  We introduce the cause of the inefficiency of bivariate glyphs by defining
the corresponding error. To recommend efficient and perceptually accurate
bivariate-glyph design, we present an empirical study of five bivariate glyphs
based on three psychophysics principles: integral-separable dimensions, visual
hierarchy, and pre-attentive pop out, to choose one integral pair
($length_y-length_x$), three separable pairs ($length-color$, $length-texture$,
$length_y-length_y$), and one redundant pair ($length_y-color/length_x$).
Twenty participants performed four tasks requiring: reading numerical values,
estimating ratio, comparing two points, and looking for extreme values among a
subset of points belonging to the same sub-group. The most surprising result
was that $length-texture$ was among the most effective methods, suggesting that
local spatial frequency features can lead to global pattern detection that
facilitate visual search in complex 3D structure. Our results also reveal the
following: $length-color$ bivariate glyphs led to the most accurate answers and
the least task execution time, while $length_y-length_x$ (integral) dimensions
were among the worst and is not recommended; it achieved high performance only
when pop-up color was added.
