
Along with the
muqarnas’ above-mentioned
component historical
pieces [7]. Nuere´s studies
work was theabout muqarnas,
precursor for newit should
studies be highlighted
based on CAD the
drawings
research works[8–10]
fromconcerning the theoretical
the architect Enriquegeometric
Nuere (lategrouping
20thofcentury),
pieces. Some whoof those studies refer
graphically to
analyzed
wooden muqarnas but other do not indicate the construction material and
muqarnas’ component pieces [7]. Nuere´s work was the precursor for new studies based on CAD only focus on their complex
geometry;
drawings [8–10] all of those studies
concerning took into geometric
the theoretical account thegrouping
deformations we have
of pieces. detected
Some in the
of those plasterrefer
studies
muqarnas of the Alhambra after analyzing the scanner 3-D data in our research.
to wooden muqarnas but other do not indicate the construction material and only focus on their
Considering the vast bibliography about the Alhambra architecture and its graphic
complex geometry; all of those studies took into account the deformations we have detected in the
representations [11] it should be pointed out that the early plans from the Sala de la Barca date
plasterfrom
muqarnas of the
1766, when Alhambra
several surveys after analyzing
of the monument thewere
scanner 3-D data
performed and in ourpublished
then research.in 1787 by
Considering the vast
the Real Academia bibliography
de Bellas Artes de Sanabout
Fernando thein Alhambra
Madrid [12], architecture andtheits
and later, in 1837, graphic
French
representations [11] it should
architect Philibert be Prangey
Girault de pointedreproduced
out that the early
those plansinfrom
surveys the about
his book Sala dethela Barca date
Alhambra [13].from
Both publications
1766, when several surveysincluded a plan
of the and a cross
monument section
were from the Comares
performed and thenpalace,
publishedwherein
it is shown
1787 by that
the Real
the ceiling from the Sala de la Barca was modified in the late half of the 19th century.
Academia de Bellas Artes de San Fernando in Madrid [12], and later, in 1837, the French architect
Philibert Girault de Prangey reproduced those surveys in his book about the Alhambra [13]. Both
publications included a plan and a cross section from the Comares palace, where it is shown that the
ceiling from the Sala de la Barca was modified in the late half of the 19th century.
The drawings of the Alhambra by architects Owen Jones and Jules Goury [14] date from 1834
and 1837 and focus on the elements’ ornamentation, which are even more interesting and significant
Sustainability 2019, 11, 316 3 of 15
The drawings of the Alhambra by architects Owen Jones and Jules Goury [14] date from 1834 and
1837 and focus on the elements’ ornamentation, which are even more interesting and significant than
the ones previously mentioned because their decorative aspect. Jones and Goury did not represent
the horizontal deformations and misalignments existing in the Nasrid palaces when they drew the
distribution plan (Figure 2); they neatly represent in detail the Sala de la Barca setting when they draw
the longitudinal cross section from the Comares palace (Figure 3) [14].
Plate X in volume I published in Goury et al. [14] includes a pendentive schematic diagram
and elevation from the Sala de la Barca (Figure 4). Jones and Goury should have been aware of the
complexity of their muqarnas drawings, and for this reason they attached an explanatory text about
the theoretical grouping process of elemental pieces (in a simplified version). The explanatory text is
the following:
“These pendentives are of a very curious mathematical construction. They are composed of
numerous prisms of plaster, united by their contiguous lateral surfaces, consisting of seven
different forms, proceeding from three primary figures on plan: they are, the right angle
triangle (A), the rectangle (B), and the isosceles triangle (C). In these (a a, a b, a c) are equal;
(b a) is equal to (b b), and the vertical angle of the isosceles triangle (C) is 45◦ . The figure
(B) has one form, in section; the figure (A) three; and figure (C) three; the third (C3) being
Sustainability 2019, 11, 316 3 of 16
a rhomboid, formed by the double isosceles triangle. The curves (x x x) of the several pieces
are similar, by which it will be seen that a piece may be combined with any one of the others
represent the horizontal deformations and misalignments existing in the Nasrid palaces when they
by either of its sides; thus rendering them susceptible of combinations as various as the
drew the distribution plan (Figure 2); they neatly represent in detail the Sala de la Barca setting when
melodies
they draw the which may be cross
longitudinal produced from
section the
from theseven notespalace
Comares of the(Figure
musical scale.”
3) [14].
Figure
Figure 2. 2. “Plan
“Plan ofofthe
theRoyal
RoyalArabian
Arabian Palace
Palace in
in the
the ancient
ancientfortress
fortressofofthe
theAlhambra.”
Alhambra.” Plate 3. Vol
Plate I. I.
3. Vol
Plans,
Plans, elevations,
elevations, sections,and
sections, anddetails
details of
of the
the Alhambra,
Alhambra, from
fromdrawings
drawingstaken onon
taken thethe
spot in 1834
spot by by
in 1834
Jules
Jules Goury,
Goury, and
and in in 1834
1834 and1837
and 1837by
byOwen
OwenJones.
Jones.
Sustainability 2019, 11, 316 4 of 15
Sustainability 2019, 11, 316 4 of 16
Figure 3. “Section through the Court of the Fish Pond, and the Hall of the Ambassadors.” Plate 7. Vol
Figure 3. “Section through the Court of the Fish Pond, and the Hall of the Ambassadors.” Plate 7. Vol I.
I. Plans, elevations, sections, and details of the Alhambra, from drawings taken on the spot in 1834 by
Plans, elevations, sections, and details of the Alhambra, from drawings taken on the spot in 1834 by
Jules Goury, and in 1834 and 1837 by Owen Jones.
Jules Goury, and in 1834 and 1837 by Owen Jones.
Plate X in volume I published in Goury et al. [14] includes a pendentive schematic diagram and
elevation from the Sala de la Barca (Figure 4). Jones and Goury should have been aware of the
complexity of their muqarnas drawings, and for this reason they attached an explanatory text about
the theoretical grouping process of elemental pieces (in a simplified version). The explanatory text is
the following:
“These pendentives are of a very curious mathematical construction. They are
composed of numerous prisms of plaster, united by their contiguous lateral surfaces,
consisting of seven different forms, proceeding from three primary figures on plan: they
are, the right angle triangle (A), the rectangle (B), and the isosceles triangle (C). In these (a
a, a b, a c) are equal; (b a) is equal to (b b), and the vertical angle of the isosceles triangle (C)
is 45°. The figure (B) has one form, in section; the figure (A) three; and figure (C) three; the
third (C3) being a rhomboid, formed by the double isosceles triangle. The curves (x x x) of
the several pieces are similar, by which it will be seen that a piece may be combined with
any one of the others by either of its sides; thus rendering them susceptible of combinations
Sustainability 2019, 11, 316
as various as the melodies which may be produced from the seven notes of the musical 5 of 15
scale.”
Figure
Figure 4. 4. “Details
“Details ofofthe
thegreat
greatarches
archesof
of the
the Hall
Hall of
ofthe
theBark.”
Bark.”Plate
Plate11.11.
Vol I. Plans,
Vol elevations,
I. Plans, sections,
elevations, sections,
and details of the Alhambra, from drawings taken on the spot in 1834 by Jules Goury,
and details of the Alhambra, from drawings taken on the spot in 1834 by Jules Goury, and in 1834 and in 1834 andand
1837 by Owen
1837 by Owen Jones. Jones.
Together
Together withthe
with theprevious
previoustext,
text, Jones
Jones and
and Goury
Goury provided
providedboth
botha aschematic diagram
schematic diagramandand
elevation
elevation drawings from the three basic shapes (triangles and rectangles), the seven muqarnas
drawings from the three basic shapes (triangles and rectangles), the seven muqarnas 6pieces, pieces,
Sustainability 2019, 11, 316 of 16
and primary combinationsamong
and primary combinations amongthemthem(Figure
(Figure 5).
5).
(a) (b)
FigureFigure 5. “Details
5. “Details of the
of the great
great arches.Hall
arches. Hallof
ofthe
the Bark.”
Bark.” Plate
Plate10.
10.Vol I. Plans,
Vol elevations,
I. Plans, sections,
elevations, and
sections,
details of the Alhambra, from drawings taken on the spot in 1834 by Jules Goury,
and details of the Alhambra, from drawings taken on the spot in 1834 by Jules Goury, and in 1834 andand in 1834 and
1837
1837 by by Owen
Owen Jones.
Jones. (a) Seven
(a) Seven basic
basic muqarnas
muqarnas pieces
pieces from
from three
three basicplanar
basic planarshapes.
shapes. (b)
(b) Plan
Plan and
and
elevation of a pendentive containing the seven prisms in
elevation of a pendentive containing the seven prisms in combination.combination.
In 1837, the Pisani brothers made some plaster molds from the Patio de los Leones [15], and
followed that formula or “recipe.” Rafael Contreras (Alhambra curator and decorator) built and
replaced a lot of ornaments using plaster since half 19th century.
It must be taken into account that on September 16, 1890, the Sala de la Barca was damaged by
an aggressive fire that destroyed the dome, according the press of that time (Figure 6a) [16].
(a) (b)
Figure 5. “Details of the great arches. Hall of the Bark.” Plate 10. Vol I. Plans, elevations, sections, and
details of the Alhambra, from drawings taken on the spot in 1834 by Jules Goury, and in 1834 and
Sustainability
1837 by 11,
2019, 316 Jones. (a) Seven basic muqarnas pieces from three basic planar shapes. (b) Plan and 6 of 15
Owen
elevation of a pendentive containing the seven prisms in combination.
In 1837,
In 1837,thethePisani
Pisanibrothers
brothers made someplaster
made some plaster molds
molds fromfrom
the the
PatioPatio
de losdeLeones
los Leones [15],
[15], and
andfollowed
followedthat thatformula
formula or “recipe.” Rafael Contreras (Alhambra curator and
or “recipe.” Rafael Contreras (Alhambra curator and decorator) built and decorator) built
andreplaced
replaceda alotlotofofornaments
ornaments using
using plaster
plaster since
since halfhalf
19th19th century.
century.
It must be taken
It must be takenintointo
account
accountthat onon
that September
September 16,16,
1890,
1890,the Sala
the SaladedelalaBarca
Barcawas
wasdamaged
damagedby byan
aggressive fire that destroyed the dome, according the press of that time (Figure
an aggressive fire that destroyed the dome, according the press of that time (Figure 6a) [16]. 6a) [16]. Nevertheless,
the Nevertheless, the photosof
photos and drawings and
thedrawings
fire eventof the fire event
showed that showed that the pendentives
the pendentives did not
did not suffer suffer
significant
significant
damage (Figure damage
6b). The(Figure 6b). The reconstruction
reconstruction of the currentofwood
the current
domewood dome was accomplished
was accomplished by the teambyled
the team
by José led by
Romera, José1960
circa Romera,
[17]. circa 1960 [17].
(a) (b)
Figure
Figure 6. Cover
6. (a) (a) Cover page
page of the
of the Universo
Universo Ilustrado
Ilustrado magazine.
magazine. (b)Picture
(b) Pictureshowing
showingthe
thefire
fireininthe
theSala
Salade
de la Barca,
la Barca, 1890. 1890.
2. Materials and Methods. Data Capture and Analysis
The unpublished graphic representations from the Sala de la Barca displayed in this paper have
originated starting from the data captured by a BLK360 laser scanner (Leica, Heerbrugg, Switzerland),
with an accuracy of 6 mm at a 10-m distance and 8 mm at 20 m. The complete point cloud was
levelled using a total station Leica TS02 (Leica, Heerbrugg, Switzerland) with 3” angular accuracy and
1.5 mm ± 2 ppm distance accuracy. The scanning process focused on the muqarnas area, although in
every scan, station data of the complete 360◦ volume were also registered. For this reason, every scan
displays floors, walls, decorations, pillars, columns, and doors. Simultaneously, to every scan we took
HDR (high definition resolution) pictures with the scanner cameras [18].
The scanner can be set to several densities for the point cloud: low, mean, and high, corresponding
to point resolutions of 20 mm, 10 mm, and 5 mm, respectively, considering a plane perpendicular to
the laser beam at a distance of 10 m. This study used average quality in all scans.
The registration process consisted of referencing all the point clouds to the same reference system,
such that homologous points (those points that belonging to different point clouds represent the same
point) match each other; for this task Recap Pro 4.0 (Autodesk, San Rafael, USA) was used. There exists
a Recap version for running on an iPad, such that the registration was performed automatically
when some constraints were satisfied, or manually in other cases (scarce overlapping, noise caused
by distorting elements, e.g., tourists walking around the scanned area). In the study, most of the
scans were manually registered because most of them showed images of tourists. Another reason for
perpendicular to the laser beam at a distance of 10 m. This study used average quality in all scans.
The registration process consisted of referencing all the point clouds to the same reference
system, such that homologous points (those points that belonging to different point clouds represent
the same point) match each other; for this task Recap Pro 4.0 (Autodesk, San Rafael, USA)was used.
There exists
Sustainability a Recap
2019, 11, 316 version for running on an iPad, such that the registration was performed 7 of 15
automatically when some constraints were satisfied, or manually in other cases (scarce overlapping,
noise caused by distorting elements, e.g., tourists walking around the scanned area). In the study,
manually
most of registration
the scans were was the limited
manually timebecause
registered we hadmostfor accessing the Alhambra,
of them showed images of so that the
tourists. priority
Another
wasreason
to take as many scans as possible.
for manually registration was the limited time we had for accessing the Alhambra, so that the
Figurewas
priority 7 shows
to takeanasexample
many scans of point cloud registration: the left image shows the scans already
as possible.
registered,
Figureand7 the right
shows anshows
example a scan about
of point to beregistration:
cloud registered (StR).
the leftThe image
image on the
shows the left corresponds
scans already
to the reference scan (RS). The panoramic images of RS and StR had common areas
registered, and the right shows a scan about to be registered (StR). The image on the left corresponds where we could
to the homologous
identify reference scanpoints.
(RS). The panoramic
Three images points
homologous of RS andwereStRselected
had common
(each areas where wepoint
homologous couldhad
theidentify
same color homologous
in RS and points.
StR) Three homologous
and Recap computed points
thewere selected (each
transformation homologous
matrix point had
of an approximated
StRthe same color
register usinginthose
RS and StR)
three and Recap computed
homologous points. The thesoftware
transformation
providedmatrix of an approximated
a graphic indicator about
StR register using those three homologous points. The software
the quality achieved by the approximated registration process: the right image in provided a graphic indicator
Figure about
7 shows
the quality
a grayscale achieved
circle with by
an the approximated
inner circumference; registration process: the color
the circumference right image
can beingreen,
Figureyellow,
7 showsorared
grayscale circle with an inner circumference; the circumference color can be green, yellow, or red
indicating that the approximated registration was good, suitable, or bad, respectively. If we accept the
indicating that the approximated registration was good, suitable, or bad, respectively. If we accept
approximated registration Recap proceeded to refine the adjustment using an iterative closest point
the approximated registration Recap proceeded to refine the adjustment using an iterative closest
(ICP) algorithm: some examples from ICP can be found in Sharp et al. [19] and Pormelau et al. [20].
point (ICP) algorithm: some examples from ICP can be found in Sharp et al. [19] and Pormelau et al.
Figure 8 shows the instant of ICP refinement of Recap after accepting the approximated registration
[20]. Figure 8 shows the instant of ICP refinement of Recap after accepting the approximated
(right upper corner).
registration (right upper corner).
Figure
316 7.7.Manual
Sustainability 2019,Figure
11, Manualregistration
registration process
process (identification
(identificationofofhomologous
homologouspoints).
points). 8 of 16
Figure8.8.Refinement
Figure Refinement registration
registration for
for aaStR
StRusing
usingan
anICP
ICPalgorithm.
algorithm.
Three
Three indicesdescribed
indices describedthe
theregistration
registration quality
quality as
asaapercentage.
percentage.The The indices areare
indices thethe
following:
following:
1) overlapping indicates the area percentage of StR shared by the RS; 2) balance
(1) overlapping indicates the area percentage of StR shared by the RS; (2) balance is a measure is a measure thatthat
encodes
encodes thethe relativeamount
relative amountofofthe
thedata
data in
in three
three orthonormal
orthonormal directions,
directions,indicating
indicatinghow
how much
muchStRStR
registration has been constrained in the three orthogonal directions; and 3) error
Figure 8. Refinement registration for a StR using an ICP algorithm.
Three indices described the registration quality as a percentage. The indices are the following:
Sustainability 2019, 11, 316 8 of 15
1) overlapping indicates the area percentage of StR shared by the RS; 2) balance is a measure that
encodes the relative amount of the data in three orthonormal directions, indicating how much StR
registration
points has been
percentage in theconstrained in thethe
StR that match three orthogonalless
SF separated directions; and Table
than 6 mm. 3) error
Recap software (Figure 10); 2) plans, elevations, and sections were derived from the point cloud using
CloudCompare software; and 3) key points were identified on plans projections and simplified
drawings have been delineated based on them, where the bounds of muqarnas groups and the main
inner axis have been detected. The starting and ending that defined different levels have been located
over sections and elevations, and when necessary, we drew the vertical in order to measure distances
Sustainability 2019, 11, 316 9 of 15
and angles.
(a) (b)
Figure 10. Point clouds in AutoDesk Recap software cleaned of unwanted noise: (a) Sala de la Barca;
and (b) east
Sustainability pendentives
2019, 11, 316 of the Sala de la Barca. 10 of 16
Figure 10. Point clouds in AutoDesk Recap software cleaned of unwanted noise: (a) Sala de la Barca;
3. Results: Muqarnas
and (b)
3. Results: Muqarnas Pendentives
east pendentives Deformations
of the Sala
Pendentives de la Barca.
Deformations
From our own photographs (Figure 11) we observed some differences between northern and
FromLater,
eastern
we compared
our own
pendentivesphotographsthe (Figure
above-mentioned
in the Sala de la Barca,
information
11) we although
observed some with the theoretical
differences
they are between
symmetric
geometric model.
northerntheir
considering and We
eastern
typology.
used the bound for dimensioning the set and we based them on photographs for drawing
pendentives in the Sala de la Barca, although they are symmetric considering their typology. a schematic
plan for the muqarnas set in order to check their geometry, hypothetical inconsistences, and axis and
angles deformations. Finally, the plan geometry, including distances and angles to confirm the
detected deformations, was analyzed.
Figure11.
Figure 11.Photographs
Photographsfrom
from the
the NE pendentive
pendentiveininthe
theSala
Saladedelala
Barca.
Barca.
TheThe
drawing
drawing from
fromJones
Jonesand
andGoury
Goury matches
matches thethe north-eastern
north-easternside, side,closer
closerto to
thethe Comares
Comares Room;
Room;
thisthis drawing
drawing showsthat
shows thatplan
planand
andelevation
elevation geometrically
geometrically matchmatcheach eachother
otherandand also thethe
also matching
matching
occurs
occurs between
between thethe drawpieces
draw piecesand
andthe
thereal
realones.
ones.
Nevertheless,
Nevertheless, wewehave
havedetected
detecteddiscrepancies
discrepancies between
betweenthe theJones
Jonesand andGoury
Goury text and
text their
and plan
their plan
drawing. According the muqarnas grouping rules, defined by the mentioned
drawing. According the muqarnas grouping rules, defined by the mentioned architects, every piece architects, every piece
should
should havehavethethe same
same module,nevertheless
module, nevertheless their
their drawing
drawing showsshowsthe theinner
innerpieces
pieces areare
smaller
smallerthat thethe
that
outer ones; the pieces deformations increase when they are closer to the upper bound circumference
outer ones; the pieces deformations increase when they are closer to the upper bound circumference
and the triangles become all unequal and stretched.
and the triangles become all unequal and stretched.
Comparing the above-mentioned drawing inconsistencies with current photos we observed that
Comparing the above-mentioned drawing inconsistencies with current photos we observed
the drawing was not wrong, i.e., the drawing deformations seem to match to the real ones. After
that the drawing was not wrong, i.e., the drawing deformations seem to match to the real ones.
analyzing the Jones’s drawings, we established a starting hypothesis in order to interpret our own
After analyzing
drawings: the the Jones’swere
muqarnas drawings,
deformedwe established a startingto
from their conception hypothesis in order To
their construction. to interpret
verify ourour
own drawings: the muqarnas were deformed from their conception to their
hypothesis, we identified the muqarnas pieces in both the photos and the point cloud, and construction. Toweverify
triedour
hypothesis,
to draw we the identified
ideal planthefollowing
muqarnasthe pieces in bothgrouping
geometric the photos and (Figure
rules the point 12)cloud, and the
without we tried
real to
draw the ideal plan
deformations following
existing in the the
room.geometric
We observegrouping rulesthe
that fitting (Figure
pieces12)
is without the real
an impossible deformations
task: in some
existing
pointsinthere
the room. We observe
are coincident that
pieces fitting
with boththe pieces is anand
overlapping impossible
hole angles task:
as in someinpoints
shown there
Figure 12;are
coincident
Figure 13pieces
marked with both
with redoverlapping and hole
and green circles, angles asthis
respectively; shownmeans in Figures
that it is12 and 13 marked
necessary to deform with
redsuch
and pieces
green to avoidrespectively;
circles, both the overlapping
this meansandthat
holes,
it isshaded by red
necessary to and green
deform areas,
such respectively,
pieces to avoid in both
theFigure 12; Figure
overlapping and 13.
holes, shaded by red and green areas, respectively, in Figures 12 and 13.
It was proved that it is impossible build the upper levels because there was no room, and
considering the horizontal dimension, the pieces would overlap. The pendentive seemed to keep
strict geometric rules; nevertheless, the Nasrid constructors designed deformed pieces to match with
the arch supporting the wood frame. The constructors even included filling volumes, which were
difficult to see.
Sustainability 2019, 11, 316 10 of 15
Sustainability 2019, 11, 316 11 of 16
Figure 12. Eastern pendentive in Sala de la Barca. Drawing and study of an ideal plan.
The transition circumference between the pendentive and the dome arc requires a detailed
study. There are three ways to trace the arc: 1) an outer arc with radius up to the bisectors intersection
from the corners to the inner of muqarnas and that cross the manifold adarajas (this solution deforms
the muqarnas); 2) an inner arc touching four points in the muqarnas set that would consequently
stretch the muqarnas; and 3) an intermediate arc with a 2.14 m radius shown in Figure 13 where we
can see irregular areas: in the blue areas the muqarnas should be compressed to match the arc, and
in the green areas,
Figure 12. the muqarnas
Eastern should
pendentive in be stretched
Sala to fill
de la Barca. the holes
Drawing andand achieve
study of an the arc.
ideal plan.
Figure 12. Eastern pendentive in Sala de la Barca. Drawing and study of an ideal plan.
The transition circumference between the pendentive and the dome arc requires a detailed
study. There are three ways to trace the arc: 1) an outer arc with radius up to the bisectors intersection
from the corners to the inner of muqarnas and that cross the manifold adarajas (this solution deforms
the muqarnas); 2) an inner arc touching four points in the muqarnas set that would consequently
stretch the muqarnas; and 3) an intermediate arc with a 2.14 m radius shown in Figure 13 where we
can see irregular areas: in the blue areas the muqarnas should be compressed to match the arc, and
in the green areas, the muqarnas should be stretched to fill the holes and achieve the arc.
Figure
Figure 13.13. Easternpendentive
Eastern pendentive in
in Sala
Sala de
de la
la Barca.
Barca. Drawing
Drawingdetail
detailofofopen
openand overlapping
and areas.
overlapping areas.
Overlapping between ideal pieces (red), open areas until the circle (green), and pieces overstepping
Overlapping between ideal pieces (red), open areas until the circle (green), and pieces overstepping the
arcthe arc (blue).
(blue).
It From this drawing,
was proved that derived from the laser
it is impossible buildscanner (Figurelevels
the upper 14), it because
was observed
therethat
wastheno
angle
room,
between northern and eastern façades was 88°, almost orthogonal; while the angle
and considering the horizontal dimension, the pieces would overlap. The pendentive seemed between the to
southern and eastern facades was 95°.
keep strict geometric rules; nevertheless, the Nasrid constructors designed deformed pieces to match
with the arch supporting the wood frame. The constructors even included filling volumes, which were
difficult to see.
Figure 13. Eastern pendentive in Sala de la Barca. Drawing detail of open and overlapping areas.
The transition circumference between the pendentive and the dome arc requires a detailed study.
Overlapping between ideal pieces (red), open areas until the circle (green), and pieces overstepping
There are three ways to trace the arc: (1) an outer arc with radius up to the bisectors intersection from
the arc (blue).
the corners to the inner of muqarnas and that cross the manifold adarajas (this solution deforms the
muqarnas);
From(2) andrawing,
this inner arcderived
touching fourthe
from points
laser in the muqarnas
scanner set that
(Figure 14), it waswould consequently
observed stretch
that the angle
thebetween
muqarnas; and (3)and
northern an intermediate
eastern façadesarcwas
with88°,
a 2.14 m radius
almost shownwhile
orthogonal; in Figure 13 where
the angle we can
between thesee
irregular areas:
southern in the blue
and eastern areas
facades wasthe muqarnas should be compressed to match the arc, and in the
95°.
green areas, the muqarnas should be stretched to fill the holes and achieve the arc.
From this drawing, derived from the laser scanner (Figure 14), it was observed that the angle
between northern and eastern façades was 88◦ , almost orthogonal; while the angle between the
southern and eastern facades was 95◦ .Sustainability 2019,
Sustainability 11, 11,
2019, 316316 11 16
12 of of 15
Figure 14. Eastern pendentive in Sala de la Barca. Plan projection from the point cloud.
Figure 14. Eastern pendentive in Sala de la Barca. Plan projection from the point cloud.
We also detected that the upper arc, where the pendentives end up, was not a sole arc. The point
where bothWe also detected that
pendentives the upper
assemble wasarc,
notwhere
in thethe hallpendentives
center; it wasendlocated
up, was216
notcm
a sole arc.the
from Thenorthern
point
where both pendentives assemble was not in the hall center; it was located
wall and 226 cm from the eastern one (Figure 14); for this reason both pendentives were inscribed 216 cm from the northern
wall and 226 cm from the eastern one (Figure 14); for this reason both pendentives were inscribed
inside arcs with different radius: the southern pendentive had a 265 cm radius and its center was
inside arcs with different radius: the southern pendentive had a 265 cm radius and its center was
displaced 53 cm from the ideal place; and the norther pendentive had a 187 cm radius and its center
displaced 53 cm from the ideal place; and the norther pendentive had a 187 cm radius and its center
was displaced 29 cm.
was displaced 29 cm.
The explanations given in the previous paragraphs confirm that the NE pendentive drawn by
The explanations given in the previous paragraphs confirm that the NE pendentive drawn by
Jones and and
Jones Goury was designed
Goury was designed with deformation
with deformation and the and northern pendentive
the northern muqarnas
pendentive were different
muqarnas were
from the southern one. The plan in Figure 14 shows the northern pendentive
different from the southern one. The plan in Figure 14 shows the northern pendentive compressed compressed inside an 88◦
angle withanside
inside 88° dimensions
angle with side of 220 and 216ofcm;
dimensions 220theandsouthern
216 cm; the pendentive was stretched
southern pendentive wasinside a 95◦
stretched
angle witha side
inside dimensions
95° angle with sideof dimensions
226 and 229ofcm. 226Both pendentives
and 229 were different
cm. Both pendentives because
were their
different contour
because
angles
theirand dimensions
contour angles andanddimensions
consequently andtheir deformations
consequently were also different.
their deformations were also different.
Finally, a cross-section
Finally, a cross-section of thehall
of the hallshowing
showing certain
certain deformations
deformations was elaborated.
was elaborated. Figure 15Figure
shows 15
marks
shows of the
marks of starting points
the starting for each
points for muqarnas
each muqarnas level with
levela with
line connecting their lower
a line connecting theirparts.
lowerThus,
parts.
horizontal lines were used as references for measuring the heights. The
Thus, horizontal lines were used as references for measuring the heights. The pendentives were pendentives were composed
of 11 levels,
composed of 11each level
levels, eachwas close
level wasto close
15 cmtoheight,
15 cm and the and
height, totalthe
pendentive height was
total pendentive 164 cm
height wasin164
thecm
northern
in the northernside. Comparing
side. Comparing thethereference
referencelines andand
lines realreal
construction,
construction,wewe observe
observe that thethe
that vertical
vertical
displacement
displacement ranged
ranged from
from 1313 toto1515cm.
cm.AAhypothetical
hypothetical explanation
explanation isisthe
thesubsidence
subsidenceofofthe thenorthern
northern
wall that was closer to the extremely overweight Comares tower (Figure
wall that was closer to the extremely overweight Comares tower (Figure 3) while the southern 3) while the southern wall
wall
supports the frame weight.
supports the frame weight.Sustainability 2019, 11, 316
Sustainability 2019, 11, 316
12 of 15
13 of 16
Figure 15.15.Eastern
Figure Easternpendentives
pendentives of
of the Sala de
the Sala de la
laBarca.
Barca.Elevation
Elevationprojection
projection from
from thethe point
point cloud.
cloud.
4. Discussion
4. Discussion
It is very
It is verycomplex
complextotoexplain
explainwhywhythethemuqarnas
muqarnassetssets in
in the
the Alhambra
Alhambra were were deformed
deformedaccording
according to
thetoJones and Goury
the Jones drawings,
and Goury as well
drawings, as as theasones
well produced
the ones producedin this
instudy. It must
this study. be taken
It must into account
be taken into
that the plaster pieces from the 16th century suffered a lot of interventions:
account that the plaster pieces from the 16th century suffered a lot of interventions: fixing, fixing, consolidation,
or consolidation,
restoration that or were not technically
restoration documented.
that were not technically documented.
AA suitable
suitableexplanation
explanationcould
could bebe that
that muqarnas
muqarnas wereweredesigned
designedintentionally
intentionally withwith deformations
deformations
before
beforetheir construction.
their construction. The
The Nasrid craftsmenwho
Nasrid craftsmen whobuilt
builtthetheSala
Saladedela la Barca
Barca pendentives
pendentives hadhad
to to
adapt the muqarnas geometry to the circumference arc supporting the upper
adapt the muqarnas geometry to the circumference arc supporting the upper dome. The craftsmen dome. The craftsmen
would
would have
have probablydeformed
probably deformed thethe muqarnas
muqarnas pieces
piecesas
asharmoniously
harmoniously asaspossible
possiblein order to solve
in order to solve
this
this problem.
problem.
Deformationscould
Deformations could also
also be
be motivated
motivated by by constructive
constructivehorizontal
horizontaldisplacement.
displacement. Along
Alongthe the
centuries the Alhambra suffered fires, explosions, earthquakes, or degradations
centuries the Alhambra suffered fires, explosions, earthquakes, or degradations because of maintenance because of
maintenance deficiencies [21]. These events caused slight displacements in the walls supporting the
deficiencies [21]. These events caused slight displacements in the walls supporting the pendentives.
pendentives. The consequence was that some fissures, breaks, and loss of parts took place because
The consequence was that some fissures, breaks, and loss of parts took place because the plaster
the plaster is a fragile material [22]. Those interventions would use plaster filling to strengthen the
is a fragile material [22]. Those interventions would use plaster filling to strengthen the muqarnas
muqarnas consolidating their distortions.
consolidating their distortions.
The vertical deformations could be caused by differential ground subsidence because the
The vertical
different weights deformations
supported by could be caused
the walls; by differential
the consequence ground
would subsidence
be the different because the different
heights observed
weights supported by the walls;
in muqarnas from the same level. the consequence would be the different heights observed in muqarnas
from the same level.
5. Conclusions
5. Conclusions
The current research provides new drawings based on advanced graphics techniques from the
The
21st current
century research
that, provides
for the first new drawings
time, document based oncomplex
the muqarnas advanced graphics
shapes techniques
from the from
14th century in the
21st
thecentury
Alhambrathat,offor the firstIttime,
Granada. does document the muqarnas
not seem necessary complex
to insist on theirshapes from the
importance for 14th century in
the suitable
theconservation
Alhambra of of Granada. It doesmedieval
these remarkable not seemIslamic
necessary
palacesto insist on their the
that overcame importance
centuries for the suitable
despite their
conservation of these remarkable medieval Islamic palaces that overcame the centuries despite their
fragile construction.
We selected a significant model from the Nasrid architecture, the muqarnas pendentives in the
fragile construction.
Sala
Wedeselected
la Barca ainsignificant
the Comares palace,
model close
from thetoNasrid
the Salón de Embajadores.
architecture, Those pendentives
the muqarnas pendentiveshaveina the
remarkable historic documentation we evaluate: the drawings by the architects
Sala de la Barca in the Comares palace, close to the Salón de Embajadores. Those pendentives Jones and Goury andhave
published in 1842–1845, who explained the process for their geometrical composition.
a remarkable historic documentation we evaluate: the drawings by the architects Jones and Goury and
published in 1842–1845, who explained the process for their geometrical composition.Sustainability 2019, 11, 316 13 of 15
Sustainability 2019, 11, 316 14 of 16
We used a laser scanner to capture the muqarnas (Figure 16) and derived our drawings:
We used a laser scanner to capture the muqarnas (Figure 16) and derived our drawings: accurate
accurate plans and elevations that unveiled significant deformations and differences between the real
plans and elevations that unveiled significant deformations and differences between the real
construction and the theoretical schemes of geometrical grouping of muqarnas defined by Jones and
construction and the theoretical schemes of geometrical grouping of muqarnas defined by Jones and
Goury and
Goury thethe
and rest ofofscientific
rest scientificbibliography.
bibliography. Our study isisthe
Our study thefirst
firstone
onethat
that unveil
unveil those
those deformations.
deformations.
Figure16.
Figure 16.Pendentives
Pendentives in
in the Sala
Sala de
de lalaBarca
Barca(point
(pointcloud).
cloud).
Figure
Figures 12 12;
and 13Figure
reveal 13that
reveal
it isthat it is impossible
impossible to buildtothe
build the pendentives
pendentives using the using the method
method described
described by Jones and Goury. Both architects’ drawings contradict some
by Jones and Goury. Both architects’ drawings contradict some pieces (Figure 4) that do not match pieces (Figure 4) that do
not match either their theoretical definition, nor the reality captured
either their theoretical definition, nor the reality captured by the 3-D laser scanner. by the 3-D laser scanner.
Figure
Figure 1414shows
showsthat that the
the pendentives
pendentivesinin thethe
SalaSala
de la
deBarca are supported
la Barca are supportedby walls bythat werethat
walls
not orthogonal, such that the northeastern construction was different
were not orthogonal, such that the northeastern construction was different to the southeastern to the southeastern one. Thatone.
un-orthogonality would force the Nasrid craftsmen made designs that did not match the usual
That un-orthogonality would force the Nasrid craftsmen made designs that did not match the usual
geometric process described in the muqarnas bibliography. The most uncertain and deformed area
geometric process described in the muqarnas bibliography. The most uncertain and deformed area of
of the pendentive was found in the upper part caused when the craftsmen tried to adapt the
the pendentive was found in the upper part caused when the craftsmen tried to adapt the muqarnas
muqarnas pieces to the circumference supporting the dome.
pieces to the circumference supporting the dome.
Figure 15 shows that the muqarnas levels were not horizontal and those in northern facade were
theFigure
lowest,15 shows
being athat the muqarnas
possible cause forlevels were notsubsidence
the ground horizontalbecause
and those thisinwall
northern facadethe
supported were
theComares’
lowest, being a possible cause
tower weight for centuries. for the ground subsidence because this wall supported the Comares’
tower weight
It shouldfor becenturies.
taken into account that the Alhambra complex has suffered big earthquakes and
It should
fires, and the beresultant
taken into account restorations
muqarnas that the Alhambra complex has
or reconstructions suffered
would big earthquakes
be limited and fires,
to fill the plaster
andfissures
the resultant muqarnas restorations or reconstructions would be limited
with the same material that would consolidate the produced deformations. Despite those to fill the plaster fissures
with the same
disasters material
it is amazing that would
that consolidate
muqarnas the produced
construction, made ofdeformations.
such a fragileDespite
material, those
hasdisasters
providedit is
amazing that muqarnas
their sustainable construction,
conservation along the made of such a fragile material, has provided their sustainable
centuries.
Finally,
conservation it is part
along the of the goal of this paper that the accurate images created along this research are
centuries.
useful documentation
Finally, it is part of the to provide a reliable
goal of this paperaccount
thatand
thetestimony
accurate of the complex
images created shapes
along ofthis
muqarnas
research
are useful documentation to provide a reliable account and testimony of the complexforshapes
and their deformations, unknown until now. Our images can be very useful not only other of
researchers
muqarnas andbut alsodeformations,
their for an increasing tourism that
unknown untildemands
now. Ourmore knowledge
images can beabout
verythe monument.
useful not only
In this respect, it should be highlighted that the Alhambra in Granada
for other researchers but also for an increasing tourism that demands more knowledge about theis nowadays part of the World
Heritage, and it is visited by around two and a half million tourists every year.
monument. In this respect, it should be highlighted that the Alhambra in Granada is nowadays part of
theAuthor
WorldContributions:
Heritage, andI. F. P.-B.,
it is A. G.-G.
visited by and J. F. R.-G.
around two took
and part in the
a half entiretourists
million researching process.
every year.
Funding: This research received no external funding.Sustainability 2019, 11, 316 14 of 15
Author Contributions: I.F.P.-B., A.G.-G. and J.F.R.-G. took part in the entire researching process.
Funding: This research received no external funding.
Acknowledgments: The present research has been made possible thanks to the collaboration of the specialized
group of research and dissemination of the Council Patronato de la Alhambra y Generalife as well as the dedicated
personnel that surveils the monument day after day. The authors thank the support from the research group
Expregrafica. Lugar Arquitectura y Dibujo (PAIDI-HUM-976), Programa de Doctorado en Arquitectura, Instituto
Universitario de Arquitectura y Ciencias de la Construcción from Universidad de Sevilla; and the research group
Ingeniería Cartográfica (PAIDI-TEP-164) from Universidad de Jaén.
Conflicts of Interest: The authors declare no conflict of interest.
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