Calculating Visual Connectivity …an animated series of slides demonstrating 2D and 3D

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 — [email protected] 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