DSCI 554 lecture 8

Depth perception and design, maps

Dr. Luciano Nocera

Outline

Depth perception and design considerations
Introduction to maps
How maps are built?
Maps projections and their uses
Working with maps

Perceptual egocentric space

Decreased depth information in towards-away because of object occlusions

Depth information and depth cues

M. J. Tovee, An introduction to the visual system, Cambridge Univ. Press, 1996

Oculomotor

Accommodation: coordinated changes in vergence, lens shape and pupil size
Convergence: movement of both eyes to center image is in the retina
Myosis: constriction (squeezing) of the pupil

Visual > Monocular > Static

Classic pictorial (i.e., in static image) cues

Occlusions

Linear perspective convergence

Relative size, familiar size

Texture gradient

Shadows

Shading

Defocus blur

Atmospheric perspective

Pictorial > Occlusions

An object blocks another

Perdreau F, Cavanagh P. Do artists see their retinas?. Frontiers in human neuroscience. 2011

Pictorial > Linear perspective convergence

Parallel lines appear to converge at some point in the distance

St. Peter Healing a Cripple and the Raising of Tabitha, Masolino, 1425

Pictorial > Relative size, familiar size: object size

Retinal projection is:

- proportional to object size

- inversely proportional to the object distance

Pictorial > Relative size, familiar size: Relative height

Object closer to the horizon are farther – up

Pictorial > Texture gradients

Density, perspective (foreshortening) and distortion of texture
elements between closer and farther away objects

Pictorial > Shadows

Dark area where light from a light source is blocked by an opaque object

Pictorial > Shading

Depicting depth in 3D models or illustrations by varying levels of darkness

Zumba Crater: Fresh 3-Km Crater, Mars. 04 May 2007, NASA/JPL University of Arizona

Pictorial > Defocus Blur

Aberration in which an image is out of focus

Pictorial > Atmospheric Effects

Farther objects:

- less distinct,

- colors less saturated,

- mountains in the back appear more blue

Paul Cézanne, Mont St. Victoire c. 1887

Visual > Monocular > Motion-based > Motion parallax

Closer objects move faster than farther away objects

Parallax scrolling uses layers of animated sprites to create the illusion of depth

Visual > Monocular > Motion-based > Occlusion in motion

With deletion and accretion a moving object appears faster than farther

Deletion
Object becomes occluded

Accretion
Object reappears

Visual > Monocular > Motion-based > Structure from motion

Depth cues from different points of view or moving object

This is an animation of a 3-d shape rocking back and forth, thus cued by relative motion. The dots that carry the motion flicker occasionally so as to eliminate the possible cue of changing local dot density. Despite the elimination of that cue and the flicker, it is relatively easy to perceive (and to judge) the 3-d shape. [M. Landy]

Visual > Binocular > Stereopsis

Depth cues from both eyes

Biological evidence: binocular cells [Hubel & Wiesel 1952, 1969], disparity detectors [Pettigrew 1967]

Some (more) illusions

Size constancy (Ponzo) illusion

Psychologist Mario Ponzo suggested that the human mind
judges an object's size based on its background

Ponzo Illusion 1911

Poggendorff illusion

Muller-Lyer Illusion

Created by German psychiatrist Franz Muller-Lyer in 1889
One explanation is that opened arrows are perceived as farther away.

Necker cube illusion

Shepard turning tables illusion [Shepard 90]

The visual system interprets 2D shape information in 3D

This illusion is based on a drawing of two parallelograms, identical aside from a rotation of 90 degrees. When the parallelograms are presented as tabletops, however, we see them as objects in three-dimensional space. Note that real tables have different geometry. Open with Inkscape: shepard_table.svg

Ames room: what cues are at play?

Relative size, familiar size, perspective convergence

Design considerations

What is wrong with this chart?

Occlusions, confusing texture, confusing shapes, Necker illusion, projection

What is wrong with these charts?

Cancer survival rates: tables, slopegraphs, barcharts, E. Tufte

Popular 3D design techniques

2.5D design

2.5D design + constrained navigation

Isometric projection: orthographic projection with coordinate axes
appearing equally foreshortened and at 120 degrees from each other

Outline

Depth perception and design considerations
Introduction to maps
How maps are built?
Maps projections and their uses
Working with maps

Original map by John Snow showing the clusters of cholera cases in the London epidemic of 1854 [Snow 1854]

Update of John Snow's London cholera epidemic [Regmarad 1960]

Thematic Maps

Dot Map	Can be used to locate each occurrence of a phenomenon. One-to-one or one-to-many.
Cartogram	Area used to display value. Distortion used to show continuous variables
Choropleth	Areas are shaded or patterned in proportion to variable.
Proportional Symbol Map	Scaled symbols show data for areas/locations. Also called Graduated Symbol Map.
Isopleth	Use contours to show continuous variables. Also called Isarithmic.

Continuous area cartograms with D3 and TopoJSON repository and example.

Dasymetric map (choropleth map) [Semenov-Tyan-Shansky 1911]

Refined choropleth map where ancillary information is used to model a phenomena

tract data

population density

land cover
(ancillary data)

dasymetric map

Mennis, J. Generating surface models of population using dasymetric mapping. The Professional Geographer, 2003.

Outline

Depth perception and design considerations
Introduction to maps
How maps are built?
Maps projections and their uses
Working with maps

How maps are built?

Reference ellipsoid

World Geodetic System 1984 (WGS 84), used for GPS

Geographic coordinates

$(\lambda, \phi) = (\text{longitude}, \text{latitude})$ angles (degrees)

Geographic vs. geocentric latitude

If not specified $\rightarrow$ geographic $\phi$

Geodetic datum

A coordinate system and reference to locate places defined by a horizontal and a vertical datum

Horizontal datum: defined by a reference ellipsoid
Vertical datum: defined by the way we measure elevation:
- Geodetic if based on ellipsoid of horizontal datum
- Tidal if based on sea levels
- Gravimetric if based on a geoid

Geoid

Geoid undulation in false color, to scale. By International Centre for Global Earth Models (ICGEM)

Geocentric vs. local geodetic datum

Defined by the type of horizontal datum used

Geocentric datum

Good for global applications

Local datum

Good for regional applications

How maps are built?

Map projection

All projections introduce some distortion Tissot’s indicatrix by Jason Davies

Properties preserved in maps

Name	Property preserved
Conformal	Shape of small regions. At any point same scale in all directions, $90^{o}$ between parallels and meridians, angles preserved at each point.
Equal-area	Areas proportional to areas on Earth
Equidistant	Scale along one or more lines, or from one or two points to all other points
Azimuthal (true direction)	Directions from a central point: great circles through the central point are straight lines

Can you have a map that is both conformal and equal-area?

Cannot flatten an orange peal without tearing!

Outline

Depth perception and design considerations
Introduction to maps
How maps are built?
Maps projections and their uses
Working with maps

Named projections types

Named after the developable surface$^{*}$ used


Cylindrical
Conical
Azimuthal

* Developable surface: surface that can be unfolded or unrolled into a plane or sheet without stretching, tearing or shrinking

Named projections sub-types

Based on intersection and orientation

	Name	Example
Intersection	Tangent or Secant

	Name	Example
Orientation	Normal
	Transverse
	Oblique

Lambert azimuthal equal area

Projection: azimuthal, equal-area

Named after Johann H. Lambert
Useful for choropleth maps

National Atlas of the United States, United States Department of the Interior (2002)

Albers conic

Projection: conic, Equal Area

Named after Heinrich C. Albers
Used by the United States Geological Survey and Census Bureau
Useful for choropleth maps

Albers USA U.S.-centric composite projection of 3 Albers equal-area conic projections. Alaska is at $0.35x$ of its true relative area.

Lambert conformal conic (LCC)

Projection: conic, conformal

Named after Johann H. Lambert
Useful for aeronautical charts

Aeronautical chart on Lambert conformal conic projection.

Mercator projection

Projection: Cylindrical, Conformal

Named after Gerardus Mercator
Standard for Web mapping applications
Variations include Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator

Google Maps uses Google Web Mercator

Universal Transverse Mercator (UTM)

Projection: Secant cylindrical transverse, conformal

Named after Gerardus Mercator
Over $61 x 6^{o}$ zones

Lidar points in UTM coordinates from Gao, Z., Nocera, L., Wang, M. & Neumann, U. Visualizing aerial LiDAR cities with hierarchical hybrid point-polygon structures, Graphics Interface Conference, 2014.

Cartesian coordinates in meters as Easting and Northing: 48 N 377299m 1483035m

Outline

Depth perception and design considerations
Introduction to maps
How maps are built?
Maps projections and their uses
Working with maps

Map formats

Raster

Vector

Map data formats and software

Format	Software
Raster image, e.g., png, jpeg	Rendered with d3
Vector image, i.e., svg	SVG created with d3
Raster or vector tiles, a.k.a. slippy maps	Leaflet, Mapbox, Google Maps ...
JSON format: GeoJSON, TopoJSON	D3, Vega-Lite, Vega, Leaflet, Mapbox...
Shapefiles (ESRI proprietary format)	Specific map map apps and specialized GIS software

Tile Maps (Slippy Maps)

Tiles are served by a Tile Maps Service (TMS)


					OSM: http://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png
					OSM B&W: http://{s}.www.toolserver.org/tiles/bw-mapnik/{z}/{x}/{y}.png
					OpenCycleMap: http://{s}.tile.opencyclemap.org/cycle/{z}/{x}/{y}.png
					MapQuest: http://otile{s}.mqcdn.com/tiles/1.0.0/sat/{z}/{x}/{y}.png
					MapQuest-OSM: http://otile{s}.mqcdn.com/tiles/1.0.0/map/{z}/{x}/{y}.png
					Stamen: http://{s}.tile.stamen.com/watercolor/{z}/{x}/{y}.jpg
					OSM Mapnik bw: http://{s}.www.toolserver.org/tiles/bw-mapnik/{z}/{x}/{y}.png

Slippy Map with Mapbox

Mapbox GL JS API

GeoJSON


				{"type":"FeatureCollection",
				  "features":[
				    {"type":"Feature",
				      "id":"01",
				      "properties":{"name":"Alabama"},
				      "geometry":{"type":"Polygon","coordinates":[[[-87.359296,35.00118],[-85.606675,34.984749],[-85.431413,34.124869],[-85.184951,32.859696],[-85.069935,32.580372],[-84.960397,32.421541],[-85.004212,32.322956],[-84.889196,32.262709],[-85.058981,32.13674],[-85.053504,32.01077],[-85.141136,31.840985],[-85.042551,31.539753],[-85.113751,31.27686],[-85.004212,31.003013],[-85.497137,30.997536],[-87.600282,30.997536],[-87.633143,30.86609],[-87.408589,30.674397],[-87.446927,30.510088],[-87.37025,30.427934],[-87.518128,30.280057],[-87.655051,30.247195],[-87.90699,30.411504],[-87.934375,30.657966],[-88.011052,30.685351],[-88.10416,30.499135],[-88.137022,30.318396],[-88.394438,30.367688],[-88.471115,31.895754],[-88.241084,33.796253],[-88.098683,34.891641],[-88.202745,34.995703],[-87.359296,35.00118]]]}},
				    {"type":"Feature",
				      "id":"02",
				      "properties":{"name":"Alaska"},
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				      "id":"72",
				      "properties":{"name":"Puerto Rico"},
				      "geometry":{"type":"Polygon","coordinates":[[[-66.448338,17.984326],[-66.771478,18.006234],[-66.924832,17.929556],[-66.985078,17.973372],[-67.209633,17.956941],[-67.154863,18.19245],[-67.269879,18.362235],[-67.094617,18.515589],[-66.957694,18.488204],[-66.409999,18.488204],[-65.840398,18.433435],[-65.632274,18.367712],[-65.626797,18.203403],[-65.730859,18.186973],[-65.834921,18.017187],[-66.234737,17.929556],[-66.448338,17.984326]]]}}
				  ]
				}

Example GeoJSON of Alabama, Alaska and Puerto Rico boundaries

GeoJSON

Geometry: Point, LineString, Polygon, MultiPoint, MultiLineString, MultiPolygon, GeometryCollection


					"geometry": {
					  "type": "Point",
					  "coordinates": [-118.2851, 34.0224]
					}

Feature: one or more geometry object with properties that can be used to encode the data


					{
					  "type": "Feature",
					  "geometry": {
					    "type": "Point",
					    "coordinates": [-118.2851, 34.0224]
					  },
					  "properties": { "name": "USC" }
					}

FeatureCollection: one or more Features


					{
					  "type": "FeatureCollection",
					  "features": [ ... ]
					}

Duplicate boundaries with GeoJSON (large file size)

TopoJSON

GeoJSON extension encoding topology where the Geometry is indexed with arcs

Up to 80% smaller than GeoJSON

See How To Infer Topology, Mike Bostok


					{
					  "type": "Topology",
					  "transform": {
					    "scale": [0.036003600360036005, 0.017361589674592462],
					    "translate": [-180, -89.99892578124998]
					  },
					  "objects": {
					    "aruba": {
					      "type": "Polygon",
					      "arcs": [[0]],
					      "id": 533
					    }
					  },
					  "arcs": [
					    [[3058, 5901], [0, -2], [-2, 1], [-1, 3], [-2, 3], [0, 3], [1, 1], [1, -3], [2, -5], [1, -1]]
					  ]
					}

topojson/topojson Wiki ▸ Introduction

Maps with D3

Using GeoJSON with d3


					<svg width="960" height="600"></svg>

					<script>
					var svg = d3.select("svg"),
					  width = +svg.attr("width"),
					  height = +svg.attr("height");

					d3.json("us.json").then(json => {  //1. load GeoJSON or TopoJSON

					var projection = d3.geoAlbersUsa()  //2. set-up a projection (lat, lon) → (x, y)
					  .fitSize([width, height], json);

					var path = d3.geoPath()  //3. set-up a geographic path generator: feature → path
					  .projection(projection);

					svg.selectAll("path")
					  .data(json.features)  //4. perform a data join with features
					  .enter()
					  .append("path")
					  .attr("fill", "white")
					  .attr("stroke", "black")
					  .attr("d", path);  //apply the path generator to set the path d attribute
					});
					</script>

d3.geoPath d3.geoAlbersUsa See d3-geo

Using TopoJSON with d3


				<svg width="960" height="600"></svg>

				<script>
				  d3.json("us-10m.v1.json").then(function (us) {  //us-10m.v1.json contains projected TopoJSON
									    
				  var path = d3.geoPath();  //set-up path generator
				  //no projection needed as TopoJSON is already projected!
  
					var svg = d3.select("svg");
				    svg.append("g")
				      .attr("class", "states")
				      .selectAll("path")
				      .data(
								topojson.feature(us, us.objects.states).features  //convert TopoJSON → GeoJSON
							)
				      .enter()
				      .append("path")
				      .attr("d", path);

				    svg.append("path")
				      .attr("class", "state-borders")
				      .attr("d", path( //generate path for GeoJSON features of interior boundaries
								topojson.mesh(us, us.objects.states, function (a, b) { return a !== b; })
							));  
				  });
				</script>

See topojson.feature, topojson.mesh

Additional Notes on GeoJSON and TopoJSON

Arbitrary extensions, e.g., .json, .geojson, .topojson
Load with d3.json
Specify geometry in geographical or projected coordinates
Encode the data:
- As separate files
- Embedded as geometry properties

DSCI 554 lecture 8

Depth perception and design, maps

Outline

Perceptual egocentric space

Depth information and depth cues

Oculomotor

Visual > Monocular > Static

Classic pictorial (i.e., in static image) cues Occlusions Linear perspective convergence Relative size, familiar size Texture gradient Shadows Shading Defocus blur Atmospheric perspective

Pictorial > Occlusions

Pictorial > Linear perspective convergence

Pictorial > Relative size, familiar size: object size

Pictorial > Relative size, familiar size: Relative height

Pictorial > Texture gradients

Pictorial > Shadows

Pictorial > Shading

Pictorial > Defocus Blur

Pictorial > Atmospheric Effects

Visual > Monocular > Motion-based > Motion parallax

Visual > Monocular > Motion-based > Occlusion in motion

Visual > Monocular > Motion-based > Structure from motion

Visual > Binocular > Stereopsis

Some (more) illusions

Size constancy (Ponzo) illusion

Poggendorff illusion

Muller-Lyer Illusion

Necker cube illusion

Shepard turning tables illusion [Shepard 90]

Design considerations

Popular 3D design techniques

2.5D design

2.5D design + constrained navigation

Outline

Thematic Maps

Dasymetric map (choropleth map) [Semenov-Tyan-Shansky 1911]

Outline

How maps are built?

Reference ellipsoid

Geographic coordinates

Geographic vs. geocentric latitude

Geodetic datum

Geoid

Geocentric vs. local geodetic datum

How maps are built?

Map projection

Properties preserved in maps

Can you have a map that is both conformal and equal-area?

Outline

Named projections types

Named projections sub-types

Lambert azimuthal equal area

Projection: azimuthal, equal-area

Albers conic

Projection: conic, Equal Area

Lambert conformal conic (LCC)

Projection: conic, conformal

Mercator projection

Projection: Cylindrical, Conformal

Universal Transverse Mercator (UTM)

Projection: Secant cylindrical transverse, conformal

Outline

Map formats

Raster

Vector

Map data formats and software

Tile Maps (Slippy Maps)

Tiles are served by a Tile Maps Service (TMS)

Slippy Map with Mapbox

GeoJSON

Duplicate boundaries with GeoJSON (large file size)

TopoJSON

Maps with D3

Using GeoJSON with d3

Using TopoJSON with d3

Additional Notes on GeoJSON and TopoJSON

Classic pictorial (i.e., in static image) cues

Occlusions

Linear perspective convergence

Relative size, familiar size

Texture gradient

Shadows

Shading

Defocus blur

Atmospheric perspective