Graph theory / modeling basics — In geometric modeling of solids, is a vertex correctly defined as the endpoint of an edge (i.e., where edges meet)?

Introduction / Context:
In solid modeling, computational geometry, and descriptive geometry, objects are represented by vertices, edges, and faces. Clear definitions prevent ambiguity when translating designs between sketches, CAD models, and manufacturing documentation.

Given Data / Assumptions:

• Vertex: a fundamental element of topology in models.
• Edge: a connection between two vertices; boundary between faces.
• Faces meet along edges; edges meet at vertices.

Concept / Approach:
The standard topological relationship is: vertices are 0D points; edges are 1D connections between pairs of vertices; faces are 2D bounded regions. Therefore, an edge terminates at vertices, and the "end of an edge" is indeed a vertex.

Step-by-Step Solution:
1) Recall definitions: vertex (0D), edge (1D), face (2D).2) Analyze their relationships: edges connect vertices; faces are bounded by edges.3) Conclude the statement is correct.

Verification / Alternative check:
Inspect any B-Rep (boundary representation) model: topology tables list vertices, edges (with start/end vertices), and faces. Edges explicitly reference vertex IDs as endpoints.

Why Other Options Are Wrong:

• Incorrect: Contradicts standard definitions.
• Only true for wireframe models: Also true for solid B-Rep models.
• Depends on projection type: Projection does not alter model topology.
• True only in 2D: Applies to 2D and 3D models.

Common Pitfalls:
Confusing geometric length with topological connectivity; mixing screen pixels with model entities; assuming faces are necessary to define vertices (they are not).

Final Answer:
Correct