Post on 04-Jan-2016
description
Calculating Visual Connectivity…an animated series of slides demonstrating 2D and 3D
visual connectivity from increasing viewer height (0’ to 20,000’)
Prepared by Joseph K. BerryKeck Scholar in Geosciences, University of Denver
Principal, Berry & Associates // Spatial Information Systems (BASIS)Fort Collins — jberry@innovativegis.comWebsite www.innovativegis.com/basis
Digital Elevation Model (DEM)(Grid Surface configured as 466 rows by 327 columns with 30m cells )
North
0 miles
6 miles
466 row
327 col
First Ridge6,312 Feet
Second Ridge7,799 Feet
++
Mount St. Helens Topography (project area) Raster Image
7,799 Feet7,799 Feet
6,312 Feet6,312 Feet
Viewer Location
3,219 feet
Point of Interest 3,267 feet
Viewer Elevation
3,219 Feet
Seen
NotSeen
(300c, 114r)Point of Interest
ViewerLocation
(33c, 454r)
.
Viewshed at 0 feet riseNorth
0 miles
6 miles
Point of Interest
Viewer Location
+
First Ridge Elevation (134c, 325r)
6,312 Feet
First Ridge
+
Minimum Visible Elevation
11,380 Feet
Calculating Visual Connectivity (Approach)
Similar triangles can be used to determine the minimum POI height needed to be visibly connected …
Tangent = Rise / Run1
POI Elevation = (Tangent * Run2) + Viewer Elevation
Similar triangles can be used to determine the minimum POI height needed to be visibly connected …
Tangent = Rise / Run1
POI Elevation = (Tangent * Run2) + Viewer Elevation
Rise
Run2
Run1
POI Height
N
Viewer Elevation
3,219 Feet
Seen
NotSeen
(300c, 114r)Point of Interest
ViewerLocation
(33c, 454r)
.
Viewshed at 0 feet riseNorth
0 miles
6 miles
Point of Interest
Viewer Location
+
First Ridge Elevation (134c, 325r)
6,312 Feet
First Ridge
+
Minimum Visible Elevation
11,380 Feet
Calculating Visual Connectivity (Approach)
N
Similar triangles can be used to determine the minimum POI height needed to be visibly connected …
Tangent = Rise / Run = (6312 ft – 3219 ft) / (SQRT[(134 – 33)2 + (454 – 325) 2 ] * 98.4251 ft) = 3093 ft / (163.835 * 98.4251 ft) = 3893 ft / 16125 ft = 0.1918
Height = (Tangent * Run) + Viewer Height = (0.1918 * (SQRT[(300 – 33)2 + (454 – 114) 2 ] * 98.4251 ft)) + 3219 ft = (0.1918 * 432.307 * 98.4251 ft) + 3219 = 11,380 Feet
Similar triangles can be used to determine the minimum POI height needed to be visibly connected …
Tangent = Rise / Run = (6312 ft – 3219 ft) / (SQRT[(134 – 33)2 + (454 – 325) 2 ] * 98.4251 ft) = 3093 ft / (163.835 * 98.4251 ft) = 3893 ft / 16125 ft = 0.1918
Height = (Tangent * Run) + Viewer Height = (0.1918 * (SQRT[(300 – 33)2 + (454 – 114) 2 ] * 98.4251 ft)) + 3219 ft = (0.1918 * 432.307 * 98.4251 ft) + 3219 = 11,380 Feet
3,219 + 500 =
3,719 Feet
Seen
Viewshed at 500 feet rise
Point of Interest
ViewerLocation
.
First Ridge
6,312 Feet
North
0 miles
6 miles+
+
…an animated series of “viewsheds” from increasing viewer heights demonstrates the importance of a 3-dimensional GIS
…advance slides for 1000’ viewer height increases
Visual Connectivity (500’ above the terrain)
N
3,219 + 1,000 =
4,219 Feet
Seen
North
0 miles
6 miles
Second Ridge Elevation (187c, 258r)
7,799 Feet
Viewshed at 1000 feet rise
Point of Interest
ViewerLocation
.
Second Ridge
+
+
Visual Connectivity (1000’ above the terrain)
N
3,219 + 2,000 =
5,219 Feet
Seen
North
0 miles
6 miles
Second Ridge
7,799 Feet
Viewshed at 2000 feet rise
Point of Interest
ViewerLocation
.
+
+
Visual Connectivity (2000’ above the terrain)
N
3,219 + 3,000 =
6,219 Feet
Seen
North
0 miles
6 miles
Viewshed at 3000 feet rise
Point of Interest
ViewerLocation
.
+
+
Second Ridge
7,799 Feet
Visual Connectivity (3000’ above the terrain)
N
3,219 + 4,000 =
7,219 Feet
Seen
North
0 miles
6 miles
Viewshed at 4000 feet rise
Point of Interest
ViewerLocation
.
+
+
Second Ridge
7,799 Feet
Visual Connectivity (4000’ above the terrain)
N
3,219 + 5,000 =
8,219 Feet
Seen
North
0 miles
6 miles
Viewshed at 5000 feet rise
Point of Interest
ViewerLocation
.
+
+
Second Ridge
7,799 Feet
Visual Connectivity (5000’ above the terrain)
N
3,219 + 6,000 =
9,219 FeetSeen
Viewshed at 6000 feet rise
Point of Interest
ViewerLocation
.
North
0 miles
6 miles
+
+
Second Ridge
7,799 Feet
Visual Connectivity (6000’ above the terrain)
N
3,219 + 7,000 =
10,219 FeetSeen
Viewshed at 7000 feet rise
Point of Interest
ViewerLocation
.
North
0 miles
6 miles
+
+
Second Ridge
7,799 Feet
Visual Connectivity (7000’ above the terrain)
N
3,219 + 8,000 =
11,219 FeetSeen
Viewshed at 8000 feet rise
Point of Interest
ViewerLocation
.
North
0 miles
6 miles
+
+
Second Ridge
7,799 Feet
Visual Connectivity (8000’ above the terrain)
N
3,219 + 9,000 =
12,219 Feet
Seen
Viewshed at 9000 feet rise
Point of Interest
ViewerLocation
.
North
0 miles
6 miles
+
+
Second Ridge
7,799 Feet
Visual Connectivity (9000’ above the terrain)
N
3,219 + 10,000 =
13,219 Feet
Seen
Viewshed at 10000 feet rise
Point of Interest
ViewerLocation
.
North
0 miles
6 miles
+
+
Second Ridge
7,799 Feet
Visual Connectivity (10000’ above the terrain)
N
3,219 + 11,000 =
14,219 Feet
Viewshed at 11000 feet rise
Point of Interest
ViewerLocation
.
SurfaceSeen
+
North
0 miles
6 miles
+
Second Ridge
7,799 Feet
Visual Connectivity (11000’ above the terrain)
Tangent = 0, therefore POI surface location is seen
N
3,219 + 11,000 =
14,219 Feet
.
ViewerLocation
Representing Geographic Space (2D and 3D)
Visual Exposure (VE)…a count of the number of times seen from specified viewer positions (0 – 11,000 feet above the terrain)
2D Plane(Pixel)
1
Seen 1 Time
All surface locations are assigned a VE valueAll surface locations
are assigned a VE value
Increasing Viewer Height (1000’ increments)
…from 0 Feet Viewer Height
Seen12
times
3D Volume(Voxel)
12
All volume locations are assigned a VE valueAll volume locations
are assigned a VE value
3-D Grid Data Structure is a direct expansion of the 2D structure with X, Y and Z coordinates defining the position in a 3-dimensional data matrix plus a value representing the characteristic or condition (attribute) associated with that location.
Point of Interest
3,219 + 12,000 =
15,219 Feet
Viewshed at 12000 feet rise
ViewerLocation
.
North
0 miles
6 miles
…continue advancing slides for viewsheds of viewer height increases to 20,000’
Visual Connectivity (12000’ above the terrain)
N
3,219 + 13,000 =
16,219 Feet
Viewshed at 13000 feet rise
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (13000’ above the terrain)
N
3,219 + 14,000 =
17,219 Feet
Viewshed at 14000 feet rise
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (14000’ above the terrain)
N
3,219 + 15,000 =
18,219 Feet
Viewshed at 15000 feet rise
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (15000’ above the terrain)
N
3,219 + 16,000 =
19,219 Feet
Viewshed at 16000 feet rise
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (16000’ above the terrain)
N
3,219 + 17,000 =
20,219 Feet
Viewshed at 17000 feet rise
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (17000’ above the terrain)
N
3,219 + 18,000 =
21,219 Feet
ViewerLocation
.
Viewshed at 18000 feet riseNorth
0 miles
6 miles
Visual Connectivity (18000’ above the terrain)
N
3,219 + 19,000 =
22,219 Feet
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (19000’ above the terrain)
N
Viewshed at 19000 feet rise
3,219 + 20,000 =
23,219 Feet
ViewerLocation
.
North
0 miles
6 miles
Visual Connectivity (20000’ above the terrain)
N
Viewshed at 20000 feet rise