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arxiv: 1907.04435 · v1 · pith:VRGG6FJ2new · submitted 2019-07-09 · 💻 cs.GR · cs.CY· cs.HC

Shadow Accrual Maps: Efficient Accumulation of City-Scale Shadows Over Time

Fabio Miranda , Harish Doraiswamy , Marcos Lage , Luc Wilson , Mondrian Hsieh , Claudio T. Silva This is my paper

Pith reviewed 2026-05-24 23:40 UTC · model grok-4.3

classification 💻 cs.GR cs.CYcs.HC
keywords shadow accumulationcity-scale shadowssun movementshadow mapsray tracingurban planningenvironmental qualityShadow Profiler
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The pith

Properties of sun movement let standard shadowing methods accumulate city-scale shadows over fixed time intervals.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that shadows cast by buildings can be accumulated efficiently across months or a year by exploiting the regular path of the sun rather than recomputing shadows at every moment. This accumulation matters because the total duration of shadow on public spaces affects pedestrian comfort, vegetation health, and sunlight access, yet computing it at city scale has been too slow for interactive use. The authors extend two existing techniques, shadow maps and ray tracing, by tracking how shadow positions shift within chosen time windows. They then embed the result in an interactive tool that lets planners compare different building scenarios in a place like Manhattan.

Core claim

We propose a simple yet efficient class of approach that uses the properties of sun movement to track the changing position of shadows within a fixed time interval. We use this approach to extend two commonly used shadowing techniques, shadow maps and ray tracing, and demonstrate the efficiency of our approach. Our technique is used to develop an interactive visual analysis system, Shadow Profiler, targeted at city planners and architects that allows them to test the impact of shadows for different development scenarios.

What carries the argument

Shadow accrual maps that record shadow positions by following the sun's predictable trajectory across a chosen time interval, thereby extending ordinary shadow maps and ray tracing without per-frame recomputation.

If this is right

  • Planners can run interactive comparisons of multiple building proposals and see their combined shadow effects over a full year.
  • The same accumulation logic applies to both shadow-map and ray-tracing pipelines without rewriting the core renderer.
  • Accumulated shadow data become cheap enough to support repeated what-if queries during early-stage urban design.
  • The method produces per-location totals of shadow hours that directly quantify impacts on vegetation and pedestrian comfort.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same accrual idea could be tested on other time-varying environmental factors such as wind or noise that also follow predictable daily cycles.
  • Because the method separates the sun-path logic from the geometry, it may transfer to cities at different latitudes with only a change in the sun-position table.
  • If the error remains low across seasons, the maps could serve as a lightweight pre-filter before more expensive lighting simulations.

Load-bearing premise

The regular daily and seasonal motion of the sun is regular enough that shadow locations can be tracked accurately over chosen time windows at city scale without large errors or scene-specific adjustments.

What would settle it

A side-by-side comparison, on a detailed Manhattan 3D model, between one year of accumulated shadow hours produced by the new maps and the same total obtained by running full ray tracing at hourly intervals, checking whether the difference in total shadow duration exceeds a few percent on representative public spaces.

Figures

Figures reproduced from arXiv: 1907.04435 by Claudio T. Silva, Fabio Miranda, Harish Doraiswamy, Luc Wilson, Marcos Lage, Mondrian Hsieh.

Figure 1
Figure 1. Figure 1: Shadow accumulation is measured as either gross shadow [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Shadow accrual map makes use of the linear movement of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: The pixel p processed by the shadow map at time i is obtained by projecting along the light direction d~, which is at an angle iθ from d~ 1. Now, consider time step t1 < i < tn, having direc￾tion d~. Due to linear move￾ment of the sun, the inter￾polation factor k = i−t1 tn−t1 = ∠(d~,d~ 1) ∠(d~ n,d~ 1) . Let ∠(d~ n,d~ 1) = θ. Then ∠(d~,d~ 1) = iθ/n. Con￾sider a point s on building mesh. Let the projection o… view at source ↗
Figure 6
Figure 6. Figure 6: Possible situation which requires inverse ac￾crual maps to be computed at multiple source levels. Effect of maximum source level. Consider the evolution of the shadow at point p in [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: A given view point can have more than one source of shadow. The l th closest source of shadow is used to represent the l th 2D slice of the inverse accrual map. Now, consider any point, say p1, on a plane. The pos￾sible sources of shadow for that point can be obtained by tracing a ray from that point in the reverse direction of light until there are no more inter￾sections. Here, each intersec￾tion correspo… view at source ↗
Figure 7
Figure 7. Figure 7: The direction graph is used to significantly improve the performance of shadow accumulation. For example, consider a case where shadows have to be accumulated over two days from 10 AM to 3 PM. Let the value of n = 60 minutes. If the di￾rection of sun light remains the same for both days un￾til 1 PM, then the resulting graph is as shown in [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: User interface of the Shadow Profiler system consists of a map widget together with a date and time selector. [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Shadow accumulation over 7 hours on June 1 at three different zoom levels when the camera is 800, 300 and 100 meters, respectively, above [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Shadow profiler supports two modes of operation. The exploration mode, which uses shadow accrual maps to compute shadow accumulation, [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Comparing the area of accumulated shadows over 1 hour periods computed using a smaller set of representative directions from the direction graph with ground truth area. Note that approximating using the direction graph does not hamper the accuracy of the shadow area. (b) Choosing the maximum source level for inverse accrual maps. Inverse accrual maps. As mentioned in Section 5, computing inverse accru… view at source ↗
Figure 12
Figure 12. Figure 12: Performance Evaluation. (a) Comparison with baselines. For each method, the times are independently sorted in increasing order. Note that both shadow accrual map and inverse accrual map consistently perform better than the naive baselines. (b) Scalability of the proposed techniques with increasing resolution. We used resolutions with an aspect ratio of 1:1 for this experiment (e.g. 512 implies a resolutio… view at source ↗
Figure 13
Figure 13. Figure 13: Testing the impact of skyscrapers that are under construction south of Central park. Shadows cast during summer and winter with the current [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: We compare the impact of shadows from new and under construction set of skyscrapers in Manhattan (left) with an alternate scenario having [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Visually comparing year long gross shadows for different neighborhoods in Manhattan. The color map is set to visualize regions with gross [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The overall effect of shadows on 3 popular Manhattan neighborhoods is mostly negative. Regions with positive yearly score, highlighted by [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
read the original abstract

Large scale shadows from buildings in a city play an important role in determining the environmental quality of public spaces. They can be both beneficial, such as for pedestrians during summer, and detrimental, by impacting vegetation and by blocking direct sunlight. Determining the effects of shadows requires the accumulation of shadows over time across different periods in a year. In this paper, we propose a simple yet efficient class of approach that uses the properties of sun movement to track the changing position of shadows within a fixed time interval. We use this approach to extend two commonly used shadowing techniques, shadow maps and ray tracing, and demonstrate the efficiency of our approach. Our technique is used to develop an interactive visual analysis system, Shadow Profiler, targeted at city planners and architects that allows them to test the impact of shadows for different development scenarios. We validate the usefulness of this system through case studies set in Manhattan, a dense borough of New York City.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Shadow Accrual Maps, a class of efficient methods that exploit predictable properties of sun movement to accumulate shadows over fixed time intervals at city scale. It extends two standard shadowing techniques (shadow maps and ray tracing) and demonstrates the approach in an interactive visual analysis system called Shadow Profiler, with case studies set in Manhattan for use by city planners and architects.

Significance. If the efficiency and accuracy claims hold, the work provides a practical tool for assessing temporal shadow impacts on urban public spaces, which has clear value for environmental quality analysis in dense cities. The grounding in external sun movement data and the provision of an interactive system are strengths that enhance applicability.

major comments (2)
  1. [Results / Validation] The validation relies on visual comparisons in the Manhattan case studies, but the manuscript supplies no quantitative error analysis, timing benchmarks, or comparison against ground truth. This is load-bearing for the central efficiency and accuracy claims at city scale.
  2. [Method / Approach] The assumption that sun movement properties permit accurate accumulation without unacceptable approximation errors or per-scene tuning is stated but not tested with controlled error metrics across varying time intervals or building densities.
minor comments (2)
  1. [Abstract] The abstract could more explicitly quantify the claimed efficiency gains or list the specific extensions made to shadow maps and ray tracing.
  2. [Method] Notation for the shadow accumulation process could be clarified with a small pseudocode listing or diagram to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. We address the two major comments point-by-point below.

read point-by-point responses

  1. Referee: [Results / Validation] The validation relies on visual comparisons in the Manhattan case studies, but the manuscript supplies no quantitative error analysis, timing benchmarks, or comparison against ground truth. This is load-bearing for the central efficiency and accuracy claims at city scale.

    Authors: We agree that the current validation is limited to visual comparisons and case-study usefulness. In the revised manuscript we will add (1) wall-clock timing benchmarks of Shadow Accrual Maps versus standard shadow mapping and ray tracing on the full Manhattan scene for representative time intervals, and (2) quantitative error measurements obtained by comparing accrual results against dense per-frame ground-truth accumulation on both the real Manhattan geometry and controlled synthetic scenes. These additions will directly support the efficiency and accuracy claims. revision: yes

  2. Referee: [Method / Approach] The assumption that sun movement properties permit accurate accumulation without unacceptable approximation errors or per-scene tuning is stated but not tested with controlled error metrics across varying time intervals or building densities.

    Authors: We acknowledge that the manuscript does not present controlled error metrics. We will add a new experimental subsection that measures accumulation error (maximum and mean shadow-area deviation) as a function of time-interval length and scene density using synthetic city blocks with known ground truth. The experiments will also confirm that no per-scene parameter tuning is required, thereby testing the core assumption. revision: yes

Circularity Check

0 steps flagged

No significant circularity; algorithmic extension is self-contained

full rationale

The paper presents an algorithmic technique extending shadow maps and ray tracing by leveraging known, external properties of solar motion to accumulate shadows over fixed intervals. No equations, fitted parameters, or derivations are shown that reduce to self-definition or to inputs by construction. The central claims rest on implementation details, Manhattan case studies, and visual comparisons that are externally verifiable and do not rely on self-citation chains or renamed empirical patterns as load-bearing steps. This is the expected non-finding for a graphics systems paper whose contribution is engineering rather than a closed mathematical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The approach rests on standard computer-graphics primitives and the physical regularity of solar motion; no new free parameters, axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5703 in / 1016 out tokens · 16634 ms · 2026-05-24T23:40:11.502771+00:00 · methodology

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