Warping a view to create a fisheye effect corrupts position and length, the chart's most accurate channels

What it is

The fisheye is not free: its warp directly edits the positions and sizes of marks — and position and length are the highest-accuracy channels a chart has. In a distorted view, the distance between two points no longer corresponds to the data distance, an element's size no longer corresponds to its magnitude, and axis tick spacing is no longer uniform. Every judgement that leans on position or length (distance, trend slope, area comparison) is untrustworthy inside the distortion zone.

Why it happens

The breakage chain is direct: magnitude reading depends on a fixed mapping between graphic properties and data values, while the fisheye's mapping is a function of spatial position — the same data value draws large in the focus and small in the compression zone; the same pair-wise distance stretches at the focus and squeezes at the periphery. Readers carry the default assumption "equal length, equal value," which now holds only in undistorted regions. Positional breakage also drags the axis system down: warped tick spacing invalidates the reference frame for interpolated reading. That is the fundamental limit of distortion views — what they preserve is existence and relative order (what is near what), and what they sacrifice is quantitative relation (by how much, how much larger).

Where it stops holding

The damage varies by task: ordinal judgements (which comes first, which is larger) survive mild distortion because order persists under monotone warp; quantitative judgements (how many times larger) are unreliable under any warp. Nor does distortion break every channel — colour, shape, and text labels are immune to geometric warp and remain the dependable reading channels in a distorted view, which is precisely the compensation design should use. The principle follows: critical information in a distortion view must travel non-positional channels (labels, colour); never ask readers to do geometric inference inside a warped space.

Applying it

• Label every critical value inside the distortion view directly (numbers, text); never rely on positional or length reading.
• Arrange quantitative comparisons in the focus zone, or provide "distortion lock" (the selected region returns to linear).
• Verification: have users compare two pairs of elements in the distorted view, one pair in the focus, one in the compression zone; a markedly higher error rate in the compressed pair is the measured distortion cost — route critical readings through labels.

Related

• Same group: U6.07.1 Fisheye achieves focus plus context by local magnification and peripheral compression · U6.07.3 Distortion shifts as the focus moves; targets drift and become hard to hit · U6.07.4 Distortion views suit navigation and location, not reading or comparison · U6.07.5 A way to switch the distortion off and return to the plain view must exist
• Nearby: U1.01.5 The ordering sets a precision ceiling that alignment and size erosion still cut · U6.06.4 The pattern saves gaze switches but adds spatial comprehension load
• Search terms: distortion cost · positional encoding · fisheye accuracy