Isovists & Viewshed

2 min read•1 page

Isovist Fields & Spatial Visibility: First formalized by Michael Benedikt in 1979, an isovist is the set of all spatial points visible from a single vantage point in space. By casting radial 360-degree sightlines until striking walls or columns, computational architects quantify human visual perception, measuring spatial openness, perimeter occlusivity, and surveillance sightlines.

Isovist Geometric Metrics:

1. Visual Area ($A_v$): Total square footage directly visible from the observation point. 2. Compactness Ratio: $4 \pi A / P^2$ measures whether the visual field is circular (open) or fractured (labyrinthine). 3. Occlusivity: Length of visual boundary segments that correspond to occluding edges rather than solid walls.

python

1import numpy as np
2
3def compute_isovist_polygon(viewpoint, obstacles, max_radius=10.0, num_rays=360):
4    """
5    Computes Benedikt (1979) 2D isovist polygon from a viewpoint.
6    Casts radial rays in 360 degrees and finds the nearest intersection with room obstacles.
7    Key metrics: Area, Perimeter, Compactness (Circularity), and Occlusivity.
8    """
9    isovist_vertices = []
10    angles = np.linspace(0, 2 * np.pi, num_rays, endpoint=False)
11    
12    for theta in angles:
13        ray_dir = np.array([np.cos(theta), np.sin(theta)])
14        closest_t = max_radius
15        
16        for segment in obstacles:
17            t = ray_segment_intersect(viewpoint, ray_dir, segment)
18            if t is not None and t < closest_t:
19                closest_t = t
20                
21        isovist_vertices.append(viewpoint + ray_dir * closest_t)
22        
23    return isovist_vertices

Viewpoint X

-0.20

Viewpoint Y

-0.40

1 min read•1 page

Cumulative Viewshed & Urban Sightlines: In regional master planning and skyline design, a viewshed identifies terrain and building zones visible from critical landmark viewpoints (such as historic monuments or observation decks). Computing mutual line-of-sight (LOS) across 3D city blocks highlights blind spots, public surveillance zones, and protected view corridors.

Viewshed Invariant:

1. Line-of-Sight (LOS): Unbroken straight line connecting observer coordinate to target point. 2. Elevation Profile: Any intervening terrain obstruction whose elevation angle exceeds the sightline causes occlusion. 3. Visual Connectivity Graph: Encodes human movement desire lines and commercial foot-traffic potential.

python

1def compute_cumulative_viewshed(dem_grid, observer_points):
2    """
3    Computes Digital Elevation Model (DEM) cumulative viewshed.
4    For each cell (x, y) on terrain, counts how many observers have unobstructed Line-of-Sight (LOS).
5    Uses Bresenham ray traversal or radial elevation profile slope comparisons:
6    tan(elevation_angle) = (z_target - z_obs) / horizontal_dist.
7    """
8    return "Cumulative Visibility Matrix (Heatmap)"

Tower Observer Height

2.00