Visibility (geometry)¶
A geometric relation in which two points see one another when the line segment joining them remains inside free space and avoids declared obstacles.
Core Idea¶
Visibility depends on whether obstacles are open or closed, boundary contact rules, dimension and metric, and supports derived structures such as visibility polygons and graphs. A straight segment between two query points is intersected with the obstacle set or tested for containment in a polygonal domain; an unobstructed segment witnesses mutual visibility. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Visibility (geometry) belongs to computational geometry and is useful where the analyst can specify the typed computational geometry carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the ambient Euclidean space and dimension, free-space and obstacle geometry, point locations, closed-segment convention, boundary and tangency rule, mutual or directed visibility, degeneracies, exact arithmetic assumptions and derived graph or region if any are explicit. The scope is broad within that domain but bounded by the need for the ambient Euclidean space and dimension, free-space and obstacle geometry, point locations, closed-segment convention, boundary and tangency rule, mutual or directed visibility, degeneracies, exact arithmetic assumptions and derived graph or region if any are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the ambient Euclidean space and dimension, free-space and obstacle geometry, point locations, closed-segment convention, boundary and tangency rule, mutual or directed visibility, degeneracies, exact arithmetic assumptions and derived graph or region if any are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Visibility (geometry). Visibility (geometry) compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed computational geometry carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the ambient Euclidean space and dimension, free-space and obstacle geometry, point locations, closed-segment convention, boundary and tangency rule, mutual or directed visibility, degeneracies, exact arithmetic assumptions and derived graph or region if any are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of computational geometry because they reuse the typed computational geometry carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets, A straight segment between two query points is intersected with the obstacle set or tested for containment in a polygonal domain; an unobstructed segment witnesses mutual visibility., and type the carrier, state every parameter and convention in the definition, test that the ambient Euclidean space and dimension, free-space and obstacle geometry, point locations, closed-segment convention, boundary and tangency rule, mutual or directed visibility, degeneracies, exact arithmetic assumptions and derived graph or region if any are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Visibility (geometry) Domain-specific
Parents (1) — more general patterns this builds on
-
Visibility (geometry) is a kind of Relation Prime
The proposed strict upward parent is
prime:relation.
Hierarchy path (1) — routes to 1 parentless root
- Visibility (geometry) → Relation
Neighborhood in Abstraction Space¶
Visibility (geometry) sits in a crowded region of the domain-specific corpus (11th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Convex Geometry & Spatial Partition (35 abstractions)
Nearest neighbors
- Line–line intersection — 0.93
- Binary space partitioning — 0.93
- Curve — 0.92
- Opaque set — 0.92
- Corner-point grid — 0.92
Computed from structural-signature embeddings · 2026-09-08