Calculating Visual Connectivity an animated series of slides

Calculating Visual Connectivity …an animated series of slides demonstrating 2 D and 3 D visual connectivity from increasing viewer height (0’ to 20, 000’) Prepared by Joseph K. Berry Keck Scholar in Geosciences, University of Denver Principal, Berry & Associates // Spatial Information Systems (BASIS) Fort Collins — jberry@innovativegis. com Website www. innovativegis. com/basis

Mount St. Helens Topography (project area) Raster Image 7, 799 Feet 6, 312 Feet Viewer Location Second Ridge 7, 799 Feet Point of Interest 3, 219 feet First Ridge 6, 312 Feet 3, 267 feet 327 col 466 row + 6 miles + North Digital Elevation Model (DEM) (Grid Surface configured as 466 rows by 327 columns with 30 m cells ) 0 miles

Calculating Visual Connectivity (Approach) Viewer Location First Ridge + Similar triangles can be used to determine the minimum POI height needed to be visibly connected … (300 c, 114 r) Point of Interest Tangent = Rise / Run 1 POI Height Rise Run 1 Run 2 POI Elevation = (Tangent * Run 2) + Viewer Elevation Point of Interest N Seen Minimum Visible Elevation 11, 380 Feet Not Seen First Ridge Elevation (134 c, 325 r) 6, 312 Feet Viewer Elevation 3, 219 Feet . Viewer Location (33 c, 454 r) 6 miles + North Viewshed at 0 feet rise 0 miles

Calculating Visual Connectivity (Approach) Viewer Location First Ridge + Similar triangles can be used to determine the minimum POI height needed to be visibly connected … Tangent = Rise / Run (300 c, 114 r) Point of Interest = (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 Point of Interest N Seen Minimum Visible Elevation 11, 380 Feet Not Seen First Ridge Elevation (134 c, 325 r) 6, 312 Feet Viewer Elevation 3, 219 Feet . Viewer Location (33 c, 454 r) 6 miles + North Viewshed at 0 feet rise 0 miles

Visual Connectivity (500’ above the terrain) + Point of Interest …an animated series of “viewsheds” from increasing viewer heights demonstrates the importance of a 3 -dimensional GIS …advance slides for 1000’ viewer height increases N Seen First Ridge 6, 312 Feet 3, 219 + 500 = 3, 719 Feet . Viewer Location 6 miles + North Viewshed at 500 feet rise 0 miles

Visual Connectivity (1000’ above the terrain) Point of Interest + Second Ridge N Seen Second Ridge Elevation (187 c, 258 r) 7, 799 Feet 3, 219 + 1, 000 = 4, 219 Feet . Viewer Location 6 miles + North Viewshed at 1000 feet rise 0 miles

Visual Connectivity (2000’ above the terrain) Point of Interest + N Seen Second Ridge 7, 799 Feet 3, 219 + 2, 000 = 5, 219 Feet . Viewer Location 6 miles + North Viewshed at 2000 feet rise 0 miles

Visual Connectivity (3000’ above the terrain) Point of Interest + N Seen Second Ridge 7, 799 Feet 3, 219 + 3, 000 = 6, 219 Feet . Viewer Location 6 miles + North Viewshed at 3000 feet rise 0 miles

Visual Connectivity (4000’ above the terrain) Point of Interest + N Seen Second Ridge 7, 799 Feet 3, 219 + 4, 000 = 7, 219 Feet . Viewer Location 6 miles + North Viewshed at 4000 feet rise 0 miles

Visual Connectivity (5000’ above the terrain) Point of Interest + N Seen Second Ridge 7, 799 Feet 3, 219 + 5, 000 = 8, 219 Feet . Viewer Location 6 miles + North Viewshed at 5000 feet rise 0 miles

Visual Connectivity (6000’ above the terrain) Point of Interest + N Seen 3, 219 + 6, 000 = Second Ridge 7, 799 Feet 9, 219 Feet . Viewer Location 6 miles + North Viewshed at 6000 feet rise 0 miles

Visual Connectivity (7000’ above the terrain) Point of Interest + 3, 219 + 7, 000 = N Seen Second Ridge 10, 219 Feet . 7, 799 Feet Viewer Location 6 miles + North Viewshed at 7000 feet rise 0 miles

Visual Connectivity (8000’ above the terrain) Point of Interest + 3, 219 + 8, 000 = N Seen 11, 219 Feet . Second Ridge 7, 799 Feet Viewer Location 6 miles + North Viewshed at 8000 feet rise 0 miles

Visual Connectivity (9000’ above the terrain) Point of Interest + 3, 219 + 9, 000 = 12, 219 Feet N Seen . Second Ridge 7, 799 Feet Viewer Location 6 miles + North Viewshed at 9000 feet rise 0 miles

Visual Connectivity (10000’ above the terrain) Point of Interest + 3, 219 + 10, 000 = 13, 219 Feet N Seen . Second Ridge 7, 799 Feet Viewer Location 6 miles + North Viewshed at 10000 feet rise 0 miles

Visual Connectivity (11000’ above the terrain) Tangent = 0, therefore POI surface location is seen Point of Interest + 3, 219 + 11, 000 = 14, 219 Feet . N Second Ridge 7, 799 Feet Surface Seen Viewer Location 6 miles + North Viewshed at 11000 feet rise 0 miles

Representing Geographic Space (2 D and 3 D) 3 -D Grid Data Structure is a direct expansion of the 2 D 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. Increasing Viewer Height Point of Interest Seen 12 times (1000’ increments) 12 3, 219 + 11, 000 = 14, 219 Feet 3 D Volume …from 0 Feet Viewer Height (Voxel) . All volume locations are assigned a VE value Seen 1 Time 2 D Plane (Pixel) 1 All surface locations are assigned a VE value Visual Exposure (VE) …a count of the number of times seen from specified viewer positions (0 – 11, 000 feet above the terrain) Viewer Location

Visual Connectivity (12000’ above the terrain) …continue advancing slides for viewsheds of viewer height increases to 20, 000’ 3, 219 + 12, 000 = 15, 219 Feet . N Viewer Location 6 miles North Viewshed at 12000 feet rise 0 miles

Visual Connectivity (13000’ above the terrain) 3, 219 + 13, 000 = 16, 219 Feet . N Viewer Location 6 miles North Viewshed at 13000 feet rise 0 miles

Visual Connectivity (14000’ above the terrain) 3, 219 + 14, 000 = 17, 219 Feet . N Viewer Location 6 miles North Viewshed at 14000 feet rise 0 miles

Visual Connectivity (15000’ above the terrain) 3, 219 + 15, 000 = 18, 219 Feet . N Viewer Location 6 miles North Viewshed at 15000 feet rise 0 miles

Visual Connectivity (16000’ above the terrain) 3, 219 + 16, 000 = 19, 219 Feet . N Viewer Location 6 miles North Viewshed at 16000 feet rise 0 miles

Visual Connectivity (17000’ above the terrain) 3, 219 + 17, 000 = 20, 219 Feet . N Viewer Location 6 miles North Viewshed at 17000 feet rise 0 miles

Visual Connectivity (18000’ above the terrain) 3, 219 + 18, 000 = 21, 219 Feet . N Viewer Location 6 miles North Viewshed at 18000 feet rise 0 miles

Visual Connectivity (19000’ above the terrain) 3, 219 + 19, 000 = 22, 219 Feet . N Viewer Location 6 miles North Viewshed at 19000 feet rise 0 miles

Visual Connectivity (20000’ above the terrain) 3, 219 + 20, 000 = 23, 219 Feet . N Viewer Location 6 miles North Viewshed at 20000 feet rise 0 miles