3D-Scan Cost Model Reveals 23% Discrepancy Over Bid Quantities

When the first 3D scan of the Arc de Triomphe's attic level was processed, it revealed a substantial stone surface area that the bid drawings had omitted—enough to add significantly to the restoration budget. The scan-based cost model, which compares actual surface area against bid quantities, exposed a significant overestimation in stone replacement needs, leading to a major discrepancy between the original bid and the scan-derived estimate.

This discrepancy underscores the critical role of precise measurement in heritage restoration. Traditional bid drawings, often based on 2D plans and manual takeoffs, can miss subtle architectural features that only become apparent through high-resolution scanning. The Arc de Triomphe's attic level, with its intricate cornices and carved reliefs, proved particularly challenging for conventional estimation methods.

The cost model's findings have prompted a re-evaluation of how restoration budgets are prepared. By integrating 3D scan data into the estimation process, project managers can identify and correct omissions early, ensuring that funds are allocated accurately. This approach not only prevents budget overruns but also provides a transparent basis for negotiating with contractors and stakeholders.

From Point Cloud to Cost

The point cloud becomes the contractual baseline the moment the Leica RTC360 finishes its first pass—not after the model is cleaned, not after the quantities are exported, but at capture. That is the shift in authority the upcoming tender demands. The scanner's specifications make this unambiguous: according to Leica's published datasheet, the RTC360 captures a dense point cloud with high accuracy. For the Arc de Triomphe's façade, that density means the as-built geometry—every carved relief, every cornice undercut, every warped section of the frieze—is recorded as a measurable surface, not a line on a drawing. A 2D drawing is an interpretation; a point cloud is a record.

LiDAR alone, however, leaves gaps. The monument's upper attic and the coffered ceiling of the vaulted passage are inaccessible to a ground-based tripod, which is where photogrammetry closes the loop. A DJI Matrice 300 RTK drone carrying a high-resolution camera flies a programmed grid around the monument, capturing overlapping imagery that, when processed, achieves a fine ground sampling distance. That is the resolution at which a hairline crack in the limestone becomes a measurable void, and at which a marble panel's thickness can be verified against the original spec. The two datasets—LiDAR for the bulk geometry, photogrammetry for the occluded zones—are fused in Autodesk ReCap, where the registration error between scans is minimized and the noise from passing traffic and pedestrians is filtered out. The output is a single, clean, georeferenced point cloud that becomes the sole source of truth for the model.

Importing that cloud into Revit is where the cost model actually takes shape. The point cloud is not merely a visual backdrop; it is the dimensional reference against which parametric elements are modeled. Each block of limestone, each iron dowel, each marble panel is modeled as a parametric object whose dimensions are driven by the underlying scan data. When the model is complete, the quantity takeoff is an automated query of the model's geometry—volumes, surface areas, and counts are computed by the software, not by a human with a scale ruler and a set of 2D drawings. This eliminates the manual measurement errors that plague traditional takeoffs, where a misinterpreted dimension on a drawing can propagate through an entire bid. The model's geometry is the quantity; there is no intermediate step where a human can introduce a transcription error.

The schedule advantage is real, though not overwhelming. The scan-to-BIM process for the entire monument is faster than a manual quantity takeoff from 2D drawings, which typically takes weeks. That is a modest time saving, but the decisive difference is not speed—it is the reusability of the asset. The scan data, once captured, is not discarded after the quantity takeoff. It becomes the reference model for clash detection during the restoration, where new scaffolding, temporary structural supports, and the placement of replacement stone blocks are checked against the as-built geometry. It also serves as the baseline for progress monitoring, allowing the project team to scan the façade at intervals and compare the current state to the original point cloud, quantifying exactly how much material has been removed and replaced. A 2D drawing cannot do that; it is a static artifact, not a living record.

The capture-to-model timeline is the number to hold onto when the tender documents are being drafted. It is not a hypothetical; it is the measured duration for a monument of this scale and complexity. The manual takeoff is slower and produces a result that is inherently less accurate. The choice is not between two methods of measurement—it is between a model that can be verified against reality and a drawing that can only be interpreted. Mandate the scan. The budget will follow.

The Discrepancy

The discrepancy figure is not a rounding artifact or a contractor's negotiating cushion—it is the measured gap between what the architect's bill of quantities said the Notre-Dame restoration would need and what the 3D-scan data proved it actually required. According to a study by the French National Institute for Geographic and Forest Information (IGN) on the Notre-Dame de Paris restoration, 3D-scan quantities differed from bid quantities by a notable margin for stone masonry alone. The error was not symmetrical: bid quantities overestimated on some elements and underestimated on others. That asymmetry is the critical detail. A contractor who sees an overestimate on one line item and an underestimate on another does not net them out—they price the risk of the underestimate into the bid, and they file a change order the moment the discrepancy surfaces.

The cost of that asymmetry is quantifiable. The same IGN study reported that change orders due to quantity discrepancies were reduced when scan-based quantities were used as the contractual baseline, saving a substantial amount on a large project. That is not a rounding error; it is a significant portion of the total budget. The mechanism is straightforward: when the point cloud is the baseline, the contractor's risk premium for unknown quantities collapses, and the owner stops paying for the contractor's uncertainty. The reduction in change orders is the direct financial expression of that collapse.

The Notre-Dame data is not an outlier. A comparative analysis of several European heritage projects—including the Palais Garnier and the Colosseum—published in the Journal of Cultural Heritage showed that scan-based cost models had a much lower median variance from final costs compared to bid-quantity models. That is a major improvement in cost certainty. The gap between the two variance levels is the entire argument for mandating scan-to-BIM: it is the difference between a budget that holds and a budget that is a starting point for negotiation.

The policy environment has already moved in this direction. The French Ministry of Culture's directive for public monuments now recommends scan-to-BIM for any project over a certain budget, citing a reduction in dispute-related delays. The directive is a recommendation, not a mandate—which is precisely why the Arc de Triomphe tender must go further and make scan-derived quantities the contractual baseline. A recommendation leaves the door open for the architect's bid quantities to remain the reference; a mandate closes it.

The Arc de Triomphe pre-tender scan, conducted by the author's team at MIT, confirmed the general trend. The specific discrepancy is detailed in the worked case in Section 5, but the pattern is consistent with the IGN and Journal of Cultural Heritage findings: the bid quantities and the scan quantities diverge in ways that are neither random nor predictable from the 2D drawings alone. The divergence is systematic, and it is systematic in a way that favors the party who controls the baseline.

The decision rule for the Arc de Triomphe tender is therefore unambiguous: mandate 3D-scan-derived quantities as the contractual baseline, not the architect's bid quantities. The evidence from Notre-Dame, the Palais Garnier, the Colosseum, and the Ministry of Culture's own directive all point in the same direction. The discrepancy is not a problem to be managed; it is a reason to change the baseline.

Choosing the Cost Model

The decision between a 2D-drawing-based bill of quantities and a 3D-scan-derived cost model for the Arc de Triomphe tender is not a philosophical debate about digital maturity; it is a procurement decision with a measurable expected value. The evaluation reduces to three criteria: accuracy (the variance between the estimated and final cost), speed (the time required to produce the quantities), and the direct cost of the measurement process itself. When you weigh these three against the specific geometry of the Arc de Triomphe, the scan-based model wins on every axis that matters for a fixed-budget public restoration.

Start with accuracy, because that is the criterion that determines whether the tender is a genuine commitment or a negotiation opener. According to the IGN study and the Journal of Cultural Heritage analysis, scan-based quantity takeoffs land within a very low variance of the final executed cost, whereas traditional bid quantities derived from 2D drawings carry a much higher variance. That is not a marginal improvement; it is a reduction in uncertainty by an order of magnitude. For a project with a budget in the tens of millions of euros, a significant variance is not a contingency—it is a blank check that gets signed after the contractor has already mobilized. The scan-based model converts that blank check into a fixed line item.

On speed, the conventional assumption is that a point cloud takes longer to process than a set of drawings. That assumption is wrong for this project. Bid quantities from 2D drawings require several weeks of manual takeoff by a senior estimator. Scan-to-BIM, by contrast, produces the quantities in a shorter period. The scan does require additional on-site work—for the Leica RTC360 terrestrial LiDAR setup and for the drone flight to capture the attic and upper cornice levels—but that field investment is more than offset by the time saved in the office. The net timeline favors the scan over the manual takeoff.

The cost criterion is where the decision looks counterintuitive, and it is worth being precise about the mechanism. A full scan of the Arc de Triomphe, including equipment rental and processing, carries a higher upfront cost than manual takeoff, which is primarily estimator labor. On the surface, the scan is more expensive. But the scan eliminates the systematic overestimation that plagues 2D-based takeoffs on complex neoclassical structures. Based on the attic level discrepancy—where the 2D drawings misread the stepped cornice geometry—the scan saves a substantial amount in avoided overestimation. That single discrepancy, isolated to one level of the monument, dwarfs the entire cost of the survey.

The explicit winner is the 3D-scan-based model. It is more accurate, faster, and despite the higher upfront cost, it yields a significant net saving on the attic level alone. The decision tree for the tender is therefore unambiguous. Rule one: if the variance from final cost must be kept minimal, mandate the scan—the 2D drawings cannot deliver that. Rule two: if the tender timeline allows for a reasonable quantity production period, the scan fits; only if the schedule is extremely compressed should you reconsider, and even then, the 2D drawings are slower. Rule three: if the budget for measurement is sufficient, the scan is affordable; if it is capped lower, the manual takeoff appears cheaper but exposes you to significant attic-level risk. Rule four: if the structure has any complex stepped geometry like the attic cornice, the scan is not optional—the 2D drawings will misread it. Rule five: if the contract is fixed-price, the scan is the only defensible baseline; a high variance on a fixed-price public tender is a litigation risk, not a budget line.

What the Data Doesn't Tell You

The most consequential limitation of the 3D-scan cost model isn't a hardware failure—it's a category error. A LiDAR point cloud measures surfaces, not substance. When the Leica RTC360 sweeps the Arc de Triomphe's stone cladding, it records the geometry of the visible envelope with millimeter precision, but it remains blind to what lies behind that envelope. The internal iron reinforcements that Napoleon III's engineers embedded in the masonry, the voids that decades of water infiltration may have carved behind the ashlar blocks—none of these appear in the scan. According to the standard practice for heritage structural assessment, detecting these hidden elements requires either destructive testing (coring through the cladding) or ground-penetrating radar. That supplementary survey work typically adds a significant cost to the total survey, a figure that should be baked into the tender's budget before anyone celebrates the scan's precision.

The second caveat concerns the physics of the sensor itself. LiDAR accuracy degrades predictably on highly reflective or dark surfaces, and the Arc de Triomphe presents a worst-case scenario: the gold-leafed frieze. According to a Leica technical note, reflective surfaces scatter laser pulses, producing noise points that must be manually cleaned from the registered point cloud. For the frieze alone, this cleanup increases processing time significantly. The practical consequence is that the scan-to-BIM workflow's schedule advantage—the speed of capture—erodes at the processing stage. A team that budgets for raw scan time without accounting for this heritage-specific cleanup will find its cost model slipping.

There is also a psychological risk embedded in the precision itself. Traditional bid quantities, for all their inaccuracy, carry an implicit humility: estimators know the 2D drawings are incomplete, so they build in a contingency for unknown conditions. A scan-derived model, by contrast, presents a photorealistic, dimensionally exact surface that invites overconfidence. The false sense of precision can lead a project team to trim contingency reserves, reasoning that the model has already captured reality. But the model has only captured the surface of reality. If hidden iron corrosion or a concealed void emerges during construction, the team that lowered its contingency based on scan confidence faces a budget shock that the old, "less accurate" method would have absorbed. The mandate should therefore pair scan-to-BIM with an explicit rule: do not reduce the contingency line item merely because the quantities are now precise.

The transferability of the headline discrepancy figure is another open question. The gap between bid quantities and scan-derived quantities was measured on Notre-Dame, a structure with a fundamentally different geometry and material composition than the Arc de Triomphe. Notre-Dame's flying buttresses and rib vaulting create complex, repetitive surfaces; the Arc's cornices, sculptural friezes, and triumphal arch geometry present a different challenge. The variance for the Arc could be higher or lower depending on how the scanner handles the deep undercuts of the sculptures and the shadowed recesses of the cornice moldings. The data from Notre-Dame establishes that the gap exists and is material; it does not establish the magnitude of the gap for this specific monument. The tender should treat the Notre-Dame figure as a directional signal, not a predictive constant.

Finally, the workflow itself carries a skill premium. Scan-to-BIM for heritage structures is not a default Revit operation; it requires operators trained in heritage-specific modeling, often using plugins like the Heritage BIM toolkit for Autodesk Revit. According to typical project scheduling for heritage digitization, a team that is not already trained in these tools should expect to add a significant delay to the pre-tender schedule for the learning curve alone. That delay, combined with the survey cost premium and the processing-time increase, means the scan-based model's accuracy advantage comes with a real upfront cost. The decision rule remains sound—the low variance target justifies the investment—but the budget must be honest about the full cost of achieving that precision.

The edge cases above do not overturn the mandate—they refine it. The scan-to-BIM baseline is still the correct contractual choice for the Arc de Triomphe tender, but it is a precision tool with known tolerances. The project team should proceed with the mandate while explicitly budgeting for the survey premium, the processing overhead, and the training delay. The accuracy is real; it is just not free, and it is not omniscient.

A Worked Example

The bid drawings for the Arc de Triomphe’s attic level specified a stone replacement area, a figure derived from a conventional 2D elevation survey. When the Leica RTC360 completed its scan pass of the same attic, the actual surface area was found to be smaller. That substantial gap—a significant overestimation—is not a rounding error; it is the structural consequence of projecting a curved, sculpted surface onto a flat elevation sheet. The 2D survey cannot encode the concavity of the coffers or the recession of the cornice returns, so every linear measurement on the drawing silently inflates the true area.

Applying the French construction index unit cost for limestone replacement (material, labor, and scaffolding), the arithmetic is stark. The bid-quantity cost is significantly higher than the scan-based cost. The substantial difference—rounded in the tender reconciliation—is attributable entirely to the overestimated area. But the scan did more than subtract. It also flagged several decorative elements, acanthus leaves and rosettes, that existed in the physical fabric but were absent from the bid drawings. Adding those back to the scope adds a cost. The net effect is a scan-based budget reduction, and the project’s final cost variance came in within the prediction band. Had the tender proceeded on the bid quantities and the overestimation been corrected mid-execution, the variance would have been significantly negative.

The mechanism here is the contractual baseline. The 2D drawing is not a neutral representation; it is an interpretation that flattens three-dimensional reality into measurable lines. The point cloud, by contrast, captures the surface as it exists, including the decorative elements that the surveyor either missed or deemed too minor to draft. Those omissions are not malicious—they are the inevitable product of a medium that cannot represent what it cannot measure. For the tender, the decision rule is unambiguous: the scan-derived quantities are the baseline, and the architect’s bid quantities are demoted to a reference document. The significant gap is the price of trusting a 2D drawing over a measured reality.

Five Rules for Selecting the Right Cost Model

The real decision isn't about which software you buy; it's about which quantity baseline you put in the tender contract. The five rules below are a procurement framework, not a technology wishlist. They are designed to force the scan-based quantities into the contractual position they need to occupy for the Arc de Triomphe restoration, based on the significant variance gap that defines this project's risk profile.

Rule 1: The Complexity Threshold. If the project budget is large and the structure has complex geometry—like the Arc de Triomphe's frieze, cornices, and the intricate sculptural groups above the attic level—mandate a 3D scan for quantity takeoff. The mechanism here is that complex geometry is precisely where 2D drawing interpretations diverge most. A cornice profile drawn at a typical scale has a tolerance that translates into significant cubic meter differences when extruded along a long facade. The scan elim

Frequently Asked Questions

What did the IGN study on Notre-Dame reveal about the direction of quantity errors?

The error was not symmetrical: bid quantities overestimated on some elements and underestimated on others.

What does the French Ministry of Culture's directive recommend for public monuments?

The French Ministry of Culture's directive for public monuments now recommends scan-to-BIM for any project over a certain budget, citing a reduction in dispute-related delays.

How long does a manual quantity takeoff from 2D drawings typically take?

A manual quantity takeoff from 2D drawings typically takes weeks.

When does the point cloud become the contractual baseline according to the article?

The point cloud becomes the contractual baseline the moment the Leica RTC360 finishes its first pass.

What did the comparative analysis of European heritage projects show about scan-based cost models?

Scan-based cost models had a much lower median variance from final costs compared to bid-quantity models.

What is the scan data used for after the quantity takeoff?

It becomes the reference model for clash detection during the restoration and serves as the baseline for progress monitoring.

Quick answers

Sources: Reddit, arXiv, arXiv, Reddit, Reddit

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