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Computational Design of Free-Form Lampshades

Hiro Nakasuji, Soma Yokota, Yutaka Ohtake, Yuki Koyama

arXiv:2610.05770v1cs.GR

TL;DR

Complex lampshade shapes make illumination difficult to control, and translucent volumetric transport compounds the design challenge. The paper optimizes internal cavity geometry and light placement with calibrated differentiable rendering, then validates the approach on five fabricated shades with uniform luminance.

  • Problem

    Complex shade geometries make illumination difficult to predict and control, while translucent volumetric light transport complicates design with a fixed outer shape.

    Source: §1 · pp. 1–2

  • Method

    The method initializes light count, positions, and cavity geometry, then jointly refines cavity geometry and light positions through constrained differentiable rendering after material calibration.

    Source: §1 · p. 2

  • Results

    Five fabricated lampshades of varying geometric complexity achieve uniform luminance consistent with the optimization target.

    Source: §9 · p. 10

  • Takeaways & Limitations

    The results support a design-to-fabrication pipeline for translucent free-form lampshades with controlled illumination.

    Source: §1 · p. 2, §9 · p. 10

    Thin features such as ears, horns, and limbs can remain underlit when their interior volume cannot contain a candidate sphere light of radius 6 mm.

    Source: §8.1 · p. 9

Abstract

from arXiv · show

Conventional lampshades are predominantly restricted to simple geometries, owing to the difficulty of controlling optical functions across complex shapes. We present a computational design method that enables 3D-printable lampshades with complex free-form shapes to achieve controlled illumination, such as uniform luminance. Given an arbitrary shape, our method determines the internal cavity geometry and the number and placement of lights in two stages: an initialization stage fixes the number of lights and establishes their initial positions and the initial cavity geometry, after which gradient-based optimization jointly refines the cavity geometry and light positions via differentiable rendering subject to geometric constraints. We calibrate the material parameters of the translucent shade material prior to optimization to improve the agreement between simulation and the fabricated result. We validate our approach by 3D-printing five lampshade designs of varying geometric complexity and demonstrate that the fabricated lampshades achieve reasonably uniform luminance.

1 Introduction

Conventional lampshades are largely limited to simple shapes because illumination is difficult to control on complex geometries. The paper presents a calibrated computational design pipeline and validates it on five fabricated free-form shades.

1 Introduction

  • Conventional shades are largely restricted to simple geometries because predicting and controlling illumination on complex shapes is difficult.The challenge is compounded by translucent volumetric light transport and a visible outer shape that cannot be altered to achieve the target illumination.Source: §1 · pp. 1–2
  • Without a principled design method, a complex free-form shade can produce a bright hot spot and dark areas instead of uniform luminance.The paper targets this gap by calibrating the translucent material before optimization to improve agreement with physical appearance.Source: Figure 2 · p. 2, §1 · p. 2
  • Five fabricated designs of varying geometric complexity achieve reasonably uniform luminance through a pipeline that jointly optimizes internal cavity geometry and light placement.The method first initializes the light count, positions, and cavity, then refines the cavity and lights with gradient-based optimization subject to geometric constraints.Source: §1 · p. 2

2 Related Work

Prior fabrication work controls light through object geometry or internal delivery pathways, while differentiable rendering offers image-based gradient optimization. This work applies these ideas to translucent free-form shades by jointly optimizing internal geometry and light placement.

2.1 Functional Fabrication with Lights

  • Earlier functional-fabrication methods modify object geometry or internal light pathways, while lampshade designs target projected patterns using perforations or stereographic patterns.Examples include geometry optimized for caustics [2010; 2011; 2014], light pipes and optical-fiber routing [2012; 2014], perforated shades [2016], and stereographic-pattern projections [2024].Source: §2.1 · p. 2
  • This work instead targets translucent 3D-printed material, jointly optimizing the internal cavity and fed-light placement for a uniformly luminous shade.Light interacts through refraction, scattering, and absorption throughout the material volume.Source: §2.1 · p. 2

2.2 Design with Differentiable Rendering

  • Differentiable rendering provides analytic image derivatives for gradient-based inverse design, while geometry gradients can be noisy and localized.Large Steps uses mesh-Laplacian preconditioning to regularize vertex updates and improve robustness for large-scale shape deformation.Source: §2.2 · pp. 2–3
  • The pipeline applies Large Steps to the internal cavity under a fixed boundary and uses Mitsuba 3 with physically calibrated participating media.Initialization and differentiable-rendering optimization produce the refined cavity geometry and light placement.Source: §2.2 · p. 3, Figure 3 · p. 3

3 Design Optimization

The method optimizes an internal cavity and light positions for a fixed exterior using an image-based objective and geometric penalties. It initializes the cavity and lights, then refines their geometry and positions while enforcing spacing and collision constraints.

3 Design Optimization

  • The design optimization assumes that translucent-material parameters have already been calibrated independently.The calibration is described separately in Section 5.Source: §3 · p. 3

3.1 Problem Formulation

  • The fixed exterior is paired with an optimizable cavity mesh and light positions, chosen to minimize rendered-image error plus collision and spacing penalties.The image fidelity term uses MSE against a target luminance image, though other differentiable losses are possible.Source: §3.1 · p. 3

3.2 Scene Initialization

  • The initial cavity is an inward offset of the exterior mesh, while greedy light placement adds valid cavity candidates that most reduce Φ until improvement stops or the cap is reached.The offset margin is 5 mm in the experiments; the 10-light cap was never reached.Source: §3.2 · pp. 3–4, Figure 4 · p. 4

3.3 Optimization

  • Differentiable rendering supplies gradients for cavity vertices and light positions; Large Steps preconditioning smooths mesh updates to reduce folds and self-intersections.The preconditioner attenuates high-frequency mesh-gradient components, favoring smooth, large-scale deformations over fine detail.Source: §3.3 · p. 4

3.4 Constraints

  • The constraint objective penalizes exterior–cavity intersections, lights approaching or crossing the cavity, and lights that are too close to each other.The constraint terms use squared hinge losses on signed distances or Euclidean distances; the experimental light radius is 6 mm.Source: §3.4 · p. 4

4 Fabrication

The lampshades are fabricated from translucent polycarbonate using pseudo sphere lights suspended at optimized positions inside the cavity.

4 Fabrication

  • Each pseudo sphere light uses a 3D-printed PLA diffuser ball coupled to a thin optical fiber, enabling placement in compact cavities and approximating the isotropic source used in simulation.Printed struts suspend the lights and route the fibers; the shade is printed as two halves that are joined during assembly.Source: §4 · p. 4

5 Material Parameter Calibration

The material parameters are calibrated to improve agreement between simulation and fabricated shades, with procedures tailored to light intensity, surface roughness, and volumetric scattering.

5 Material Parameter Calibration

  • Material calibration targets the optical parameters of the translucent shade because errors in them can make simulated appearance diverge from fabricated results.The parameters depend on the material and printer, so users can run the procedure for their own setup.Source: §5 · p. 5

5.1 Light Intensity

  • Light intensity is calibrated by matching the mean aperture-region pixel intensity in a photograph to a rendering of the same scene.The bright source requires lower ISO and faster shutter speed to avoid saturation; intensity must be rescaled for later exposure settings.Source: §5.1 · p. 5

5.2 Surface Roughness Parameters

  • Roughness is fitted from reflection-decay distances along both surface tangent directions, using an opaque cube to isolate surface reflection from volumetric scattering.The calibrated parameters are αu = 0.091 and αv = 0.434.Source: §5.2 · p. 5, Figure 6 · p. 5

5.3 Volumetric Scattering Parameters

  • Volumetric scattering parameters σt, albedo, and g are jointly fitted to cube photographs from three viewing directions using a weighted image objective.The calibrated values are σt = 0.273 mm−1, albedo = 0.870, and g = 0.481; the pixel mask excludes boundary regions.Source: §5.3 · p. 5

6 Experiments

The experiments show that joint optimization improves the squirrel lampshade’s target appearance, while material calibration improves simulation agreement and geometric constraints keep designs physically realizable.

6.1 Setup

  • Three-view cube calibration precedes optimization; the squirrel target is luminance 0.4 over its silhouette, and each 30,000-iteration run takes about 10 h.Source: §6.1 · pp. 5–6, Figure 7 · p. 6

6.2 Design Optimization Results

  • MSE falls from 0.0159 for the naive single-light design to 0.0131 after initialization and 0.0054 after optimization, whose fabricated result appears visually uniform.Source: §6.2 · p. 6, Figure 8 · p. 6

6.3.1 Effect of Material Parameter Calibration.

  • Calibrated parameters make the simulation more closely match the fabricated lampshade, while uncalibrated parameters fail to reproduce its appearance.Source: §6.3.1 · pp. 6–7, Figure 9 · p. 7

6.3.2 Effect of Geometric Constraints.

  • Without C(x), violations worsen from mesh penetration and an embedded light at 10,000 iterations to a light exiting the outer mesh by 30,000, making designs unrealizable.Source: §6.3.2 · p. 7

7 Demonstrations

Four additional shapes demonstrate the method across different geometries: their main surfaces are relatively uniformly illuminated, while narrow extremities can remain underlit.

7 Demonstrations

  • Four additional shapes—cube, Spot, Bimba, and Stanford Bunny—were demonstrated with uniform-luminance targets and relatively uniform results on their main surfaces.Source: §7 · p. 7
  • Four lights produce uniform luminance across the cube’s flat faces, though its corners and edges are slightly dimmer than face centers.Source: §7 · p. 7
  • Spot’s two lights yield relatively uniform luminance on the body, but thin limbs, horns, and ears stay dark because they cannot fit a sphere light.Source: §7 · p. 7
  • With C(x), the internal mesh and lights remain within the valid cavity; without it, violations worsen until a light exits the external mesh.Source: Figure 10 · p. 7
  • Bimba’s four lights—two in the head and two in the body—produce relatively uniform luminance despite detailed surface features.Source: §7 · p. 7
  • Three lights produce relatively uniform luminance over the Stanford Bunny’s main body, while its narrow ears remain insufficiently illuminated.Source: §7 · p. 7

8 Discussion

The discussion identifies limits in target specification, simulation-to-fabrication fidelity, and design expressiveness, then outlines extensions and more rigorous evaluation. These include structured targets, multiple viewpoints, color, and spatially varying material properties.

8.1 Limitations

  • Users set the target image’s absolute luminance, and an infeasible value can bias the solution or leave luminous flux unused.Proposed remedies are a scale-invariant objective or joint optimization of light intensity.Source: §8.1 · p. 7
  • Simulation and fabrication can differ because of imperfect material estimates, idealized emitters, incompletely modeled print anisotropy, and unmodeled strut shadows.Surface roughness is estimated from black PLA rather than translucent PC, and the omitted strut shadows can create localized dark regions.Source: §8.1 · p. 9
  • Thin features can remain underlit when the inward-offset cavity leaves no room for a contained 6 mm-radius light.The radius is a fabrication choice that could be reduced toward the fiber thickness; adaptive initialization is another proposed remedy.Source: §8.1 · p. 9
  • Cavity and light-position variables may not direct enough flux into very thin or deeply concave regions; spatial material maps or internal reflectors could add control.The proposed material-map direction includes locally adding high-reflectance or high-scattering material to difficult-to-illuminate areas.Source: §8.1 · p. 9, §8.2 · p. 9

8.2 Future Work

  • Non-uniform luminance targets require no fundamental formulation change, but reliable pattern reproduction depends on better simulation-to-fabrication fidelity and remains experimentally unvalidated.Small simulation errors can distort spatially structured patterns.Source: §8.2 · p. 9
  • The current objective uses one front-facing image, so a target met from that view does not guarantee the same luminance distribution from other directions.A weighted combination of renderings from multiple viewpoints is proposed.Source: §8.2 · p. 9
  • Experiments optimize grayscale luminance; color-pattern design would require a multi-channel target and an appropriate colorimetric loss.The passage notes that differentiable path tracers such as Mitsuba 3 support multispectral rendering.Source: §8.2 · p. 9
  • Simulation is assessed with MSE, but fabricated appearance is evaluated qualitatively; photometric measurements and perturbation tests could assess transfer and robustness.Perturbations to optimized light positions and cavity geometry could clarify the contribution of gradient-based refinement.Source: §8.2 · p. 9

9 Conclusion

The paper presents a two-stage computational method for designing free-form 3D-printed lampshades, refining internal cavities and light positions with differentiable rendering. Calibration and fabrication of five designs support the reported result of uniform luminance consistent with the optimization target.

9 Conclusion

  • The method initializes design variables, then jointly refines cavity geometry and light positions through constrained gradient-based optimization with differentiable rendering.The design variables include the internal cavity and the number and placement of lights.Source: §9 · pp. 9–10
  • Material calibration improves simulation-to-fabrication agreement, and five fabricated lampshades of varying complexity achieve uniform luminance consistent with the target.Source: §9 · p. 10
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