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Ellipse in Plane

lay a correct ellipse onto the face

round
score
best

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Fitting an ellipse to a face seen at an angle

A box in two-point perspective arrives with one face highlighted, and you lay the ellipse belonging to that face onto it. Sweep the whole way round; lifting does not end the attempt, since a press near where you stopped joins the pieces — no trackpad crosses a 250px closed arc in one contact. The stroke is fitted, and handles appear to nudge centre, length, tilt and width; handles mode skips the sweep. Three faces per round, each turned further away.

This is the plate-on-a-table, wheel-on-an-axle problem: a circle only reads as lying on a surface when its ellipse belongs to that surface. The reveal draws the axle — the face’s real 3D normal projected through the same camera, not your minor axis extended — because the minor axis runs down the axle, straight out along the hub of a wheel. It prints the true ellipse’s degree — the number templates are sold in — and names whichever of placement, tilt or size you missed by most, so you leave with a direction, not just a mark.

What a locked plate is marked on

The truth is not sampled and fitted: the face’s inscribed circle lives in 3D and its conic is pushed straight through the plane-to-screen homography, so the revealed ellipse is that circle’s image to floating-point precision. Your attempt is scored on three errors: centre offset, normalized by the face’s mean projected diagonal; axis angle, which counts for less the rounder the truth is, since a near-circle points nowhere in particular; and size, which is scale plus the error in the degree itself, capped so it cannot zero an otherwise sound ellipse. Anything inside the full-credit zone reads 100; that zone is 2% of the face diagonal on a pen, doubled on a trackpad, and floored at five eased pixels, since 2% of a 150px phone face is smaller than a fingertip’s jitter. No model reads the sweep: your ellipse is reduced to a centre, two axes and a tilt, and those numbers are compared with the true ones.

More form & perspective drills: Cylinder Ends · Cast Shadow · Horizon Read · the whole catalogue