Point Segment Clamped Nearest Point

Description

Find the clamped nearest point on a nondegenerate planar segment and its Euclidean distance; finite number arithmetic, not a spatial index.

Planar geometry operates on two-coordinate Cartesian points and explicit shape boundaries. A closed rectangle includes its edges, while a segment parameter locates a point along a supporting line. Signed cross products, areas and axis gaps preserve orientation or direction information that a magnitude alone would lose.

Find the clamped nearest point on a nondegenerate planar segment and its Euclidean distance; finite number arithmetic, not a spatial index.

When to use this tool

Use this tool to find the clamped nearest point on a nondegenerate planar segment and its Euclidean distance; finite number arithmetic, not a spatial index.

How to use the tool and how it works

Enter point, start, end using the input definitions below.
Run the operation. Resolve malformed-input errors before interpreting the result.
Read result.parameter, result.point, result.distance. Interpret signs, units, ordering and null values using the rules below.

Compute the supporting-line projection parameter, clamp it to [0,1], interpolate the nearest point, and return its Euclidean distance from the supplied point. Reject a zero-length segment.^[1]

Input field	Meaning and units	Accepted input
point	Planar point [x,y] in the shape’s coordinate units.	Dense list of at most 128 finite numbers, subject to the stated integer/shape rules.
start	Segment start [x,y], corresponding to parameter zero.	Dense list of at most 128 finite numbers, subject to the stated integer/shape rules.
end	Segment end [x,y], corresponding to parameter one.	Dense list of at most 128 finite numbers, subject to the stated integer/shape rules.

Output field	Interpretation
result	Object containing the fields below.
result.parameter	Nearest-point segment parameter clamped to [0,1].
result.point	Resulting planar [x,y] point in coordinate units.
result.distance	Euclidean separation in the supplied coordinate units.

json

{
  "input": {
    "point": [
      3,
      1
    ],
    "start": [
      0,
      0
    ],
    "end": [
      2,
      0
    ]
  },
  "output": {
    "result": {
      "parameter": 1,
      "point": [
        2,
        0
      ],
      "distance": 1.4142135623730951
    }
  }
}

Limitations and assumptions

Distance uses the planar coordinate units; geographic/geodesic distance and uncertain measurement bounds are outside this model.
Point components and rectangle bounds are finite within ±1,000,000,000. Rectangles use [minX,minY,maxX,maxY] with ordered inclusive bounds. Floating arithmetic is used without an implicit robustness tolerance.
Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.

Alternative or Complementary methods

Choose the boundary and coordinate convention explicitly. Use robust geometric predicates or a topology-aware library when near-coincidence, holes, invalid polygons or geographic coordinates matter.

References

Tool behavior and example: Point Segment Clamped Nearest Point — tool.io

Similar or alternative tools

Point Segment Projection Parameter
Project a point onto the infinite supporting segment line and return the unclamped parameter; a degenerate segment is rejected.
Rectangle Point Clamp
Clamp a finite planar point to a closed axis-aligned rectangle, allowing degenerate rectangle axes; no polygon or geographic containment.