Domain: Humanities and Social Sciences — Geography
Target concept: Map Projection: Winkel Tripel Projection

Video generation prompt: First, the Earth is represented as a sphere and the latitude and longitude grid is displayed. Then, the Winkel Tripel projection is applied to gradually present a final planar world map with balanced, minimized distortion across regions.

Evaluation guide:
(i) Target concept: Visual demonstration of how Winkel Tripel projection transforms a spherical Earth model into a planar map while achieving balanced distortion compromise.
Minimum mechanism: Continuous geometric morphing from spherical coordinate system to planar projection space, preserving topological continuity of graticule and enforcing Winkel Tripel"s defining geometric constraints (curved parallels, straight central meridian, symmetric lateral compression).
(ii)Storyline: [Frame 0–3] Fixed-view rotating sphere with full latitude/longitude grid visible; grid conforms to spherical geometry (meridians converge, parallels are concentric circles). → [Frame 3–7] Smooth morphing begins: meridians gradually straighten except central one; parallels acquire gentle outward curvature; lateral compression increases symmetrically toward map edges. → [Frame 7–10] Morph completes: stable planar map with unbroken, continuous graticule; central meridian remains perfectly straight; all other meridians are symmetrically curved; parallels are uniformly curved; no region shows disproportionate distortion. Perspective remains locked; lighting, color, and line integrity preserved throughout.

Manual:
Experimental Procedure
1. Display a rotating transparent sphere with clearly labeled latitude and longitude grid lines.
2. Animate gradual flattening and warping of the sphere surface while preserving grid line continuity.
3. Final state: stable planar world map with curved parallels, straight central meridian, and symmetrical lateral compression.
Observation of Experimental Phenomena
- Sphere appears first with evenly spaced circular parallels and converging meridians.
- Grid lines bend smoothly during transformation: parallels curve outward near equator, meridians compress laterally toward poles.
- Final map shows balanced distortion: no extreme stretching at poles or equator; continents retain recognizable shapes and relative sizes.
Summary of Experimental Principles
Winkel Tripel projection is a compromise map projection that minimizes distortion in area, shape, and distance simultaneously by averaging the coordinates of the equirectangular and Aitoff projections — resulting in curved parallels, straight central meridian, and symmetrical lateral compression.

Prompt Grounding rubric:
level_1: No sphere with a latitude/longitude grid appears at any point; no Winkel Tripel-style planar map is shown; the final planar world map is missing or unrecognizable as a map.
level_2: Either the sphere or the latitude/longitude grid appears but not both together; no projection transformation into a flat map is shown; the final map is missing or is clearly a different projection shape (e.g., a rectangular Mercator-style map or a polar-view map).
level_3: A sphere with a visible latitude/longitude grid appears first, then a planar world map appears, with a visible transition between them; however the final map is missing clear Winkel Tripel traits such as curved parallels, a bulging equatorial belt, or symmetric compression toward the sides.
level_4: A sphere with a complete latitude/longitude grid appears first, then a smooth transition leads to a planar map showing all three Winkel Tripel traits (curved parallels, a straight central meridian, and symmetric lateral compression near the poles), but one of these three is hard to make out (e.g., the curvature is barely visible at the rendered scale).
level_5: A sphere with a fully visible, evenly spaced latitude/longitude grid appears first, then one continuous, unbroken transformation occurs; the final map clearly shows all three Winkel Tripel traits (curved parallels, straight central meridian, symmetric lateral compression) with no conflicting features such as extra straight meridians, extreme pole stretching, or a rectangular cylindrical-projection look.

Scientific and Causal Correctness rubric:
level_1: The video shows no visible cause-and-effect between the sphere-to-map transformation and the projection being applied; the distortion is clearly not balanced (e.g., extreme stretching only at the poles or only at the equator); the latitude/longitude grid on the sphere is missing or drawn with the wrong spacing; the final map contradicts Winkel Tripel's goal of a balanced compromise.
level_2: The sphere and grid appear, but the grid spacing doesn't match true spherical geometry (e.g., the angular spacing between lines is visibly uneven); the transformation doesn't end in a flat map; the final map shows one dominant kind of distortion (e.g., only area distortion or only shape distortion) rather than a balanced mix.
level_3: The sphere shows a geometrically correct latitude/longitude grid; the transformation produces a planar map; overall distortion looks reduced compared to the sphere, but it is not evenly spread, for example Greenland or Antarctica changes size or shape noticeably more than regions near the equator, which goes against Winkel Tripel's balanced-compromise design.
level_4: The sphere shows an accurate latitude/longitude grid and the transformation produces a planar map with visibly reduced distortion, as in level 3; in addition, the reduced distortion is spread fairly evenly across continents, with no single region dominating; any leftover asymmetry in lateral compression or parallel curvature is minor and doesn't defeat the balanced-compromise look.
level_5: The sphere shows a geometrically accurate latitude/longitude grid and the map shows evenly spread, reduced distortion, as in level 4; in addition, the balanced compromise is unambiguous: continent shapes look better preserved than on a Mercator map, area exaggeration is visibly smaller than on an equal-area map, and no single region (poles, equator, or any continent) shows noticeably more shape, area, or angle distortion than the rest.

Spatiotemporal Consistency rubric:
level_1: Hard cut between the sphere and the map, with the sphere vanishing and the map appearing instantly and no visible morphing in between; the grid lines teleport or flicker on and off; the surface tears, pixelates, or snaps into place instead of smoothly deforming; the viewpoint jumps to a completely different angle between the sphere and the map with no continuous camera motion.
level_2: The sphere and the map appear as separate shots with mismatched camera framing, so the transition doesn't read as one continuous transformation; grid lines vanish and reappear rather than bending into their new shape; the map emerges through a zoom or cross-fade instead of visible geometric deformation; the central meridian's position shifts noticeably partway through the transition.
level_3: The viewpoint stays fixed and the sphere-to-map change happens within one continuous shot; the grid lines bend continuously but show visible flaws such as a broken segment, a moment where a line is hidden, or a line that changes thickness; once flattened, the map settles with a small amount of residual wobble or drift.
level_4: The viewpoint stays fixed and the sphere-to-map change happens within one continuous shot, as in level 3; in addition, every grid line bends smoothly from its curved meridian/parallel shape to its final shape with no breaks, no hidden segments, and constant line thickness; once flattened, the map holds completely still with no wobble or flicker; the coastlines and continent outlines keep a constant color and line weight throughout, with no separate shading or brightness change on the sphere or map beyond what the projection's own deformation explains; the graticule never splits or kinks.
level_5: Every grid line bends smoothly with constant thickness and no breaks or hidden segments, and the map holds completely still once flattened, as in level 4; in addition, the deformation looks like one continuous mathematical bend from sphere to map with no stutter; the sphere's surface texture and the grid-line color/opacity stay constant throughout; once the map settles, its edges and coastlines are crisp and stable, with no lingering wobble, shimmer, or blurred/ragged edges where lines meet.