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Cathédrales en guerre XVIe-XXIe siècle

 | 
Xavier Boniface
, 
Louise Dessaivre

Destructions

E-Cathédrale: numérisation de la cathédrale d’Amiens et reconstitution des trajectoires balistiques de l’artillerie allemande en avril 1918

Fabio Morbidi et El Mustapha Mouaddib

Texte intégral

Acknowledgements: The authors would like to thank L. Dessaivre-Audelin, director of the library of the Université de Picardie Jules Verne (UPJV), and A. André, archivist at Amiens Diocese, for their generous assistance in the research of the documents concerning the bombardment of Amiens during WWI. The authors are also grateful to P. Nivet and X. Boniface, professors of modern history at the UPJV, and to É. Hamon, professor of art history at the University Lille, for useful discussions.

Introduction

Motivation and related work

1As reported in the bronze inscription set around the central marble plaque of the labyrinth in the nave floor [1, Note 7], the construction of the cathedral of Notre-Dame of Amiens started in 1220 and was completed by 1269, surviving a fire in 1258, which damaged the walls of the unfinished church, setting construction back. According to the same medieval-French inscription, the cathedral was built by three master masons: Robert de Luzarches, followed by Thomas de Cormont (possibly his former companion and lieutenant) and his son Regnault [2]. In art history books, Amiens Cathedral is often referred to as an archetype of Gothic architecture in France [3] for its great stylistic unity due to the relatively short construction period (see Fig. 1(a)). According to the renowned nineteenth-century architect E. Viollet-le-Duc, it is pre-eminently an “ogival church”.

Fig. 1. (a) West front of Amiens Cathedral as appeared in March 2016; (b) Corresponding view of the 3-D digital model developed in the e-Cathedral program.

Fig. 1. (a) West front of Amiens Cathedral as appeared in March 2016; (b) Corresponding view of the 3-D digital model developed in the e-Cathedral program.

2The tallest complete cathedral in France, the internal height of the nave reaches 42.3m (surpassed only by the incomplete Beauvais Cathedral at 48.5m): it also has the greatest interior volume of any French cathedral, estimated at 200,000m3 (almost double the volume of Notre-Dame of Paris). The height of the spire of the church is 112.7m, the length of the longitudinal axis is 145m, the length of the transept is 70m, and the width of the nave is 14.6m, for a total area of 7700 m². Amiens Cathedral is recognized as a historical monument since 1862, and it has been listed as a Unesco World Heritage Site since 1981. The church had an average of 734,000 visitors per year in 2002-2009. A wealth of research works have been dedicated by art historians to Amiens Cathedral in the last century: see, for example, the authoritative monograph of G. Durand [4], and more recently [5], [6] for a geometric analysis of plan and spaces, and for the study of the openwork flying buttresses, respectively. In line with the increasing public awareness about cultural heritage preservation, work in this area has accelerated and the cathedral has lately attracted the attention of the scientific community at large. For instance, the authors in [7] have studied the structural strength of the cathedral against lateral wind, while in [8] a chemical corrosion analysis of the iron chain surrounding the triforium of the church (a reinforcement installed in 1497 to avoid the collapsing of the transept cross pillars) has been carried out. In the last decade, the digital technologies at the service of cultural heritage have reached a sufficient level of maturity to experience a large diffusion in architectural archeology, structural engineering and art history. In particular, 3-D modeling from laser data (lasergrammetry) or from aerial views of a site of interest (photogrammetry), is increasingly used for digital heritage [9]-[11]. Some notable examples include the Great Buddha [12] and the Bayon Digital Archival [13] projects. Other initiatives, such as CyARK [14] (a non-profit international organization founded in 2003) has the “mission of using new technologies to create a free, 3-D online library of the world’s cultural heritage sites before they are lost to natural disasters, destroyed by human aggression or ravaged by the passage of time”. As such, properly speaking, CyARK is not a research project, but a 3-D model production project. As far as the 3-D reconstruction problem is concerned, the digital modeling of large-scale environments, such open-air archeological sites [15], [16] or even entire cities [17] has met with increasing success in the last few years [18], as also witnessed by some ambitious research projects carried out in South Korea [19] or in France by the Institut Géographique National (IGN) and by the French Ministry of Culture and Communication [20]. Other recent research relevant to this work, is [21] and [22]. In the former, the authors digitally reconstructed the temple of Bel, one of the Syrian heritage monuments, which was destroyed in September 2015 by Daesh, by either using public domain touristic imagery or by combining it with professional panoramic photos. In [22] a robust and efficient method is proposed to estimate the pose of a virtual camera with respect to complex 3-D textured models of the environment: as a case study, the authors considered the model of the basilica of Sagrada Família in Barcelona, which contains more than 100,000 points.

Original contributions

3The program of digital modeling of Amiens Cathedral, e-Cathedral, is in line with the aforementioned research efforts in the emerging field of digital heritage of large-scale environments. The program, however, has faced unique challenges due to the size of the building, the difficult access to the uppermost parts, the use of heterogeneous measurement devices (laser scanners, perspective and omnidirectional cameras), and the fragility and intricate details of the sculptural elements which populate the interior and exterior. The friable limestone statues of the south and west fronts of the cathedral and the wooden spire require, in fact, continuous maintenance and renovation works because of atmospheric corrosion and air pollution: the need to digitally fix the appearance of the monument at a given monument it time to preserve it, has then become extremely urgent. This called for innovative theoretical and technical tools to guarantee the completeness and uniformity of the optical measurements. Beside the immediate repercussions of e-Cathedral on the study of Gothic sculpture and architecture, the program has also provided fertile ground for basic research in computer vision, 3-D graphics and visualization, and human-machine interfaces. In fact, the joint use of computer-vision tools, historical sources, physical modeling of the gun, and statistical data analysis were instrumental in elucidating the details of 1918 German bombing of Amiens in World War I (WWI).

E-cathedral: objectives and methods

4E-Cathedral is a multidisciplinary 15-year research and development program funded by the French government (Amiens Métropole, DRAC de Picardie, Conseil Régional de Picardie), launched on 18 October 2010. The program consists of two main axes [23]:

  • Creation of a full-scale, accurate digital representation of the interior and exterior of Amiens Cathedral,
  • Exploitation of the model of the cathedral, and design of new human-machine interfaces for displaying the digital content.

5The program relied on different techniques, ranging from lasergrammetry and aerial, terrestrial and close-range photogrammetry, to topography and omnidirectional vision (spherical panoramas). In particular, lasergrammetry, performed with the scanners Leica ScanStation C10 and Faro Focus3D X 130, played a prominent role in the model-building process. Data collection for e-Cathedral took place in six different campaigns: the most important ones were conducted out in 2010, 2011, 2012 and 2013, and resulted from the collaboration of the MIS laboratory, the IGN, the ENSG and Amiens Métropole. Data treatment and scan matching for the first four years of the program ended in May 2014: no campaign was launched in 2015. The last two campaigns, in 2016, were carried out by the members of the MIS laboratory. At the present stage, after the end of the sixth data-collection campaign, the 3-D model of Amiens Cathedral counts about 10 billion colored points (corresponding to 150GB of data using a binary format with three fields: Cartesian coordinates in millimeters, RGB values [0, 255], reflectance [−2048, 2048]) taken from around 300 stations positioned at up to five levels above the ground (the 5th being the base of the spire over the central crossing), see Fig. 1(b). An average of 4 (sphere or disk) artificial targets per station were manually placed in the environment: they were used for correlating the point clouds from each station and fusing them to obtain a single homogeneous model in post-processing. Establishing a connection between the stations inside and outside the church was particularly delicate and time-consuming: in fact, trial-and-error approach was adopted. The measured 3-D point-clouds were colored using photos of the cathedral taken by the cameras integrated in the laser scanners or by hand-held digital cameras, with proprietary or automatic algorithms based on dense image registration developed by our group [25]. The maximum resolution of the 3-D model of the Cathedral is 1mm, in correspondence to the sculptural groups of the portals, with an average resolution between 2mm and 5mm as per program specification. Note that while the angular step of the rotating beam of the scanners can be tuned, we did not have a direct control on the resolution of the measured points (which is also affected by the data-fusion process). Although the variance of the measurement noise of the laser scanners is known, the impact of other sources of uncertainty on model accuracy (such as sunrays randomly reflected by the spinning mirrors of the scanners, laser beam refraction due to atmospheric moisture, temporary occlusion of laser beam by passing pedestrians producing “ghost-like” 3-D artifacts) proved much harder to quantify. Modeling the laser beam propagation through a non-uniform transparent medium (the stained-glass windows of the cathedral), also represents a challenging open problem.

6In the next section, we will describe an application scenario for our 3-D digital model of Amiens Cathedral, which opens new perspectives for historical investigation.

Digital model of Amiens cathedral and WW1 ballistic reconstruction

7In this section, we will leverage the traces of damages (or “scars”) of Amiens Cathedral identifiable in our 3-D digital data and the available historical record (war diaries and photographic documents), to reconstruct the location of German heavy artillery during the 1918 Spring Offensive. To the best of our knowledge, only circumstantial evidence exists on the bombing, and the exact location of the artillery is still a matter of debate among the specialists: our objective will be then to confirm (or disprove) with the modern tools of computer science, some of the hypotheses advanced by the WWI historians. This is not an easy task, because of the fragmentary photographic and written accounts, and the inaccurate (and sometimes conflicting) historical sources on the position and model of the guns used by the German army.

Bombardment of Amiens in spring-summer 1918

8Several international newspapers chronicled the damages caused by the German bombardment to Amiens Cathedral in summer 1918: see, e.g. the June 15, 1918 issue of the The Auckland Star [32] and the August 17, 1918 issue of the The New York Times [33]. However, these Allied Forces’ publications had an evident propagandistic intent to cause popular outrage against German attacks, and provide scarce details about the actual extent of damages. On the contrary, a rich source of documental information about the city of Amiens and its cathedral during WWI, are the book of A. Chatelle [29] and the monograph of G. Héracle-Leroy [34].

Fig. 2. Approximate front line on 5 April 1918 (dashed line) marking the stabilized westward position reached by the German army during the Spring Offensive (figure based on maps in [26]).

Fig. 2. Approximate front line on 5 April 1918 (dashed line) marking the stabilized westward position reached by the German army during the Spring Offensive (figure based on maps in [26]).

According to the historical record, the locations marked in red are the most likely to have harbored the German artillery which damaged Amiens Cathedral.

Table I. List of projectiles that damaged Amiens Cathedral in April 1918 (cf. Fig. 3 and Fig. 4).

  • 1 Chapel XXIII is also known as the Chapel of St. John the Baptist.
  • 2 Chapels IV and VI are also known as the Chapels of St. Christopher and of Our Lady of Faith (or of (...)
Date Hour Impact point Type Damages n° photos
1 April 9, 1918 11:15 a.m. Roof, south side of the choir Shell Roof pierced, but vault undamaged 7 [27]–[29]
2 April 12, 1918 6:30 a.m. Buttress outside chapel XXIII1 Shell Buttress pierced, mullions broken 5 [27], [29], [30]
3 April 12, 1918 About noon South ambulatory in front of chapel XVIII Shell Roof and rib vault pierced, mark on the floor 4 [28]–[30]
4 April 18, 1918 Outside the north choir Shell Flying-buttress and gargoyles damaged 1 [31]
5 April 22, 1918 1:30 p.m. Triforium near the pipe organ Shell Two columns shattered, organ damaged 3 [29], [31]
6 April 22, 1918 2:00 p.m. Buttress between chapel IV and VI2 Shell Roof and chapels damaged 2 [29], [31]
7 April 11, 1918 8:30 a.m. At the foot of the gate surrounding the sacristy, rue Cormont Shell Stone wall and iron gate damaged 2 [29], [31]
8 April 11, 1918 At a distance of 40m in rue Robert de Luzarches Incendiary shell Splinters above the south portal ?
9 April 12, 1918 About noon Square St. Michael, apse of Maccabees Chapel Shell Iron gate and Choirboys Chapel damaged 2 [31]

The last column reports the number of distinct historical photos showing the entity of damages, that we were able to locate in the archives.

Fig. 3. Points of impact (stars) of the German projectiles that damaged Amiens Cathedral in April 1918.

Fig. 3. Points of impact (stars) of the German projectiles that damaged Amiens Cathedral in April 1918.

The stars 1 to 6 refer to the projectiles that struck the fabric of the church, while the stars 7 to 9 indicate those that exploded at a certain distance outside the building (the position of the blue stars on the southeast side is indicative, and not to scale). Plan adapted from [24, Plan II].

9Due to conflicting use of terms in the literature, henceforth projectile will refer to a device designed for ballistic performance: two examples are artillery shells (“obus” in French) fired by cannons, and bombs (“bombes” and “torpilles” in French) dropped by aircraft. It seems that the German airplanes, the “Gothas”, never targeted Amiens Cathedral. Several shells damaged buildings around the church (e.g. a shell fell in rue Robert de Luzarches and set fire to three buildings, only 40m from the south front of the cathedral), which shows that although the church was not a target, its spire served as a reference to German artillery.

Fig. 4. Historical photos of the damages caused to the cathedral by six shells.

Fig. 4. Historical photos of the damages caused to the cathedral by six shells.

(a) Shell 1; (b) Shell 2; (c) Shell 3; (d) Shell 4; (e) Shell 5; (f) Shell 6.

Photo (a) was taken on 28 June 1918, probably from a balcony of Amiens courthouse [27, photo E04918]. Photos (b) and (c) were taken by the Scottish war photographer T.K. Aitken immediately after the events occurred [28]. Photos (d), (f) are available in the digital archive [31].

10The period of intensive bombardment of Amiens in spring-summer 1918, lasted 147 days. The airplanes first attacked the city on March 22, 1918, and bombings stopped on 15 August 1918 at 9:45 pm. The aerial raids lasted 28 days, and 872 bombs were dropped on the city. The bombardment by cannon started on 4 April 1918 and finished on 2 August 1918, for a total of 80 days. Daily bombardments occurred from April 4 to May 23, 1918, and from May 27 to June 23, 1918. The city was shelled by long range guns only on 11 July and on 2 August 1918. The total number of shells fired over Amiens was 11,130. The reported calibers were 130, 150, 210 et 240mm, being 210mm very common (the caliber of a shell corresponds to the internal diameter or bore of the gun barrel). The German artillery which bombarded Amiens was located in five cities: Albert (27.7km as the crow flies, northeast), Villers-Bretonneux (15.7km, south-east), Harbonnières (26.9km, south-east), Marcelcave (20.1km, south-east), and Moreuil (18.8km, south-east), see Fig. 2. It is Moreuil from which the bombardments appeared to be the most active. The Australian 8th Infantry Brigade and Field Company Engineers captured a long-range German railway gun (a Krupp 28cm SK L/40 “Bruno” a.k.a. “Amiens Gun”) east of Harbonnières, about 180m in front of the front line on 8 August 1918 (the 3rd Australian infantry battalion also seized a large long-range fixed gun between Chuignes and Chuignolles on 23 August 1918, that most likely participated or was going to be utilized in the bombardment of Amiens, cf. Fig. 2). Note that the five cities above were all located along important railroads (Paris-Lille junction, Amiens-Laon axis) which likely facilitated the transportation of German heavy artillery. However, only Albert, Villers-Bretonneux and Moreuil had train stations in 1918 (they opened between 1846 and 1883). The bloodiest bombing day was between April 14 (noon) and April 15 (noon) 1918, with 35 people killed and 34 injured. These 24 hours were among the most intense in bombardments, with 400 shells falling on the city [34, p. III-IV]. Starting from 19 April 1918, the population of Amiens was evacuated for four months, and thus, the number of civilian casualties significantly reduced thereafter. Table I reports the list of projectiles that damaged Amiens Cathedral in April 1918, according to the detailed accounts in [29, pp. 193–202, pp. 243–248] and in [34, pp. 1–4]. Six out of the nine projectiles damaged the fabric of the church: their impact points are shown on the plan of the cathedral in Fig. 3 (red stars), and some of the relative historical photos of the damages are reported in Fig. 4. Shell 1 (cf. Table I), which exploded just above the south roof of the choir without damaging the underlying vault, is the most photographically documented, with at least 7 images from different viewpoints. The shell came from southeast. Only for Shell 2, we have photos of the damages inside (4 images) and outside the cathedral (1 image, see Fig. 8(b) [29, pp. 199]). Shell 5 damaged the triforium and the chamber containing the wind system of the pipe organ (which was disassembled by the Paris Fire Brigade only in May-June 1918). Shell 6 struck the buttress separating chapel IV and VI: the thick lead roof of chapel IV was perforated by shrapnel impact (see Fig. 4(f) and Fig. 8(c)) and chapel VI was severely damaged by the 150mm shell. Finally, for Shell 3 there exist rich historical sources and marks in the masonry of the south aisle of the choir, still visible today (see Fig. 4(c) and Fig. 5(a)). According to [29, p. 198]:

« Un obus éventre la plate-forme et la voûte du collatéral Sud à la hauteur de la grille. Le culot pénétra avec violence dans les dalles de marbre du sol, à proximité de la clôture de “Saint-Firmin” et y resta, inoffensif, jusqu’en mars 1919 ».

11Similarly, according to [34, p. 2] (which, however, reports the wrong date of April 9, 1918 at 11:00 a.m.):

« Il traversa la plate-forme en plomb de la couverture des chapelles du déambulatoire, perça la voûte sous un angle de 65° par rapport à l’horizontale, et éclata. Le culot s’enfonça dans le pavement avec une force considérable et n’en fut retiré qu’au mois de mars 1919 ».

12As a memorial, the impact point of the base plate of the shell on the floor of the cathedral was later marked with a cross, as shown in Fig. 5(b).

Fig. 5. (a) Rib-vaulted ceiling of the south ambulatory as it appears today: note that the paler plaster used in the restoration works allows to easily identify the damages caused by Shell 3. (b) Impact point of the base plate of Shell 3 on the marble paving of the south aisle of the choir marked with a cross. To situate the point of impact on the plan of the cathedral, see the black cross in front of Chapel XVIII in Fig. 3.

Fig. 5. (a) Rib-vaulted ceiling of the south ambulatory as it appears today: note that the paler plaster used in the restoration works allows to easily identify the damages caused by Shell 3. (b) Impact point of the base plate of Shell 3 on the marble paving of the south aisle of the choir marked with a cross. To situate the point of impact on the plan of the cathedral, see the black cross in front of Chapel XVIII in Fig. 3.

Photos (a) and (b) were taken by the authors in September 2015.

Determination of the most probable location of German heavy artillery

13In the forthcoming analysis, we will uniquely focus on the first six shells reported in Table I. Note that we do not know whether these shells were all fired by the same gun and whether its position did not change between April 9 and April 22, 1918. However, owing to the short firing time elapsed, Shells 2 and 3, and analogously Shells 5 and 6, most likely originated from the same piece of artillery. Our ballistic reconstruction will only exploit the measurable effects of the shells on the fabric of the cathedral, and will leverage three complementary elements of information:

  1. Physical modeling of the gun,
  2. Line-of-sight image constraint of Shell 3,
  3. Battles of Moreuil Wood and of the Avre.
  • 3 Heavy artillery means that the caliber of the gun is greater or equal to 120mm. German heavy artill (...)

141) Physical modeling of the gun and reconstruction of the trajectory of the projectiles: The documental information relative to the German artillery which fired over Amiens in April 1918 is unfortunately rather sparse and ambiguous. Three options for German heavy artillery3 were considered in this study: i) Krupp 21cm Mörser 16, ii) Krupp 15cm Kanone 16, iii) Krupp 15cm SK L/40 i.R.L.

  • 4 A howitzer is a short gun for firing shells on high trajectories at low velocities: in fact, the ba (...)

15i) The Krupp 21cm Mörser 16 heavy howitzer4 fits well with most of the historical sources [29], [34] (cf. Sect. IIIA and see Fig. 6(a)), as far as the caliber (211mm), years of service (1916-1950) and barrel elevation (−6° to 70°) are concerned. By considering the effect of air drag, the upper values of this elevation interval are consistent with the angle of impact of two documented shells: 60° with respect to the horizontal axis (a shell which penetrated in the foundations of the south wing of Amiens City Hall, few hundred meters from the cathedral, on 17 April 1918, at 1:45 pm [34, p. 5]) and 65° (Shell 3 in Table I). However, the maximum firing range of this howitzer, 11.1km, is incompatible with the distance of the five candidate cities which might have harbored the German artillery: in fact, the closest one, Villers-Bretonneux (which lay on the German front stabilized on 5 April) is about 16km from Amiens, and thus largely out of range.

16ii) The exceptional range length of the Krupp 15cm Kanone 16 (L/43) heavy field gun, over 22km, made it safe from counter-battery fire, unless railway heavy artillery was employed (see Fig. 6(b), (c), (d)). With their high-explosive 150mm shells, they proved particularly efficient during the German 1918 offensive, where they caused significant damages to the Allies headquarters and logistic centers. The mobility of this gun was excellent, and the setting in firing position quick. The weapon had been designed from the beginning for transportation by mechanized tractors in two loads or in a single load. They were delivered to the units from 1917, but they became significantly present on the front from the end of 1917. They demonstrated their superiority against all Allies comparable weapons until the end of the war. For more details on the technical specifications of this gun [35], see Table II.

17iii) During the development of the new 15cm Kanone 16, the only temporary solution consisted in using barrels designed for the Imperial German Navy. This is how the 15cm SK L/40 i.R.L (“SK” = Schnelllade-Kanone = rapid loading gun; “i.R.L.” = in Räder Lafette = on wheeled carriage) was proposed by Krupp on the basis of 15cm Navy guns using a recoil recuperation system mounted on a carriage for land use (Fig. 6(c)-(e)). The stability of this heavy gun and the recoil efforts not totally compensated, made necessary the use of a heavy custom firing platform. The very long barrel allowed to reach impressive distances (18.7km with swallow elevation angles: −8° to 32°), at the detriment of an almost prohibitive weight (the gun plus the platform weighed around 18 tons) that handicapped its mobility. The transportation had to be performed in three heavy separate loads. Appeared as early as the beginning of 1915, and produced up to a total quantity of 150 units, the 15cm SK L/40 i.R.L was gradually replaced from the beginning of 1917 by the new 15cm guns, lighter and easier to transport, and with a longer range (e.g. the 15cm Kanone 16), or by railway heavy artillery such as the Krupp 28cm SK L/40 “Bruno” gun (cf. Sect. III-A). Bruno was originally a naval gun which was adapted for land service after its ships were disarmed beginning in 1916 [36], and it could shoot targets up to 27.75km with an elevation angle between 0° and 45°. In conclusion, the Krupp 15cm Kanone 16 appears to be the gun that best fits with the historical documents on the bombardment of Amiens Cathedral in terms of ballistic range, caliber, and mobility, and its technical specifications will be then used in the sequel to reconstruct the trajectory of a hypothetical shell fired by the German artillery. Note that this choice automatically makes Albert and Harbonnières the least probable candidate cities in our investigation: in fact, if the 15cm Kanone 16 were located there, Amiens would have lain outside its firing range.

Table II. Technical specifications of the Krupp 15cm Kanone 16.

  • 5 The muzzle velocity is the velocity of the projectile when it leaves the barrel of the gun.
Designed 1916 (Krupp)
Produced 1917-1918 (Krupp)
In service 1917-1945
Number built 370 (Krupp), 50 (Rheinmetall)
Weight in firing position 10.87 tons
Length 6.81m
Caliber 149.3mm
Barrel length 6.41m = 43 calibers (L/43)
Number of barrel’s grooves 48, right-hand twist
Rifling 1 in 25 calibers, gain twist of 7°
Breech Horizontal sliding block
Elevation (pitch angle y) − 3° to 42°
Traverse (bearing angle)
Rate of fire 3rpm
Muzzle velocity5 v0 = 757m/s
Maximum firing range 22.8km
Weight of the shell 51.4kg
Carriage Box trail

Fig. 6. (a) A group of unidentified Australian journalists inspecting captured guns. They are taking a closer look at a 21cm howitzer fitted with mud plates (Harbonnières area, photo taken on 4 September 1918); (b) A “Rubber” (high velocity) gun, a Krupp 15cm Kanone, captured by the Australians near Morcault [sic] (Morcourt?, Morlancourt?), during the offensive of 8 August 1918 (Bray Proyart area, Morcourt, photo taken on 8 August 1918); A 15cm SK L/40 gun ((c) foreground, (d) right) captured by the 45th Battalion on 8 August 1918 at Caroline Wood, south of Morcault [sic]: a 15cm Kanone 16 L/43 ((c) center, (d) left) was also captured by the same battalion; (e) Australian army soldiers showing interest in a captured 15cm SK L/40 gun with “buntfarben” late 1918 camouflage paintwork (Somme area, photo taken on 29 August 1918).

Fig. 6. (a) A group of unidentified Australian journalists inspecting captured guns. They are taking a closer look at a 21cm howitzer fitted with mud plates (Harbonnières area, photo taken on 4 September 1918); (b) A “Rubber” (high velocity) gun, a Krupp 15cm Kanone, captured by the Australians near Morcault [sic] (Morcourt?, Morlancourt?), during the offensive of 8 August 1918 (Bray Proyart area, Morcourt, photo taken on 8 August 1918); A 15cm SK L/40 gun ((c) foreground, (d) right) captured by the 45th Battalion on 8 August 1918 at Caroline Wood, south of Morcault [sic]: a 15cm Kanone 16 L/43 ((c) center, (d) left) was also captured by the same battalion; (e) Australian army soldiers showing interest in a captured 15cm SK L/40 gun with “buntfarben” late 1918 camouflage paintwork (Somme area, photo taken on 29 August 1918).

All the photos are drawn from [27]: the original captions of the photos have been amended.

Fig. 7. (a) Simulated trajectory of the center of mass of the projectile of the 15cm Kanone 16, and (b) time-evolution of the velocity v for a pitch angle y = 30.2° (red), y = 35.8° (green), and y = 37.3° (blue); (c) Location of Amiens Cathedral and of the five candidate cities using geodetic coordinates in decimal degrees (DD); (d) Location of Amiens Cathedral and of the five candidate cities using local East, North, Up coordinates, and simulated trajectory of a projectile fired from Villers-Bretonneux (red), Moreuil (green) and Marcelcave (blue).

Fig. 7. (a) Simulated trajectory of the center of mass of the projectile of the 15cm Kanone 16, and (b) time-evolution of the velocity v for a pitch angle y = 30.2° (red), y = 35.8° (green), and y = 37.3° (blue); (c) Location of Amiens Cathedral and of the five candidate cities using geodetic coordinates in decimal degrees (DD); (d) Location of Amiens Cathedral and of the five candidate cities using local East, North, Up coordinates, and simulated trajectory of a projectile fired from Villers-Bretonneux (red), Moreuil (green) and Marcelcave (blue).

18Fig. 7(a) and Fig. 7(b) respectively show the simulated trajectory of the center of mass of the projectile of the 15cm Kanone 16 and the time-evolution of the magnitude of velocity v for a pitch angle ψ = 30.2° (red), ψ = 35.8° (green), and ψ = 37.3° (blue). Fig. 7(c) reports the location of Amiens Cathedral and of the five candidate cities in geodetic coordinates. Finally, Fig. 7(d) shows the location of Amiens Cathedral and of the five candidate cities in local East, North, Up (ENU) coordinates, and the 3-D trajectory of the projectiles computed in Fig. 7(a) for Villers-Bretonneux (red), Moreuil (green) and Marcelcave (blue). Note that the geodetic coordinates of the center of the transept of Amiens Cathedral are (49.8944873, 2.2998477, 38) where the latitude φ and longitude λ are in decimal degrees (DD) and the height in meters, and the geodetic coordinates of Albert, Villers-Bretonneux, Harbonnières, Marcelcave and Moreuil are, respectively: (50.0013743, 2.6516017, 67), (49.8672619, 2.5156054, 91), (49.8474659, 2.6696338, 91), (49.848427, 2.5705266, 91), (49.7793693, 2.4991702, 105), where Google Maps was used for the computation of the latitudes/longitudes and for the altimetry. For uniformity, we considered the geodetic coordinates of the City Hall of all candidate cities, with the exception of Moreuil for which we reported the coordinates of the memorial located 1km northeast of the city center. For the simulated trajectory with ψ = 35.8° (green in Fig. 7(a)), we can estimate an impact angle with respect to the horizontal axis of 26.56° at time tf = 34.96 s and a supersonic impact velocity v(tf) = 446.77m/s. The kinetic energy of the projectile at the impact point is thus mv²(tf)/2 = 5.1298 MJ. Finally, since the barrel of the 15cm Kanone 16 was rifled with 1 turn in ℓ = 25 calibers (cf. Table II), the initial spin of the projectile as it left the gun, can be calculated as (2πv0)/ℓd = 1274.3 rad/s where the gain twist of 7° has been neglected in the formula.

Fig. 8. Close-ups of the damages caused by: (a) Shell 1, (b) Shell 2 (note the pierced buttress), and (c) Shell 6.

Fig. 8. Close-ups of the damages caused by: (a) Shell 1, (b) Shell 2 (note the pierced buttress), and (c) Shell 6.

The three photos, which provide us with useful directional information, are reproduced from [29, p. 199].

192) Line-of-sight image constraint of Shell 3: In this subsection, we will extract further information on the location of German artillery from the historical photos of the damages caused by Shell 3 to the ambulatory of cathedral (see also Figs. 4(c), 5 and 10). Our goal will be to frame the problem within the computer-vision paradigm [37]. The photo in Fig. 4(c) and the one reported in [29, p. 199] show the damages to the rib vault and roof of the cathedral from two viewpoints: they were taken by two different cameras, henceforth referred to as C1 and C2, respectively (see Fig. 9(a)). We respectively used 18 and 9 pairs of corresponding points (shown in magenta in Fig. 9(a)) to register the two photos to the 3-D model of the cathedral, and simultaneously estimate the intrinsic and extrinsic parameters of cameras C1 and C2via an iterative optimization algorithm (Levenberg-Marquardt). We manually determined the point correspondences, since the poor quality of the photos prevented us from using an automatic procedure. The following calibration matrices were obtained:

20where (u0, v0) are the coordinates (in pixels) of the principal point of C1, and αu = f suv = f sv), where f is the focal length of C1, and su, sv are scaling factors along the horizontal and vertical directions, respectively [38]. The estimated rigid-body transformations between frames {C1} and {W}, and frames {C2} and {W} are, respectively:

21and

22Since the ambulatory is 0.692m above the transept floor (i.e. above the xy-plane of {W}), from the third entry of the fourth column of matrices wMc1 and wMc2, we deduce that C1 and C2 were positioned at a height of 2.018m and 1.148m, respectively. This means that the photographer probably supported the first camera with a tripod.

23Let us now make the assumption that the two holes produced by Shell 3 on the roof and rib vault of the ambulatory, and the center of {C1} lie along a straight line, since the photographer intentionally positioned the camera to have them aligned. By knowing that the image coordinates of the center of the hole in the roof (see the white spot in Fig. 4(c)) are u = 286 pixels and v = 152 pixels, we can determine the line-of-sight, i.e. the straight line passing through the center of {C1} and the hole. In fact, the known (homogeneous) coordinates of the center of {C1} (i.e. the fourth column of wMc1) and those of the point,

24uniquely define the sought after line-of-sight, depicted in red in Fig. 9(b). This figure also reports the cone (blue) defined by the contour of the hole in the rib vault computed from 18 image points using the equation above, and the 3-D points (magenta) used for the registration of the first photo. The same procedure was repeated for C2 by knowing that the image coordinates of the center of the hole in the roof are u = 688.4 pixels and v = 926.4 pixels this time (see Fig. 9(c)). In conclusion, we found that the orientation of the lines of sight of the two cameras in the xy-plane of {W} are −13.99° and −13.03°, respectively, which are consistent with the direction of Moreuil (at −18.8°). The orientation of the lines of sight in the xz-plane of {W} (i.e. the estimated angles of impact) are 55.12° and 53.42°.

 

25Remark: Note that the trace left by the base plate of Shell 3 on the floor of the cathedral (cf. Fig. 5) was not considered in our analysis, since it is incompatible with the projectile trajectories described in Sect. III-B.1.

26In fact, it is quite evident that by perforating the roof and vault of the ambulatory, the base plate underwent a deflection in the northeast direction.

Fig. 9. Line-of-sight constraint of Shell 3: (a) 3-D camera setup (photo 2 has been reproduced from [29]); (b), (c) Estimated lines of sight of C1 and C2, respectively (red), and cones defined by the contour of the hole in the rib vault (blue).

Fig. 9. Line-of-sight constraint of Shell 3: (a) 3-D camera setup (photo 2 has been reproduced from [29]); (b), (c) Estimated lines of sight of C1 and C2, respectively (red), and cones defined by the contour of the hole in the rib vault (blue).

The 3-D magenta points have been used to register photo 1 and photo 2 to the 3-D model.

273) Battle of Moreuil Wood and of the Avre: Two well-documented battles in March-April 1918 help us to shed further light on the location of the German artillery which bombarded Amiens [39, Ch. 10-11]. The Battle of Moreuil Wood took place on the banks of the Arve River on 30 March 1918: the Canadian Cavalry Brigade attacked and forced the German 23rd Saxon Division to withdraw from Moreuil Wood, a commanding position on the river bank controlling the Amiens-Paris railway. This defeat contributed to the halt of the German Spring Offensive of 1918. On 31 March, a German attack recaptured most of the wood, and the nearby Rifle Wood, 1.6km to the northeast. Despite German forces eventually regaining control of the Moreuil wood and surrounding area, general Ludendorff ended the offensive on 5 April. The Moreuil Wood was finally taken from the Germans in August 1918 by French forces, with elements of the Canadian Cavalry taking Rifle Wood. Two war memorials along departmental road D23 between Moreuil and Démuin confirm these events and certify the presence of German heavy artillery in this precise area. The first one, a memorial to the 31st French army corps led by General P.L.A. Toulorge, is located 1km outside the city of Moreuil in the direction of Démuin at the crossroads of D23 and D28. The second memorial, dedicated to Lieutenant Gordon Flowerdew of Lord Strathcona’s Horse and to the Rifle Wood battle, is located 3km from the previous one in the direction of Démuin, at the intersection of D23 and D934. The Battle of the Avre (4-5 April 1918), part of the First Battle of Villers-Bretonneux (30 March-5 April), was the final German offensive towards Amiens in WWI and was fought against defending Australian and British troops.

Fig. 10. Traces of the passage of Shell 3: (a) Top side of the vault (cf. Fig. 5(a)); (b) Grayscale panoramic image of the terrasson (restored by E. Viollet-le-Duc, in 1850-1860); Close-ups ((c) photo, (d) colored 3-D point cloud) of the main cavity in the terrasson; (e) Reconstruction of the three layers of the terrasson, and sketch of the main cavity (drawing not to scale): the estimated top diameter of the conical frustum is dm = 25.74cm, and the thickness of the two upper layers is dt = 15.4cm.

Fig. 10. Traces of the passage of Shell 3: (a) Top side of the vault (cf. Fig. 5(a)); (b) Grayscale panoramic image of the terrasson (restored by E. Viollet-le-Duc, in 1850-1860); Close-ups ((c) photo, (d) colored 3-D point cloud) of the main cavity in the terrasson; (e) Reconstruction of the three layers of the terrasson, and sketch of the main cavity (drawing not to scale): the estimated top diameter of the conical frustum is dm = 25.74cm, and the thickness of the two upper layers is dt = 15.4cm.

28The attack was an attempt to secure Amiens and the surrounding high ground from which artillery bombardments could systematically destroy the town and render it useless to the Allies, where other aspects of General Ludendorff’s Operation Michael (started on 21 March 1918) had failed. On 4 April, the Germans attempted to capture Villers-Bretonneux with 15 divisions but were repulsed by troops from the British 1st Cavalry Division and Australian 9th Brigade. After the first battle, the forces that had secured the town were relieved and by late April the area around Villers-Bretonneux was largely held by the 8th Division. An attempt by the Germans to renew the offensive on 5 April (the so-called “Battle of the Ancre”) failed, and by early morning the British troops had forced the enemy out of all but the south-eastern corner of the town. German progress towards Amiens, having reached its farthest point westward, had finally been held, and Ludendorff called a halt to the offensive.

Conclusion and future works

29According to the evidence accumulated in the previous sections, we can conclude that between April 9 and April 22, 1918 Amiens Cathedral was likely bombarded with a Krupp 15cm Kanone 16 gun located 1 to 4km northeast of the city of Moreuil. The attempt to digitally restore the trajectories of artillery fire shows that the Germans did not target Amiens Cathedral and therefore did not seek to damage it in 1918. Above all, they wanted to destroy a city that was a crossroads for the allies in the context of their offensive. On the other hand, they took and assumed the risk of reaching the cathedral. Current techniques, combined with archival sources, make it possible to scientifically refute certain assertions of the propaganda of the Great War.

30In this work, we have presented e-Cathedral, an advanced digital-modeling program of the Gothic Cathedral of Amiens in France. Several research fields have benefited from our large-scale, dense 3-D virtual model: as an original application, we showed how our digital model can be used to shed light into the bombardment of the cathedral during WWI, thus opening new exciting perspectives for historical inquiry.

31E-Cathedral is an ongoing research program, which serves as the basis for more ambitious future undertakings. At present, the laser scanners and photographic equipments are manually placed in the 3-D environment: in the future, we aim at designing a cooperative robotic platform (composed of wheeled and aerial robots) to fully automatize the measurement process. We are also interested in developing multi-sensory interfaces (e.g. virtual/mixed-reality headsets) to improve the immersive experience of real or virtual visitors of the cathedral, and new navigation devices tailored to people with disabilities.

Bibliographie

[1] S. Murray, “Looking for Robert de Luzarches: The Early Work at Amiens Cathedral”, Gesta, 1990, vol. 29, n° 1, p. 111–131.

[2] S. Murray, Notre-Dame, Cathedral of Amiens: The Power of Change in Gothic, Cambridge University Press, 1996.

[3] H. Jantzen, High Gothic: The Classic Cathedrals of Chartres, Reims, Amiens, Princeton University Press, 1984. Translated by J. Palmes.

[4] G. Durand. Monographie de l’église Notre-Dame, cathédrale d’Amiens. Imprimerie Yvert et Tellier, Amiens, 1901, Tome I - Histoire et Description de l’Édifice.

[5] S. Murray, J. Addiss, “Plan and Space at Amiens Cathedral: With a New Plan Drawn by James Addiss”, J. Soc. Archit. Hist., 1990, vol. 49, n° 1, p. 44–66.

[6] R. Bork, R. Mark, S. Murray, “The Openwork Flying Buttresses of Amiens Cathedral: ‘Postmodern Gothic’ and the Limits of Structural Rationalism”, J. Soc. Archit. Hist., 1997, vol. 56, n° 4, p. 478–493.

[7] S. Coccia, M. Como, F. Di Carlo, “Wind strength of Gothic Cathedrals”, Eng. Fail. Anal., 2015, vol. 55, p. 1–25.

[8] J. Monnier, D. Neff, S. Réguer, P. Dillmann, L. Bellot-Gurlet, E Leroy, E. Foy, L. Legrand, I. Guillot, “A corrosion study of the ferrous medieval reinforcement of the Amiens cathedral. Phase characterisation and localisation by various microprobes techniques”, Corros. Sci., 2010, vol. 52, n° 3, p. 695–710.

[9] G. Pavlidis, A. Koutsoudis, F. Arnaoutoglou, V. Tsioukas, C. Chamzas, “Methods for 3D digitization of cultural heritage”, J. Cult. Herit., 2007, vol. 8, n° 1, p. 93–98.

[10] G. Sansoni, M. Trebeschi, F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation”, Sensors, 2009, vol. 9, n° 1, p. 568–601.

[11] B. Alsadik, M. Gerke, G. Vosselman, “Automated camera network design for 3D modeling of cultural heritage objects”, J. Cult. Herit., 2013, vol. 14, n° 6, p. 515–526.

[12] K. Ikeuchi, T. Oishi, J. Takamatsu, R. Sagawa, A. Nakazawa, R. Kurazume, K. Nishino, M. Kamakura, Y. Okamoto, “The Great Buddha Project: Digitally Archiving, Restoring, and Analyzing Cultural Heritage Objects”, Int. J. Comput Vision, 2007, vol. 75, n° 1, p. 189–208.

[13] Bayon Digital Archival Project, [web] www.cvl.iis.u-tokyo.ac.jp/projects.html

[14] CyARK organization, [web] http://cyark.org

[15] B.T. Andrade, O.R. Pereira Bellon, L. Silva, A. Vrubel, “Digital preservation of Brazilian indigenous artworks: Generating high quality textures for 3D models”, J. Cult. Herit., 2012, vol. 13, n° 1, p. 28–39.

[16] R. Zlot, M. Bosse, K. Greenop, Z. Jarzab, E. Juckes, J. Roberts, “Efficiently capturing large, complex cultural heritage sites with a handheld mobile 3D laser mapping system”, J. Cult. Herit., 2014, vol. 15, n° 6, p. 670–678.

[17] S. Agarwal, Y. Furukawa, N. Snavely, I. Simon, B. Curless, S.M. Seitz, R. Szeliski, “Building Rome in a Day”, Commun. ACM, 2011, vol. 54, n° 10, p. 105–112.

[18] I. Stamos, M. Pollefeys, L. Quan, P. Mordohai, Y. Furukawa, “Special Issue on Large-Scale 3D Modeling of Urban Indoor or Outdoor Scenes from Images and Range Scans”, Comput. Vis. Image Und., 2017, vol. 157, p. 1–2.

[19] Y. Bok, D.G. Choi, Y. Jeong, I.S. Kweon, “Capturing Village-level Heritages with a Hand-held Camera-Laser Fusion Sensor”, 2009, In Workshop on eHeritage and Digital Art Preservation, in conjunction with the IEEE Int. Conf. Comput. Vis., 2009.

[20] 3D Monuments program, [web] www.map.archi.fr/3D-monuments/

[21] W. Wahbeh, S. Nebiker, G. Fangi, “Combining Public Domain and Professional Panoramic Imagery for the Accurate and Dense 3D Reconstruction of the Destroyed Bel Temple in Palmyra”, ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences, 2016, vol. III, n° 5, p. 81–88.

[22] A. Rubio, M. Villamizar, L. Ferraz, A. Penate-Sanchez, A. Ramisa, E. Simo-Serra, A. Sanfeliu, F. Moreno-Noguer, “Efficient Monocular Pose Estimation for Complex 3D Models”, In Proc. IEEE Int. Conf. Robot. Automat, 2015, p. 1397-1402.

[23] Programme E-Cathédrale, [web] https://mis.u-picardie.fr/E-Cathedrale

[24] G. Durand, Monographie de l’église Notre-Dame, cathédrale d’Amiens. Imprimerie Yvert et Tellier, Amiens, 1903, Tome III - Atlas.

[25] N. Crombez, G. Caron, E. Mouaddib, “3D Point Cloud Model Colorization by Dense Registration of Digital Images”, The International Archives Photogrammetry, Remote Sensing and Spatial Information Sciences, 2015, vol. 40, n° 5, p. 123–130.

[26] Michelin & Cie, Amiens Before and During the War, Michelin’s Illustrated Guides to the Battle-fields (1914-1918). Naval and Military Press, 1919.

[27] Australian War Memorial, [web] www.awm.gov.au/collection

[28] National Library of Scotland: http://digital.nls.uk/first-world-war-official-photographs

[29] A. Chatelle, Amiens pendant la guerre (1914-1918), Imprimerie du Progrès de la Somme, 1929.

[30] P. Léon, Amiens. La Cathédrale, L’Art et les Artistes, Paris, 1918. Numéro spécial.

[31] La Médiathèque de l’Architecture et du Patrimoine, Base Mémoire: Archives photographiques, [web] www.culture.gouv.fr/public/mistral/memsmn_fr

[32] “Amiens Cathedral Bombarded: One of the Glories of Gothic Art”, The Auckland Star, 15 June 1918, vol. XLIX, n° 142, p. 17.

[33] H.W. Nevinson, “Amiens Cathedral Hit Only Three Times: Famous Edifice Only Slightly Damaged, Though Nearby Building Were Wrecked”, The New York Times, 17 August 1918, p. 2.

[34] G. Héracle-Leroy, Le bombardement d’Amiens en 1918, Monographies des villes et villages de France, Le Livre d’historie-Lorisse, Paris, 2014. Re-edition of the 1919 text.

[35] I.V. Hogg, German Artillery of World War Two, Stackpole Books, 2nd edition, 1997.

[36] F. Guy, Eisenbahnartillerie: Histoire de l’artillerie lourd sur voie ferrée allemande des origines à 1945, Histoire et Fortifications, Paris, 2006.

[37] R. Hartley, A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge University Press, 2nd edition, 2003.

[38] Y. Ma, S. Soatto, J. Košecká, S.S. Sastry, An Invitation to 3-D Vision: from Images to Geometric Models, Springer, 2004.

[39] J.F. Williams, ANZACS, the Media and the Great War, UNSW press, 1999.

Notes

1 Chapel XXIII is also known as the Chapel of St. John the Baptist.

2 Chapels IV and VI are also known as the Chapels of St. Christopher and of Our Lady of Faith (or of the Annunciation), respectively.

3 Heavy artillery means that the caliber of the gun is greater or equal to 120mm. German heavy artillery is also known as “Fußartillerie” or foot artillery.

4 A howitzer is a short gun for firing shells on high trajectories at low velocities: in fact, the barrel of the 21cm Mörser 16 only measures 2.67m.

5 The muzzle velocity is the velocity of the projectile when it leaves the barrel of the gun.

Table des illustrations

Titre Fig. 1. (a) West front of Amiens Cathedral as appeared in March 2016; (b) Corresponding view of the 3-D digital model developed in the e-Cathedral program.
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-1.jpg
Fichier image/jpeg, 198k
Titre Fig. 2. Approximate front line on 5 April 1918 (dashed line) marking the stabilized westward position reached by the German army during the Spring Offensive (figure based on maps in [26]).
Légende According to the historical record, the locations marked in red are the most likely to have harbored the German artillery which damaged Amiens Cathedral.
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-2.jpg
Fichier image/jpeg, 295k
Titre Fig. 3. Points of impact (stars) of the German projectiles that damaged Amiens Cathedral in April 1918.
Légende The stars 1 to 6 refer to the projectiles that struck the fabric of the church, while the stars 7 to 9 indicate those that exploded at a certain distance outside the building (the position of the blue stars on the southeast side is indicative, and not to scale). Plan adapted from [24, Plan II].
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-3.jpg
Fichier image/jpeg, 236k
Titre Fig. 4. Historical photos of the damages caused to the cathedral by six shells.
Légende (a) Shell 1; (b) Shell 2; (c) Shell 3; (d) Shell 4; (e) Shell 5; (f) Shell 6.
Crédits Photo (a) was taken on 28 June 1918, probably from a balcony of Amiens courthouse [27, photo E04918]. Photos (b) and (c) were taken by the Scottish war photographer T.K. Aitken immediately after the events occurred [28]. Photos (d), (f) are available in the digital archive [31].
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-4.jpg
Fichier image/jpeg, 392k
Titre Fig. 5. (a) Rib-vaulted ceiling of the south ambulatory as it appears today: note that the paler plaster used in the restoration works allows to easily identify the damages caused by Shell 3. (b) Impact point of the base plate of Shell 3 on the marble paving of the south aisle of the choir marked with a cross. To situate the point of impact on the plan of the cathedral, see the black cross in front of Chapel XVIII in Fig. 3.
Crédits Photos (a) and (b) were taken by the authors in September 2015.
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-5.jpg
Fichier image/jpeg, 256k
Titre Fig. 6. (a) A group of unidentified Australian journalists inspecting captured guns. They are taking a closer look at a 21cm howitzer fitted with mud plates (Harbonnières area, photo taken on 4 September 1918); (b) A “Rubber” (high velocity) gun, a Krupp 15cm Kanone, captured by the Australians near Morcault [sic] (Morcourt?, Morlancourt?), during the offensive of 8 August 1918 (Bray Proyart area, Morcourt, photo taken on 8 August 1918); A 15cm SK L/40 gun ((c) foreground, (d) right) captured by the 45th Battalion on 8 August 1918 at Caroline Wood, south of Morcault [sic]: a 15cm Kanone 16 L/43 ((c) center, (d) left) was also captured by the same battalion; (e) Australian army soldiers showing interest in a captured 15cm SK L/40 gun with “buntfarben” late 1918 camouflage paintwork (Somme area, photo taken on 29 August 1918).
Crédits All the photos are drawn from [27]: the original captions of the photos have been amended.
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-6.jpg
Fichier image/jpeg, 291k
Titre Fig. 7. (a) Simulated trajectory of the center of mass of the projectile of the 15cm Kanone 16, and (b) time-evolution of the velocity v for a pitch angle y = 30.2° (red), y = 35.8° (green), and y = 37.3° (blue); (c) Location of Amiens Cathedral and of the five candidate cities using geodetic coordinates in decimal degrees (DD); (d) Location of Amiens Cathedral and of the five candidate cities using local East, North, Up coordinates, and simulated trajectory of a projectile fired from Villers-Bretonneux (red), Moreuil (green) and Marcelcave (blue).
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-7.jpg
Fichier image/jpeg, 412k
Titre Fig. 8. Close-ups of the damages caused by: (a) Shell 1, (b) Shell 2 (note the pierced buttress), and (c) Shell 6.
Crédits The three photos, which provide us with useful directional information, are reproduced from [29, p. 199].
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-8.jpg
Fichier image/jpeg, 300k
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-9.jpg
Fichier image/jpeg, 33k
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-10.jpg
Fichier image/jpeg, 29k
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-11.jpg
Fichier image/jpeg, 32k
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-12.jpg
Fichier image/jpeg, 16k
Titre Fig. 9. Line-of-sight constraint of Shell 3: (a) 3-D camera setup (photo 2 has been reproduced from [29]); (b), (c) Estimated lines of sight of C1 and C2, respectively (red), and cones defined by the contour of the hole in the rib vault (blue).
Légende The 3-D magenta points have been used to register photo 1 and photo 2 to the 3-D model.
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-13.jpg
Fichier image/jpeg, 264k
Titre Fig. 10. Traces of the passage of Shell 3: (a) Top side of the vault (cf. Fig. 5(a)); (b) Grayscale panoramic image of the terrasson (restored by E. Viollet-le-Duc, in 1850-1860); Close-ups ((c) photo, (d) colored 3-D point cloud) of the main cavity in the terrasson; (e) Reconstruction of the three layers of the terrasson, and sketch of the main cavity (drawing not to scale): the estimated top diameter of the conical frustum is dm = 25.74cm, and the thickness of the two upper layers is dt = 15.4cm.
URL http://books.openedition.org/septentrion/docannexe/image/87851/img-14.jpg
Fichier image/jpeg, 464k

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Laboratoire MIS, Université de Picardie Jules Verne

Laboratoire MIS, Université de Picardie Jules Verne

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