Isovists & Viewshed

3 min read•1 page

Isovist Geometric Metrics:

1. Visual Area (A_v): Total square footage directly visible from the observation point. 2. Compactness Ratio: 4 π 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

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.

Viewpoint X

-0.20

Viewpoint Y

-0.40

4 min read•1 page

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

1import numpy as np
2
3def compute_cumulative_viewshed(dem_grid, observer_points, observer_height=1.7):
4    """
5    Computes Digital Elevation Model (DEM) cumulative viewshed across a 2D terrain grid.
6    Scans radial Line-of-Sight (LOS) rays from each observer and tracks the running
7    maximum horizon elevation slope tan(alpha) = (z_cell - z_obs) / dist.
8    """
9    rows, cols = dem_grid.shape
10    viewshed = np.zeros((rows, cols), dtype=int)
11
12    for ox, oy in observer_points:
13        z_obs = dem_grid[oy, ox] + observer_height
14        for ty in range(rows):
15            for tx in range(cols):
16                steps = max(abs(tx - ox), abs(ty - oy))
17                if steps == 0:
18                    viewshed[ty, tx] += 1
19                    continue
20                max_slope = -np.inf
21                visible = True
22                for s in range(1, steps + 1):
23                    cx = int(round(ox + (tx - ox) * (s / steps)))
24                    cy = int(round(oy + (ty - oy) * (s / steps)))
25                    dist = np.hypot(cx - ox, cy - oy)
26                    slope = (dem_grid[cy, cx] - z_obs) / max(dist, 1e-6)
27                    if s < steps and slope > max_slope:
28                        max_slope = slope
29                    elif s == steps and slope < max_slope:
30                        visible = False
31                if visible:
32                    viewshed[ty, tx] += 1
33    return viewshed

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.

Tower Observer Height

2.00

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