Domain: Humanities and Social Sciences — Geography
Target concept: Equal-area projection: No area distortion (Greenland is smaller than Africa), with slight shape distortion

Video generation prompt: Start with a familiar Mercator world map, and gradually transition to an equal-area map. Emphasize the proportional rescaling of land areas, while coastlines undergo slight distortion. Clearly label Greenland and Africa. Focus solely on the process of projection change.

Evaluation guide:
Target concept: Equal-area projection is a cartographic method that preserves relative surface area between geographic features while permitting controlled, non-uniform shape distortion. Minimum mechanistic assumptions: (i) map projections are mathematical transformations of spherical coordinates onto a plane; (ii) area preservation implies Jacobian determinant of the transformation equals 1 everywhere (up to scale); (iii) shape distortion arises from unequal scaling along orthogonal directions (e.g., meridional vs. parallel stretching). Expected phased storyline: (Phase 1: Anchor) Start with canonical Mercator: Greenland oversized, vertical meridians, sharp coastlines. (Phase 2: Causal Transition) Smooth morph where meridians curve, parallels compress near poles, and Greenland's bounding box shrinks *proportionally* while warping, simultaneously validating area reduction and shape change. (Phase 3: Verification State) End on equal-area frame where Greenland is unambiguously smaller than Africa, coastlines are recognizably distorted but intact, and labels remain anchored. Visibility constraints: Must be viewable at 1080p on standard monitor; Africa must span noticeably more horizontal screen width than Greenland in the final frame (Africa's real east-west extent is roughly 19% of a full 360°-wide equirectangular map, versus Greenland's much narrower span, so exact percentages will vary with framing but the size relationship must be unambiguous); all distortion must be discernible without zoom or annotation.

Manual:
I. Basic Demonstration Information
Demonstration Title: Equal-Area Projection Transformation (Mercator → Equal-Area) Demonstration
Subject: Humanities and Social Sciences - Geography - Map Projections
Demonstration Purpose: To visually demonstrate how equal-area projections eliminate area distortion (e.g., Greenland is correctly shown smaller than Africa) while introducing slight shape distortion; to contrast the familiar Mercator projection with an area-accurate alternative; and to train visual recognition of projection-driven rescaling versus shape warping.

II. Demonstration Carrier/Equipment
Core Carrier: Animated digital world map sequence (10-second video)
Auxiliary Equipment: High-resolution display (≥1920×1080), neutral gray background, vector-based projection morph engine (e.g., D3.js or custom geospatial interpolator)

III. Demonstration Content Description
Layout: Full-screen centered world map on neutral background. No UI chrome, no navigation controls, no scale bar.
State Control: Animation runs autonomously at 30 fps; starts paused on Mercator, then plays once — no user interaction.
Comparison Baseline: Mercator frame (t=0s) and final equal-area frame (t=10s) serve as fixed visual anchors; Greenland and Africa are the sole labeled landmasses.

IV. Observation of Core Phenomena
Mercator Frame (t=0s): Greenland occupies ~⅓ the vertical height of the map and appears larger than Africa; meridians are perfectly vertical and parallel; coastlines are crisp and familiar.
Transition Phase (t=1s–9s): Greenland visibly shrinks in area *while* its shape distorts — east-west width compresses, north-south length shortens asymmetrically; Africa expands relatively, with gentle coastal bending (e.g., Gulf of Guinea softens, Horn of Africa rounds); meridians gradually curve inward toward poles; parallels space more evenly.
Equal-Area Frame (t=10s): Greenland is clearly smaller than Africa (area ratio ~1:14); coastlines retain recognizability but show measurable shape deviation (e.g., Greenland’s northern coast curves inward, southern tip flattens); labels ‘Greenland’ and ‘Africa’ remain centered, legible, and unmoving relative to landmass centroids.
Characteristic Stability: Throughout, no landmass changes color, opacity, or texture; no extraneous objects (ships, clouds, borders) appear; projection change is the *only* dynamic variable.

V. Summary of Key Knowledge Points and Principles
Core Concept Definition: Equal-area projection preserves relative surface area across the entire map — enabling accurate comparison of landmass sizes — at the expense of exact shape fidelity (Tissot’s indicatrix shows circles become ellipses of equal area).
Geographic Significance:
• Area Integrity: Enables correct quantitative reasoning (e.g., Africa’s 30M km² vs. Greenland’s 2.1M km² is visually proportionate).
• Shape Trade-off: Coastline distortion is necessary and bounded — it does not obscure identification but reflects mathematical compromise.
• Cognitive Reorientation: Challenges intuition built on Mercator (used in web maps), reinforcing that map projections are *choices*, not truths.

VI. Demonstration Precautions
• Animation must be mathematically interpolated — no cross-fade or scale-only transform.
• Labels must use absolute positioning tied to landmass centroids, not screen coordinates.
• Final frame must match a canonical equal-area projection (e.g., Mollweide, Eckert IV, or Hammer) — not a custom approximation.
• Duration strictly 10 seconds (±0.2s); no audio, no narration, no annotations beyond two labels.

Prompt Grounding rubric:
level_1: No Mercator-style map appears at any point; there is no visible transition to a different map projection; Greenland and Africa are missing, unlabeled, or the labels are swapped onto the wrong landmass; Greenland appears the same size as or larger than Africa throughout; the coastlines of both landmasses look identical in every frame, showing no change in shape at all.
level_2: A single static world map is shown (either Mercator-style or equal-area-style), but there is no visible transition between the two; Greenland and Africa both appear on screen but are unlabeled, or their labels sit far from the corresponding landmass; Greenland still looks as large as or larger than Africa; the coastlines look the same before and after, with no visible reshaping.
level_3: The video clearly shows two distinct map states: it opens on a Mercator-style map with Greenland drawn oversized, then switches, without a gradual in-between, directly to an equal-area-style map; Greenland and Africa are both labeled, though the labels may flicker, overlap the coastline, or briefly lose contrast against the map; by the final frame Greenland is visibly smaller than Africa; however the coastlines of Greenland and Africa look essentially identical in the opening and closing frames, with no visible reshaping in between.
level_4: The map morphs smoothly and continuously from the Mercator-style view to the equal-area-style view over the full clip (roughly 8–10 seconds), rather than cutting abruptly between the two; 'Greenland' and 'Africa' are labeled in high-contrast, easy-to-read text that stays on screen and stays legible throughout; Greenland's on-screen size shrinks gradually relative to Africa's rather than jumping straight to its final size; both coastlines visibly reshape over the course of the clip (e.g., Greenland's outline narrows, Africa's outline softens slightly) in a way that looks consistent across the whole map rather than only in one region; no extra elements appear on screen (no grid overlay, no legend box, no hands, no on-screen narration text).
level_5: The full ~10-second clip shows a single continuous morph: it opens on a recognizable Mercator-style map (Greenland enlarged near the top, coastlines crisp, meridians running straight up and down) and ends on a recognizable equal-area-style map; Greenland's on-screen size shrinks steadily across the whole clip rather than in sudden jumps, while Africa's on-screen size stays visibly the larger of the two at every point after the transition begins; both landmasses' coastlines visibly reshape in a plausible, gradual way (e.g., Greenland's outline becomes noticeably more compact, Africa's outline shifts only slightly) rather than snapping to a new shape; the 'Greenland' and 'Africa' labels stay legible and positioned over their respective landmasses for the entire clip, never overlapping or drifting onto the wrong landmass; there are no frozen frames, sudden jumps, or stray visual glitches anywhere in the sequence.

Scientific and Causal Correctness rubric:
level_1: Greenland looks as large as or larger than Africa in every frame, including the last one; nothing about the animation suggests the size change is driven by a change in map projection (e.g., the map could just as easily be zooming or panning); the 'Greenland' or 'Africa' label sits over the wrong landmass; the grid of meridians and parallels, if shown, bends in ways that don't correspond to any real projection (e.g., lines tear or cross themselves).
level_2: By the final frame Greenland still looks close to Africa in size, appearing more than roughly 70% of Africa's visual on-screen area, rather than clearly smaller (a real equal-area map would show Africa roughly 14 times Greenland's area); the transition looks like a simple zoom, pan, or cross-fade rather than a projection change, so there's no visual cue that a different projection is being used; the meridian and parallel grid lines, if present, stay perfectly straight and evenly spaced throughout, which would not happen in a real Mercator-to-equal-area transition.
level_3: By the final frame Greenland is clearly and unambiguously smaller than Africa, matching the real-world area relationship; however the transition itself doesn't visually demonstrate why: for example the map cross-fades or swaps instantly between the two states rather than morphing, and any grid of meridians and parallels stays static rather than curving inward or compressing near the poles.
level_4: The projection change is visually grounded in what a real Mercator-to-equal-area transition looks like: meridians that are straight and parallel in the opening frame curve and converge more toward the poles by the final frame; parallels that are stretched apart near the poles in the opening frame become more evenly spaced by the final frame; Greenland's outline narrows in step with its shrinking area rather than shrinking uniformly in every direction; Africa's outline also shifts slightly, consistent with a real equal-area re-projection, and nothing in the map appears to both stretch and shrink in the same spot at the same time.
level_5: The projection change stays scientifically consistent throughout: Greenland never becomes visually larger relative to Africa at any point during the morph, only smaller or equal as time progresses; Greenland's outline compresses more in one direction (east-west) than the other, consistent with how real equal-area projections reshape it; Africa's coastline shifts only mildly and unevenly (for instance, one coast bending slightly more than the opposite coast), matching how real equal-area projections such as Eckert IV distort Africa; the meridian and parallel grid, if shown, curves and compresses toward the poles in a smooth, symmetric way around the map's center line, consistent with a genuine projection formula rather than an arbitrary warp.

Spatiotemporal Consistency rubric:
level_1: The map jumps between visually unrelated states with no morph connecting them (e.g., it cuts from the Mercator-style map straight to an entirely different-looking sketch); the 'Greenland' or 'Africa' label suddenly disappears and reappears in a different spot; Greenland or Africa rotates or flips to a totally different orientation from one frame to the next; the video freezes on a single frame for a long stretch or plays part of the sequence backward.
level_2: The transition contains at least two noticeable cuts or freezes rather than one continuous morph; a label jumps to a new position more than twice without smoothly sliding there; Greenland and Africa change size on noticeably different schedules (e.g., Greenland finishes shrinking while Africa is still visibly changing size well afterward); grid lines, if shown, blink on and off rather than deforming continuously; the pacing feels uneven, e.g. a long freeze on the Mercator map followed by a rushed transition.
level_3: The morph is mostly continuous, but with a few noticeable rough spots: a label visibly jumps or jitters at least once; Greenland and Africa stay in roughly the same on-screen positions relative to each other, but their resizing isn't quite synchronized (one clearly finishes changing size well before the other); any grid lines shown lose their symmetry around the map's center for a stretch of the clip; the clip's overall pacing feels a little jerky rather than smooth, even though it runs roughly the expected length.
level_4: The morph looks smooth and well-synchronized throughout: the 'Greenland' and 'Africa' labels track their landmasses with no visible lag or overshoot; any grid lines shown deform in step with the landmasses rather than lagging behind; every frame shows Greenland and Africa as intact, non-overlapping shapes with no torn or self-intersecting coastlines; the pacing feels even and consistent from start to finish, without any single moment of visible speed-up or freeze.
level_5: Spatiotemporal continuity holds up at every point in the clip: Greenland's on-screen size shrinks in one smooth, uninterrupted motion with no point where the shrinking visibly reverses, stalls, or jumps to a different rate; Greenland's outline reshapes gradually and continuously as it shrinks, with no abrupt jump from one outline to a very different one between adjacent frames; Africa's on-screen position stays essentially still while only its outline reshapes smoothly, so it reads as a stable anchor throughout the clip; any grid lines shown deform continuously and keep a plausible, evenly-changing spacing, with no lines crossing, vanishing, or bunching up abruptly; the whole clip plays back smoothly with no ghosting, stutter, or flicker visible anywhere.