Question

Which of the following options is/are CORRECT in the context of line-area spatial relationship?

• A. Line is contained in area
• B. Line crosses area
• C. Line is parallel to area
• D. Line is nearest to area

Hint:

Topological relations between a line and an area are defined only by how the line's points fall relative to the polygon's interior, boundary and exterior, not by direction (parallel) or by distance (nearest), which are metric properties instead.

Answer 1

The Correct Option is A, B

Step 1: Recall how spatial relationships between features are classified.
In GIS, the spatial relationship between two features is generally described using topological relations, which depend only on how the boundaries and interiors of the two features touch, overlap or stay apart, not on any measured distance or compass direction between them. Standard frameworks such as the dimensionally extended nine intersection model classify feature pairs using terms like disjoint, touch, overlap, cross, within and contains.

Step 2: Explain "line is contained in area".
A line is said to be contained in (or within) an area when every point of the line lies inside the interior or boundary of the polygon, with no part of the line extending outside it. This is a standard, well defined topological relation, for example an internal road that lies entirely inside a park polygon is contained in that polygon, so this is a valid line-area spatial relationship.

Step 3: Explain "line crosses area".
A line is said to cross an area when part of the line lies inside the polygon and part lies outside it, so the line's interior intersects both the interior and the exterior of the polygon, entering and leaving through the boundary. This too is a standard topological relation, for example a highway that enters and exits a district polygon crosses that polygon, so this is also a valid line-area spatial relationship.

Step 4: Explain why "parallel to" is not a valid topological relation.
Parallelism is a purely directional, metric concept, it depends on the orientation (bearing or slope) of the line compared to some reference direction associated with the area, such as one of its edges. It says nothing about whether the line touches, enters, or stays away from the polygon's interior or boundary, and it is not preserved under the kind of topological transformations (stretching, bending without tearing) that define topological relations, so it is not recognized as a line-area topological relationship.

Step 5: Explain why "nearest to" is not a valid topological relation.
Nearness is a metric, distance based concept, it requires measuring and comparing distances, which again is not a topological property, two features can be "near" or "far" while their topological relationship (disjoint, touching, crossing, contained) stays exactly the same regardless of how far apart they are, so proximity is a separate, non-topological spatial query, not a defined line-area relationship type.

Step 6: Conclusion.
Of the four listed options, only "line is contained in area" and "line crosses area" are recognized line-area spatial (topological) relationships.

\[ \boxed{\text{Line is contained in area, and Line crosses area}} \]