2. Polyfoils: PART 2
Part 2 describe image processing used in Polyfoils, especially
oPs. For any document electronically presented in more than
two dimensions, optimizing the viewer's visual comfort is critical.
The evolution of perception endows document users with
performance demands that are not properly addressed in
current dynamical 3D text processing. This part explains the
background inventions that make Polyfoil documents pleasant
to look at.
The default Polyfoil, oP, is described from page 3 to 8. Then
an “internal invention” is explained, the Polyfoil rotation. This
is not a standard 3D transformation. It resolves viewer
discomfort
issues found in watching computer generated rotations. This
runs from page 9 to 27, culminating in a process called
“Structure From Motion.”
2
3. Polyfoil Construction
Polyfoil Document Processing Patent Pending Application
62264325 is a 162 page patent, with 70 pages of images &
flowcharts. It demonstrates a new way to structure and
format electronic documents. Because of novelty, and broad
importance of documents, the invention is both expansive
and detailed in depth. Multiple inventions are embedded
within it.
oPs, kPs, cPs, mPs, and other Polyfoils, have methods,
attributes,objects and functions that engage component
inventions within the patent. An overview of key Polyfoils
demonstrates this.
This denotes an
embedded invention:
3
4. 4
oP – the default Polyfoil
Most electronic readers have a tripartite display. Users barely
notice, because planar surfaces framing a document, above &
below horizontally scrolled pages, or on either side of vertically
scrolled ones, are vacant.
The default Polyfoil reader has side or top and bottom panels
that repose at angles. They denote 3D volume. They are oPs.
4
5. Prism Construction
An oP is a uniform n-prism, each prism face a rectangle. Two
adjacent faces form the n-prism's central angle. An oP presents
a distinct combinatorial shape in 3D space, each 2D panel in
3D
space. An oP is anchored to a position in a document core. It
egresses from this anchor sideways (or top/bottom) sliding into
view in a rotation.
Content is rendered in 2.5D perspective on 2D surfaces in 3D
image space. Prior art usually renders content in 3D projection
in 3D object space.
5
6. oP Science
Over dozens of generations, people adapted to physical
books. They now love word processor convenience, tablet
reading, and quick news on their phone. But many struggle
to enjoy screen text.
oPs increase the parameters of screen reading. They
rotate, angle, and otherwise challenge ordinary human
perception.
In a prior era, the need to systematically analyze
biophysical responses to computer generated images
would take a lifetime. Today, perception science,
technology use research and programming history provide
a foundation to build on. Using this knowledge base I
devised solutions to user difficulties with virtual content-
bearing surfaces that rotate, branch, and so forth.
6
7. Human Perceptual Quirks
People think a repose
angle like this … is an angle like this.
over-
estimate
angle
People think a rotation
like this … is a rotation like this.
over-
estimate
rotation
People dislike angled text. Some feel ill at text rotation
7
8. Reasons to be Quirky
Perceptual quirks are due to
mismatch between physiology
& normative reality. Our optical
system records a hyperbolic
field. A ~1% area is in focus.
Peripheral cognition detects
motion, depth & groups, all
that's 3D, none in central focus.
Readers exploit peripheral
vision to smooth lateral eye
movements and preprocess
words at margins. Electronic
documents lack hyperbolic
curvature used by peripheral
systems for edge information.
Meanwhile, a computation
intense 3D rendering pipeline
transforms hyperbolic space
into a square shaped frustum
called orthogonal, with an entire
plane in focus.
People value this, because they
scan the cubic plane easily.
But angled text & text rotations
challenge peripheral systems,
making orthogonal transforms
palpable and discomforting.
8
9. Adapting to Perception
Document Frustum User's Conventional
Surface Space Sightlines Viewport
Adjacent
panel has
rounded
Edge
Adjacent
panel has
sharp edge
Polyfoil
shape
accords
with
peripheral
vision.
Near-plane Semi-spherical orthographic
Coordinates transform into space
9
10. Rotation Ills
Not just oP, also cP, gear and science Polyfoils rotate.
Acceptance of virtual documents is sensitive to perceptual
discomfort. Some users find digital documents unsettling. Rotation
causes “text rotation disorder,” TRD*. It must be cured.
Polyfoil rotation has 4 inside inventions that contribute to
Structure From Motion, to cure TRD.
Focal Length X Time for Space
Viewpoint path maintains Sinusoidal equations modify
constant distance from motion velocity to optimize
content surface, not axis. volumetric information.
Heading My Way: Estimation Error Resolution:
Rotates isomorphic view- Viewpoint activity modifies
point path ½ its external future view path expectations
angle & pivots forward. offsetting prediction error.
Structure From Motion
uses variable rotation velocities, keeps constant focal length,
obtains forward heading, and transitions to the next panel's
on a trajectory that follows norms but adjusts for error.
*TRD is a TIC (“tongue in cheek”) theory
10
11. Focal Length X (a)
A typical document page,
viewed orthogonally in a
viewport, has a surface
exactly on a frustum near-
plane. Under rotation it
then breaks the near-plane.
Fore-shortened surfaces
loom disconcertingly.
If a renderer culls near-plane
violations, it appears capricious.
A rotating prism's surfaces rise & fall. Is the object moving, or us?
Haptic (touch), balance & proprioception (muscle feedback) says
we're not. An unconscious visual response kicks in, to pull eye
lenses flatter or fuller, constrict pupils as surfaces recede, and
rotate eyes inward if the opposite. We expect to see an object like
a merry go-round.
But the display is flat! Virtual images and our involuntary
muscle behaviors don't match. That triggers unease. In pre-
modern life, a sensory mismatch (seeing images that have no
physical correlate) was a hallucination, most commonly caused by
eating rotten food or poisonous leaves. That's explains why people
feel nauseous watching virtual rotations: it's a purge.
11
12. Focal Length X (b)
Conventional approach: from surrounding circle C, viewpoint
sightlines aim at prism axis D as they rotate. All are the same
distance to D, but each has different distance to a prism face.
Sightline A is perpendicular to a prism circumradius, the prism point
closest to D. B is perpendicular to its apothem, prism point
furthest from D.
As viewpoint or prism rotate smoothly, the focal-length changes
constantly, in conventional rotation displays.
Yet C is everywhere the
same distance from D.
All sightlines the have
same distance to D, but
each is a different distance
from the prism face. B is a
longer focal length than A.
12
13. Focal Length X (c)
The Focal Length X internal invention:
A viewpoint path is kept at a constant distance to the rendered
surface.* The central axis changes distance, but it's invisible.
The rotation generates little optical response expectation.
Computer generated rotations use distance to the invisible axis
as datum for math transforms, so the surfaces rise and fall.
Instead of adapting to users, this adapts to math. Given Polyfoil
regularity, distances can be preprocessed.
*Over 80% of a surface. At 10%
distance from edge, the view-
A – move sideways, no rotation point rotates quickly.
Bo – around corner 0
B1 – around corner 1
13
14. Heading My Way (a)
To feel in control of motion, people look where they're
going. It's called a heading.
Ordinary 3D rotation presents a view absolutely orthogonal to
this. Your path is to either side of where you look.
Heading is necessary for controlled locomotion, especially on
curved paths, where headings are tangents. When headings
are to the side, as in virtual rotation, people must estimate
the tangents they're on. They do so from habit.
People feel head and eye aiming determines movement
accuracy, but ordinary rotations prevent it.
The University of Washington's Human Interface Technology
Laboratory found viewers of virtual motion were
uncomfortable when their predicted path tangents proved
incorrect. Accurate predictions increased enjoyment and
reduced unease.
14
15. Heading My Way (b)
1) From centerpoint, a viewpoint moves sideways, perpendicular
to a content surface.
2) About halfway to its edge, viewpoint pivots towards that edge.
To remain at a fixed focal length, the path moves forward.
3) After the sightline passes the edge, viewpoint pivots reverses,
4) About halfway to next centerpoint, the viewpoint becomes
perpendicular to surface.
5) The viewpoint moves sideways to the next centerpoint.
1 – moves sideways 3 – reverse pivots & backs up
2 – pivots towards next panel 4 – perpendicular again
& moves forward 5 – sideways to next center
15
16. Time for Space (a)
Most word processors, webpages & some ebooks spread
content vertically. Readers scroll. The bottom of one page is
contiguous to the top of the next. This emphasizes linearity.
Sideways rotation is different. People move sideways through
physical books. The bottom of a page is contiguous to the
bottom of the next. Readers must change eye plane. A turned
page draws attention to document bulk and one's position in
it, perceptually satisfying. It's a book's volumetric aspect.
Digital documents, in contrast, convey position with a nav bar,
a narrow, single dimension tool, perceptually unsatisfactory.
Polyfoil structure, the scale and layout of Polyfoil panels,
can be visually appreciated by readers. Ordinary rotations
don't
optimize an object's structural view.
Users rotate a Polyfoil with finger, eye, arrow key, or mouse
input. Unlike a physical book, little resistance decelerates
input. Resulting rotation may under or over-shoot the next
page center.
16
17. Time for Space (b)
Velocity, a time function, exposes a Polyfoil volume's spatial
dimensions. In the following, the first maximizes reading; the next
maximizes volume assessment. Deceleration maximizes.
Max deceleration at
apothem minimizes
volume & maximizes
reading
Perspective
Max deceleration at
circumradius max's
area view
of object.
View of
Reading
Pages
View of
Volume
Optimal velocity merges both. Rotation accelerates from
apothem, satisfying need to reach and read the next page.
Then decelerating
when perpendicular to
the circumradius
provides global
position insight.
17
18. Estimated Error Resolution
Object rotation and circling round the object are, in
standard rotation algorithms, indistringuishable,
mathematically and visually. But viewers usually project
themselves circling the object.
All circular locomotion has headings tangential to the circle. A
virtual rotation's viewer thus imagines headings peripheral
(sideways) to their sightline. When intuitive heading
estimates contain errors, it's called heading bias. When
detected (unconsciously) unease develops.
Viewpoint pivoting induces a different bias, called pointing error.
As one's head pivots, eyes counter-pivot, reducing overall
motion. Habitual, unconcious processes adjust heading
accordingly, to account for the counter-pivot.
But a virtual viewpoint pivot doesn't induce eye rotation.
Habitual rotation expectations cause pointing error: people
overshoot actual trajectories.
18
19. People use ecological and biomechanical feedback to
continuously adjust perception predictions, reducing error.
Perceptions wobble
as people walk.
Imprecise biomechanical
activity induces
compensatory visual
system response.
Dopamine
(a pleasrable
neurotrasmitter)
increases after positive
feedback confirms that
compensatory visual or
motor action reduces
path prediction error.
It's so habitual
that if people
are forced to
move slowly
across smooth
surfaces, they
make more
peceptual
errors.
People feel
more fit if they
err and fix a
prediction, than
if they dead-
reckoned
without error.
Estimated Error Resolution
19
20. Estimated Error Resolution
Research on heading bias finds peripheral tangents 40˚ to 90˚ from a
sightline have 8˚ to 30˚ estimation bias towards the rotation axis.
For 16-prism, a frustum with focal-length 1.67 (x the page width) has
a 13˚ to 20˚ heading bias.
Pointing error, on the other hand, ranges from 5˚ to 15˚ in the
direction of pivot rotation.
Heading bias and pointing error increase with extent and velocity.
A standard model of heading and pointing error follows. Viewpoint X
is at the center of the small circle. Arcs are expressed in radians.
A: Initial sightline
B: Arctangent …0.79 rads
C: Actual Pivot Target
D: Estimated Pivot Target
Pointing Error PE = C-D … 0.11 rads
E: Estimated Heading Target
F: Actual Heading Target
Heading Bias HB = F-E …-0.44 rads
Note PE is clockwise, HB counterclockwise.
20
21. The Estimated Error Resolution invention cancels out heading bias
with pointing error. The viewer's pleasure from error compensation
is produced by this algorithm.
Estimated Error Resolution with a 16-prism
1st
sequence:
HB is Heading Bias, PE is Pointing Error
clockwise: counterclockwise:
Vector S actual heading
Vector R estimated heading
J has center sightline N
Frustum width = 2n
K rotates O on path
K pivots and moves forward
(to maintain focal length)
path HB, pivot PE
HE – PE 0.
L points P, M points Q, the same way.
T is the next center sightline
Estimated Error Resolution
21
22. When PE & pivot equal the initial HB, error terms cancel.
When a sightline pivots enough to reach the joint between pages,
or half the distance to the next center sightline T, it should cancel
half the HE. Given a 16-prism, the pivot is 0.22 rads, or 12.8˚.
The pivot must be unwound prior to reaching T. The viewpoint is
now on an inferred circumvection path R.
PE=
PivotRadians × 2Td
nPaTan × m
PivotRadians = pivot in rads
nPaTan = nPrism arcTan in rads*
Td = S Length
m/Td = movement on S
*given 16-Prism = 0.785
HB = 0.3˚ × Heading tanoffset
given 16-prism:
0.3˚ x 66˚ = 19.8˚ HB
Estimated Error Resolution
22
23. Structure From Motion
The Structure From Motion (SFM) internal invention
combines the previous four solutions: Estimated Error
Resolution (which itself incorporated others), Focal Length
X, Heading My Way, and Time for Space.
SFM is modeled with optical flow concepts.
A visual system tracks an object, or moves through objects,
with key features centered in the fovea. The much larger
background forms motion vectors, often peripheral flows that
expand or contract around a fixation point. This is an optical
flow pattern.
Optical flow patterns are categorized:
Laminar Flow Slant Flow
Radial Flow Shearing Flow
23
24. Translation (sideways) movements generate laminar flows.
Pivoting generates complex radial flows.
A prism rotates around an axis. As surfaces approach the screen,
they generate looming vectors; when receding, their optical
vectors are occluded.
Content vectors move together in the same direction, but
perspective slants these flows to edge laminar vectors gradually
apart. The result is slant flow.
Looming is the most troublesome rotational flow pattern. It occurs
as slant flows decompose with an accelerated dilation of laminar
flow by radial flow. Viewers physically react, pulling away from the
screen as if afraid.
Optical flow patterns from
looming objects decohere.
Structure From Motion
24
25. 1. Laminar flow has a longer latency, remaining in
consciousness longer than radial flow. Move towards a
surface while pivoting away, and the surface doesn't loom,
because the pivot's flows are remembered more than
movement forward.
2. Translational movement combined with pivoting induces
shearing flows (beyond the fixation point content seems to
move outward, if closer, it appears to contract.) The looming
surface falls into the zone that's squeezed together.
Because optical flow patterns
depend on velocity, the SFM
invention accelerates and
decelerates to maximize effects.
Structure From Motion
25
26. In Figure A, frustums progress to the next prism surface. Each
frustum shows a cross-section of the surfaces that get viewed in
that position in the sequence.
In Figure B, the viewpoint is examined. It immediately pivots and
rapidly moves sideways towards the surface. Looming, and
pointing error, are minimized because of movement velocity. The
facing page's content vection appears horizontal rather than
slanted.
Once the viewpoint aims at the next panel, it reverses vection and
decelerates, to generate a sweeping view of the next panel.
Structure From Motion
26
27. Page rotatation goal: get to next page.
Rotation vistas quickly turn, so
most of rotation time features
the next page.
Sequence
Starts
But rotation
decelerates
midway,
orthogonal
to apothem,
to display
structure in
space. This
is useful for
navigation.
Structure From Motion
27
28. The shift from fast motion with pivot, to sweeping overview,
reconstructs the effect of physical page turns.
Turning a physical page generates, first, radial & laminar flows.
The next page, or back of the page, is revealed in sweeping
overview. Figure C shows how the page has curled vection.
Structure from Motion generates similar optic flow patterns. Figure
D shows combined radial and laminar flows, a midway structure
view, then sweeping curled vection.
.
Structure From Motion
28
