Domain: Humanities and Social Sciences — Geography
Target concept: Projection

Video generation prompt: Select different map projections sequentially (Mercator projection → Transverse Mercator projection). Display projection distortion maps with error annotations. Set up a color scale legend for the distortion metric and keep it visible and unchanged throughout. Smoothly switch between projections to demonstrate changes in distortion distribution on the map.

Evaluation guide:
(i) Target concept: Cartographic projection distortion is a function of mathematical transformation from sphere to plane; different projections prioritize different geometric properties (conformality, equivalence, equidistance), resulting in spatially structured, predictable error fields.
Minimum mechanism: The video must encode distortion magnitude as a continuous scalar field over the map surface, mapped to color, with annotation markers placed only where field magnitude exceeds a perceptible threshold, and this field must transform continuously under valid projection reparameterization.
(ii)Storyline: Frame 0–3: Mercator projection dominates screen; distortion map overlays with high-error annotations near Greenland/Antarctica; legend shows red (high) → blue (low) scale. Frame 4–6: Seamless morph begins: graticule curves smoothly, landmasses stretch/compress along meridians, error annotations migrate toward new high-distortion zones. Frame 7–10: Transverse Mercator stabilizes; central meridian aligns vertically; annotations now sparse along center, dense at left/right edges; legend unchanged in position/appearance; all geographic features remain topologically intact and coherently registered to overlay.

Manual:
Experimental Procedure
1. Display world map in Mercator projection with distortion map overlaid and error annotations.
2. Smoothly transition to Transverse Mercator projection while maintaining same map extent and distortion visualization.
3. Set up a color scale legend for the distortion metric at the start; keep its position, size, and color key unchanged for the entire sequence.
Observation of Experimental Phenomena
- Mercator: area distortion increases toward the poles, while coastline shapes and angles stay visibly undistorted at every latitude (consistent with Mercator's conformal property); annotations cluster near high latitudes.
- Transverse Mercator: distortion minimal along central meridian, increases symmetrically east/west; annotations concentrate away from centerline.
- Color scale legend remains fixed; transition shows continuous redistribution of distortion pattern.
Summary of Experimental Principles
Mercator preserves local angles and shapes but distorts area increasingly poleward; Transverse Mercator minimizes distortion along the chosen central meridian, making it suitable for narrow north-south regions.

Prompt Grounding rubric:
level_1: Neither the Mercator projection nor the Transverse Mercator projection is shown; no distortion-color overlay appears on any map; no color scale legend is present; there is no second projection for the video to switch to.
level_2: Only one of the two projections (Mercator or Transverse Mercator) ever appears: the other is entirely absent; or a distortion overlay or legend is missing for the projection(s) that do appear; no second projection appears for switching to occur.
level_3: Both the Mercator and the Transverse Mercator projection appear somewhere in the video, each paired with its own distortion-color overlay and error-annotation markers, and a color scale legend is visible at some point, but Transverse Mercator is shown before Mercator, or the legend appears for only one of the two projections, or annotation markers are missing from one projection's map.
level_4: Mercator appears first with its own distortion overlay and error annotations, followed by Transverse Mercator with its own distortion overlay and error annotations, in that exact order; the color-scale legend is visible during both projection segments; the Mercator segment, the Transverse Mercator segment, and the legend are all present with none omitted or swapped for the wrong projection's data.
level_5: Mercator appears first, correctly labeled and paired with its own distortion overlay and annotations concentrated near the poles; Transverse Mercator appears second, correctly labeled and paired with its own distortion overlay and annotations concentrated at the left/right map edges; the legend stays aligned with whichever map is on screen, its color key never swapped or replaced by an unrelated legend; no projection's distortion data is ever overlaid on the other projection's map.

Scientific and Causal Correctness rubric:
level_1: The distortion pattern shown contradicts both projections' known behavior: e.g. Mercator's overlay darkens most at the equator instead of near the poles, or Transverse Mercator's overlay shows its lightest (least-distorted) band running east-west instead of along a vertical central meridian.
level_2: One projection's distortion pattern matches its true behavior (e.g. Mercator's overlay darkens toward Greenland/Antarctica as expected), but the other contradicts its known geometry (e.g. Transverse Mercator's overlay is darkest along the central meridian instead of at its edges); error-annotation markers are missing or placed away from the darkest regions.
level_3: Both overlays show qualitatively correct gradients (Mercator darkens progressively from equator to poles, Transverse Mercator darkens progressively away from the vertical central meridian toward the left/right edges), and annotations are present on both, but the markers are scattered rather than concentrated in each map's darkest regions.
level_4: Mercator's overlay shows increasing area distortion (map features visibly enlarging) from equator toward the poles while coastline shapes and angles stay recognizably undistorted at every latitude, consistent with Mercator preserving local shape; Transverse Mercator's overlay shows near-zero distortion along the vertical central meridian and symmetric increase toward the left and right edges; annotation markers cluster only in the visibly darkest regions of each map; the legend's color-to-value key (e.g., blue = low distortion, red = high distortion) matches the colors used in both overlays.
level_5: Mercator's overlay shows area distortion growing with latitude (small near the equator, extreme near the poles) while coastline shapes and angles remain visibly undistorted at every latitude, correctly reflecting that Mercator preserves local shape/angle and distorts area only; Transverse Mercator's overlay shows a mirror-symmetric gradient centered on the vertical meridian, near-zero at center and growing symmetrically toward both edges; every annotation marker sits inside a color region matching its own severity on the legend; the legend's color key is identical for both projection segments and never changes definition mid-video.

Spatiotemporal Consistency rubric:
level_1: The map jumps to a new position, orientation, or zoom level between frames with no visible motion; the map or legend vanishes and reappears; the background lighting abruptly switches (e.g., a bright frame is immediately followed by a dark one, or the reverse) with no scene change to explain it; coastlines or graticule lines visibly fracture or disconnect; the distortion overlay flashes independently of the map beneath it.
level_2: Transition between projections contains at least one hard cut; map viewport shifts discontinuously (e.g., center jumps); legend moves or resizes without smooth interpolation; distortion overlay appears/disappears without fade or morph.
level_3: Map remains fixed in frame throughout; legend remains in same screen region; transition between projections is continuous (no cut), but contains visible warping artifacts (e.g., pinching, tearing, or non-uniform scaling); distortion overlay maintains alignment with coastlines/graticules in both states, but briefly misaligns during mid-transition.
level_4: Map viewport remains perfectly stable; legend position and size remain constant; transition is smooth and globally coherent (no tearing, pinching, or local inversion); distortion overlay stays rigidly registered to geographic features across entire transition; no lighting/shadow shift or flicker occurs.
level_5: Zero spatial discontinuity: map geometry deforms continuously and invertibly during transition (no self-intersection, no topology change); legend remains visually fixed in identical position, size, and orientation; distortion overlay stays precisely aligned with graticule intersections and coastlines at all frames, with no visible drift or gap; lighting, contrast, and ambient shading are fully consistent and temporally invariant.