Worlds-in-Miniature (WiMs): AR & Exoplanets

• Worlds-in-Miniature (WiMs) are either small-scale, manipulable models in AR/VR for navigation and interactive layout, or sub-Earth exoplanets that extend the mass-radius spectrum below terrestrial scales.
• In AR applications, WiMs leverage live depth data and scale transforms to create miniature representations that support free-form object placement and dynamic spatial manipulation.
• In exoplanet studies, WiMs (or STEPs) serve as observational testbeds for evaluating planet formation, atmospheric loss, and detection methods using transit, TTV, and Doppler techniques.

Worlds-in-Miniature (WiMs) denotes, in one research lineage, a small-scale, manipulable model of an environment that users can inspect and manipulate to effect changes in the full environment; in another usage present in the literature, the label is applied to sub-Earth-mass exoplanets that extend the planetary mass-radius distribution below terrestrial scales, into the regime occupied by Mercury, Mars, and large moons. In the first sense, WiMs originated as a VR interaction technique and were later adapted to AR through live depth-based reconstruction of a real room. In the second, WiMs correspond to what the exoplanet literature in 2013 termed subterrestrial exoplanets (STEPs), treated as an observational frontier and a testbed for planet-formation and atmospheric-evolution models (Ihara et al., 7 Jan 2026, Sinukoff et al., 2013).

1. Terminology and scope

In VR and AR, a World-in-Miniature is a small-scale, manipulable model of the environment that functions simultaneously as a map and an interaction surface. The concept originates in VR in the work of Stoakley et al. (CHI ’95), and typical uses include navigation, manipulation, and situational awareness. The AR literature summarized in 2026 uses “WIM” in the singular for the technique and notes that “WiM” and “WiMs” are often used interchangeably for the concept (Ihara et al., 7 Jan 2026).

In the exoplanet literature summarized in 2013, the same label is used in the provided material for worlds below Earth mass. There, the underlying paper itself uses the term subterrestrial exoplanets (STEPs), but the scope explicitly includes Mercury-like, Mars-like, and lunar-regime bodies, as well as planets in the Mars–Venus mass gap (Sinukoff et al., 2013).

Usage	Definition	Source
XR interaction technique	Small-scale manipulable model of an environment used to change the full environment	(Ihara et al., 7 Jan 2026)
Exoplanetary shorthand in the provided literature	Sub-Earth-mass worlds extending the mass-radius distribution below terrestrial scales	(Sinukoff et al., 2013)

The two usages are therefore linked by scale rather than by domain. In XR, the miniature is a representational interface. In planetary science, the miniature world is the object of detection and characterization.

2. WiMs as an AR interaction technique

The AR implementation described in “AR Object Layout Method Using Miniature Room Generated from Depth Data” reconstructs a room from live depth data acquired by Microsoft HoloLens 2 and converts that reconstruction into a manipulable miniature room. Users then manipulate miniature proxies of virtual objects inside that room to drive the placement and scaling of full-scale AR content anywhere in the actual room, including regions without feature points and regions behind other virtual content (Ihara et al., 7 Jan 2026).

The system is built with Unity 2019.4.22f1 and MRTK 2.6.2. Hand tracking and raycasting are provided by MRTK, and the default “Hand-Ray” interaction serves as the study’s baseline condition. Depth sensing is provided through HoloLens 2 onboard spatial mapping via MRTK’s Spatial Awareness System, which continuously reconstructs and updates the environment as a triangle mesh in real time. The miniature room is generated by shrinking that live mesh through a scale transform. Although the Spatial Awareness API provides a wireframe mesh, the authors add surface shading to improve recognition of room structure.

The miniature-generation pipeline comprises depth capture and spatial mapping through MRTK, direct use of the SDK’s dynamic triangle mesh, application of a scale transform to produce the miniature, rigid alignment of the miniature to the world frame, creation of miniature object proxies for each full-scale virtual object, and real-time updates as the room mesh changes. The implementation emphasizes limited processing load because it relies on MRTK’s built-in spatial mapping rather than custom meshing, remeshing, or segmentation. Plane detection and room segmentation are not implemented; the miniature is a direct shrink of the entire spatial map, so real objects in the room appear automatically as geometry in the miniature.

This design places WiM-based AR layout in contrast with feature- or plane-based AR placement methods such as SnapToReality and Projective Windows. Its defining characteristic is free-form placement rather than placement constrained by detected surfaces or alignment heuristics.

3. Coordinate mapping, interaction primitives, and constraints

The miniature is modeled as a scaled, rigidly transformed copy of the real room. If $\mathbf{x}_m$ is a point in miniature coordinates and $\mathbf{x}_w$ is the corresponding point in world coordinates, the mapping is

$$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$

where $s<1$ is the room scale factor, $\mathbf{R}$ is a rotation matrix, and $\mathbf{t}$ is a translation. In homogeneous form, the paper writes

$$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$

with $\mathbf{S}=\mathrm{diag}(s,s,s,1)$, $\mathbf{T}_{mr}$ mapping miniature local coordinates to a canonical room frame, and $\mathbf{T}_{dw}$ mapping from device to world frame under HoloLens stabilization (Ihara et al., 7 Jan 2026).

Manipulation propagates through this transform chain. A change in miniature proxy position $\mathbf{x}_w$0 yields

$\mathbf{x}_w$1

For rotation, if $\mathbf{x}_w$2 is the miniature rotation, then $\mathbf{x}_w$3 under aligned axes. Object scale is handled separately: scaling a miniature proxy by factor $\mathbf{x}_w$4 scales the world object’s local scale by the same factor $\mathbf{x}_w$5, independently of the room shrink factor $\mathbf{x}_w$6.

Interaction is based on direct manipulation. A one-handed pinch moves the miniature room or a miniature object; a two-handed pinch scales it, with a bounding box providing grab affordance and improved scaling precision. Because the gestures for room and object manipulation are identical, the system introduces an explicit mode switch. A hand menu exposes a button to toggle between “miniature room manipulation” and “miniature object manipulation,” and a palette of virtual objects to instantiate 1 m in front of the user. A bounding box around the miniature room signals room-manipulation mode and disappears in object-manipulation mode.

The system mirrors edits bidirectionally between miniature proxies and full-scale objects, providing immediate visual feedback. However, it does not implement surface snapping, collision avoidance, plane alignment, geometric occlusion, or collision constraints for miniature interactions. A reported failure case is miniature visibility being blocked by nearby virtual objects; the proposed mitigation is to render nearby content translucent. The lack of constraints is both an affordance and a limitation: arbitrary placement is possible, but precision support found in constraint-based AR systems is absent.

4. Empirical evaluation in AR layout

The evaluation used a within-subjects comparison between Hand-Ray and Miniature conditions in a $\mathbf{x}_w$7 room with two desks. There were $\mathbf{x}_w$8 participants, comprising 10 male and 2 female CS students, with mean age 23.17 years ($\mathbf{x}_w$9) and mean VR/AR familiarity 2.67 ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$0) on a 1–5 Likert scale. Two scenarios adapted from SemanticAdapt were used: Productivity and Leisure. Each scenario contained eight virtual objects, and participants placed 16 objects per task. Desk arrangements A1 and A2 were counterbalanced, and no arrangement effect was found. Training used a sphere for move and scale operations. Tasks were free-form and not speed-focused; participants placed objects until satisfied. Post-task measures included NASA-TLX, SUS, two additional 7-point items, and open-ended feedback (Ihara et al., 7 Jan 2026).

Measure	Hand-Ray	Miniature
Total time	560 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$1)	593 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$2)
Moving time	225 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$3)	221 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$4)
Scaling time	60.8 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$5)	52.6 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$6)
Confirmation time	275 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$7)	320 s ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$8)
NASA-TLX overall	60.2 ($$f(\mathbf{x}_m)=s\mathbf{R}\mathbf{x}_m+\mathbf{t},$$9)	49.8 ($s<1$0)
Physical demand	75.8 ($s<1$1)	45.5 ($s<1$2)
Temporal demand	30.4 ($s<1$3)	22.1 ($s<1$4)
SUS	73.3 ($s<1$5)	73.8 ($s<1$6)

The inferential results are central. Total manipulation time did not differ significantly: Wilcoxon $s<1$7, $s<1$8. Moving time was also not significantly different: Wilcoxon $s<1$9, $\mathbf{R}$0. Scaling time was not significantly different: paired $\mathbf{R}$1, $\mathbf{R}$2. Confirmation time was significantly longer for Miniature: Wilcoxon $\mathbf{R}$3, $\mathbf{R}$4. NASA-TLX overall was not significantly different: $\mathbf{R}$5, $\mathbf{R}$6. Physical demand was significantly lower with Miniature: $\mathbf{R}$7, $\mathbf{R}$8. Temporal demand was also significantly lower with Miniature: $\mathbf{R}$9, $\mathbf{t}$0. Mental demand, Performance, Effort, and Frustration showed no significant differences. SUS likewise showed no significant difference: Wilcoxon $\mathbf{t}$1, $\mathbf{t}$2. The additional items—“easy to place at desired location” and “easy to create intended AR layout”—also showed no significant differences.

Qualitative feedback explains the metric pattern. Participants associated Miniature with reduced physical fatigue because it required lower arm elevation and smaller motions, and with lower temporal pressure because the bird’s-eye view made size, position, and “balance of the whole” easier to understand. At the same time, confirmation overhead increased because users frequently alternated attention between miniature and full-scale views, and some reported orientation mismatches. Participants also distinguished between coarse and fine control: Miniature was judged better for large movements, while Hand-Ray was judged better for fine adjustments. The authors therefore propose a hybrid design in which miniature manipulation supports coarse layout and direct manipulation supports final refinement.

5. WiMs as sub-Earth exoplanets: definition and detection

In the exoplanetary usage summarized from “Below One Earth Mass: The Detection, Formation, and Properties of Subterrestrial Worlds,” WiMs correspond to sub-Earths or STEPs. The definition is based on radius $\mathbf{t}$3 and mass $\mathbf{t}$4 under an Earth-like rocky composition. Using the Valencia et al. (2007) mass–radius relation,

$\mathbf{t}$5

the STEP boundary is set at $\mathbf{t}$6, corresponding to $\mathbf{t}$7 for rocky compositions. On this definition, a Venus twin at $\mathbf{t}$8 and $\mathbf{t}$9 lies just above the threshold, while Mercury at $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$0, $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$1 and Mars at $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$2, $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$3 are canonical cases. The scope also includes bodies in the Mars–Venus mass gap and extends to the lunar regime exemplified by PSR B1257+12A at approximately $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$4. As of April 2013, Kepler had identified 7 confirmed STEPs and 36 candidates (Sinukoff et al., 2013).

Kepler transit photometry was the principal discovery channel. The transit depth obeys $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$5, and the repeated-transit detection significance scales approximately as $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$6, where $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$7 and $$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$8 is the relevant CDPP. Rearranging, the paper gives

$$\mathbf{X}_w=\mathbf{T}_{dw}\mathbf{S}\mathbf{T}_{mr}\mathbf{X}_m,$$9

with $\mathbf{S}=\mathrm{diag}(s,s,s,1)$0 as the adopted threshold. The practical implication is improved sensitivity around smaller stars and at shorter periods. A $\mathbf{S}=\mathrm{diag}(s,s,s,1)$1 planet produces approximately 20 ppm around a G5 dwarf and approximately 50 ppm around an M2 dwarf. Assuming 6.8 years of Kepler observing and using M-dwarf parameters from Muirhead et al. (2012b), the study found that if all additional planets transited, Kepler could detect sub-Earth-size planets out to $\mathbf{S}=\mathrm{diag}(s,s,s,1)$2 days around approximately 50% of those stars. The detectability parameter $\mathbf{S}=\mathrm{diag}(s,s,s,1)$3 peaks near 80 ppm across Kepler targets, and about a quarter of targets have $\mathbf{S}=\mathrm{diag}(s,s,s,1)$4 ppm. For the 25% most favorable targets, Kepler should detect roughly 1% of $\mathbf{S}=\mathrm{diag}(s,s,s,1)$5 planets to $\mathbf{S}=\mathrm{diag}(s,s,s,1)$6 d, while detection efficiency for STEPs in the $\mathbf{S}=\mathrm{diag}(s,s,s,1)$7–10 d range is approximately 5–10%.

Transit timing variations provide a complementary route, but the signal is intrinsically small for sub-Earth perturbers. The amplitude is given as

$\mathbf{S}=\mathrm{diag}(s,s,s,1)$8

with $\mathbf{S}=\mathrm{diag}(s,s,s,1)$9. Because $\mathbf{T}_{mr}$0 scales with perturber mass, WiM-mass companions generally yield very small TTVs, at or below approximately 20 s for Earth-mass perturbers near resonance. HST can reach approximately 5 s in select cases, but the paper judges practical TTV detectability for this regime to be more plausible with JWST.

For Doppler detection, the RV semi-amplitude for circular orbits is

$\mathbf{T}_{mr}$1

A $\mathbf{T}_{mr}$2 planet at $\mathbf{T}_{mr}$3 d around a $\mathbf{T}_{mr}$4 star gives $\mathbf{T}_{mr}$5 cm s$\mathbf{T}_{mr}$6, and approximately 14 cm s$\mathbf{T}_{mr}$7 around a Sun-like star. These values sit below the performance of many precision spectrographs then operating at 1–3 m s$\mathbf{T}_{mr}$8, though HARPS had reached on-sky detections near 51 cm s$\mathbf{T}_{mr}$9 in the contested $\mathbf{T}_{dw}$0 Cen B claim. The paper identifies HARPS-North, ESPRESSO, and CODEX as steps toward the required cm s$\mathbf{T}_{dw}$1 regime.

Microlensing extends sensitivity to wider separations, near a few AU. Ground-based surveys had reached a few Earth masses, but space-based, diffraction-limited photometry was judged necessary for routine Earth-size detections in crowded Bulge fields. Euclid, WFIRST, and the NEW-WFIRST concept are described as capable of detecting Mars-size planets, and for dwarf sources potentially down to a few lunar masses. The 2.4 m hardware in the NEW-WFIRST concept could triple the Mars-mass planet yield relative to the WFIRST design reference mission.

The section of the paper on exomoons is adjacent to the WiM concept because moon transits, mutual events, and TTV/TDV pairs can reach Mars-scale satellites. Kipping (2009) is cited as estimating that Kepler could detect exomoons with masses $\mathbf{T}_{dw}$2 via TTV/TDV alone, but the HEK program had not yet produced a robust detection.

6. Demographics, formation channels, and mass-budget scaling

The 2013 census lay near Kepler’s completeness boundary. Planet occurrence was described as rising steeply with decreasing size down to approximately $\mathbf{T}_{dw}$3, appearing flat from 3 to $\mathbf{T}_{dw}$4, and in first-pass pipelines sensitive to approximately $\mathbf{T}_{dw}$5 remaining flat or increasing below $\mathbf{T}_{dw}$6 for $\mathbf{T}_{dw}$7–10.8 d, although the detection rate there was below 50%. From approximately 33,000 favorable targets and an assumed approximately 5% detection efficiency at $\mathbf{T}_{dw}$8–10 d, the authors estimated that at least 2–3% of stars host $\mathbf{T}_{dw}$9–$\mathbf{x}_w$00 planets with $\mathbf{x}_w$01 d; the estimate was explicitly described as tentative and likely a lower limit because of uncertainties in completeness, stellar radii, and stellar noise (Sinukoff et al., 2013).

The demographic role of M dwarfs was treated as mixed. Small stellar radii improve transit detectability, but many M dwarfs are faint and photometrically noisy in Kepler data. Correcting systematically overestimated KIC M-dwarf radii would improve the detectability metric $\mathbf{x}_w$02. Theory suggests that low-mass stars might preferentially host smaller planets if disk surface density scales down with stellar mass, but the observational support was described as weak, and small-planet occurrence in the $\mathbf{x}_w$03–$\mathbf{x}_w$04 regime was noted as broadly independent of metallicity.

Formation pathways are multiple rather than unique. The paper identifies in situ accretion through oligarchic growth and giant impacts, migration of embryos under Type-I torques with accompanying scattering and inward shepherding, collisional stripping that produces Mercury-like high-density remnants, and photoevaporation that removes atmospheres and, in ultra-hot cases, even mantles. The mass budget is set by the initial disk surface density $\mathbf{x}_w$05. In Kokubo (2006), assuming $\mathbf{x}_w$06, the mean masses of the largest and second-largest planets between 0.5 and 1.5 AU scale as $\mathbf{x}_w$07 and $\mathbf{x}_w$08, where $\mathbf{x}_w$09 is the surface density at 1 AU. The Minimum Mass Solar Nebula is given as $\mathbf{x}_w$10, whereas a Minimum-Mass Extrasolar Nebula inferred from Kepler super-Earths is described as approximately $\mathbf{x}_w$11 MMSN and therefore conducive to larger planets.

For late M dwarfs interior to approximately 0.1 AU, MMSN-like disks rarely form planets more massive than Mars. A $\mathbf{x}_w$12 MMSN disk can produce 3–5 close-in planets averaging 0.7–0.8 $\mathbf{x}_w$13. The interpretation offered in the summary is that WiM production is favored in lower-$\mathbf{x}_w$14 environments and-or for lower-mass stars, especially where migration is less efficient.

7. Physical properties, atmospheric escape, and observational outlook

The physical characterization problem begins with bulk density. If transit radii are paired with Doppler masses, the mean density $\mathbf{x}_w$15 can be compared with rocky, volatile-rich, and metal-rich mass–radius curves. The paper notes, however, that practical inference is limited by cm s$\mathbf{x}_w$16-level RV requirements, stellar radius errors of at least 3%, and interior-model degeneracies, so only the most extreme compositions are likely to be distinguishable robustly (Sinukoff et al., 2013).

Atmospheric retention is framed by escape velocity and irradiation. The relevant scalings are

$\mathbf{x}_w$17

and

$\mathbf{x}_w$18

For a tidally locked, atmosphere-free planet with Mercury-like albedo, the substellar temperature scales as

$\mathbf{x}_w$19

In the energy-limited hydrodynamic regime, the mass-loss rate is approximated by

$\mathbf{x}_w$20

and the paper also adopts the simplified order-of-magnitude form

$\mathbf{x}_w$21

With stellar X-ray, EUV, and Ly$\mathbf{x}_w$22 histories from Ribas (2005) and Sanz-Forcada (2011), the paper concludes that even Mercury-size planets at approximately 10-day periods can lose thousands of bars over Gyr, especially around Sun-like stars.

The threshold to hydrodynamic escape is described through the Jeans parameter $\mathbf{x}_w$23, with transition when $\mathbf{x}_w$24 at the exobase. Under a conductive-balance treatment for $\mathbf{x}_w$25 atmospheres, the paper shows that Mercury would have lost any $\mathbf{x}_w$26 atmosphere at all considered epochs, while Mars and Venus would have undergone hydrodynamic loss in the past. M-dwarf cases are somewhat mitigated by lower luminosities but can still yield escape for very short-period planets. Additional erosion by stellar-wind sputtering and impacts further disfavors atmosphere retention on hot WiMs.

At the most irradiated end, WiMs may host magma oceans and silicate-vapor atmospheres containing SiO, O, and Si. Continuous escape may erode silicate mantles and leave high-density “iron planets.” KIC 12557548 is cited as an observational hint: a variable-depth transit interpreted as a disintegrating Mercury-size object with a dust coma. Around very low-luminosity M dwarfs, equilibrium temperatures are stated to be approximately ten times lower, making silicate mantle loss unlikely.

The principal characterization prospect discussed is JWST eclipse photometry and thermal phase-curve analysis. Atmosphere-free WiMs should show large day–night contrast and pronounced orbital phase modulation, whereas thick-atmosphere planets should exhibit muted phase curves. For a transiting WiM orbiting an M0 dwarf at 10 pc, the study assesses NIRCam and MIRI and concludes that practical detectability is limited not by isolated-source sensitivity but by photometric stability in subtracting the stellar signal during secondary eclipse. Spitzer had achieved approximately $\mathbf{x}_w$27 fractional stability; WiM detection generally requires $\mathbf{x}_w$28. Under $\mathbf{x}_w$29 stability, JWST could detect thermal emission from sub-Earths lacking substantial atmospheres; at $\mathbf{x}_w$30, detection would be limited to larger or hotter cases.

The broader observational outlook combined Doppler and microlensing advances. HARPS-N was described as operational at approximately 50 cm s$\mathbf{x}_w$31, ESPRESSO as targeting approximately 10 cm s$\mathbf{x}_w$32 with a goal of a few cm s$\mathbf{x}_w$33, and CODEX as aiming at approximately 2 cm s$\mathbf{x}_w$34. At approximately 2 cm s$\mathbf{x}_w$35, Mars-size planets with $\mathbf{x}_w$36 d around nearby bright stars were judged within reach if stellar jitter could be sufficiently averaged down. Space microlensing was expected to provide a complementary census at several AU, routinely reaching Mars masses and potentially lunar masses for dwarf sources.

The notable systems emphasized in the synthesis include Kepler-37b at approximately $\mathbf{x}_w$37, the compact Kepler-42 system around an M dwarf, the five-planet Kepler-20 system containing two sub-Earths, KOI 55.01 and 55.02 around a hot subdwarf with dayside temperatures above 8000 K, the Spitzer candidates UCF-1.01 and UCF-1.02, and the lunar-mass pulsar planet PSR B1257+12A. Collectively, these cases exhibit the diversity of below-Earth worlds in orbital period, host type, and likely evolutionary pathway.