Calculator Inputs
Overall page uses a single-column content flow.Formula Used
Given: point P, ray origin A, and direction vector d.
Supporting line parameter: t = ((P − A) · d) / (d · d)
Ray clamp: tray = max(0, t)
Closest point on the ray: C = A + trayd
Distance: distance = ||P − C||
If the raw projection parameter is negative, the perpendicular foot falls behind the ray origin.
In that case, the nearest point is the origin itself, not the line projection.
How to Use This Calculator
- Select whether your problem is 2D or 3D.
- Enter the point coordinates for P.
- Enter the ray starting coordinates for A.
- Enter the direction vector components for d.
- Choose decimal precision and plot scale.
- Press Calculate Distance to show the result above the form.
- Review the closest point, projection status, and graph.
- Use the CSV or PDF buttons to export the current result summary.
Example Data Table
| Case | Dimension | Point P | Ray Origin A | Direction d | Expected Behavior |
|---|---|---|---|---|---|
| Example 1 | 2D | (4, 3) | (0, 0) | (5, 1) | Projection falls on ray. |
| Example 2 | 2D | (-2, 5) | (1, 1) | (3, 0) | Closest point becomes the origin. |
| Example 3 | 3D | (3, 2, 6) | (1, 0, 0) | (2, 1, 2) | Uses full spatial projection. |
Frequently Asked Questions
1. What does this calculator measure?
It measures the shortest straight-line distance from a point to a ray. A ray starts at one point and extends forever in one direction.
2. Why is a ray different from a line?
A line extends infinitely both ways. A ray has a fixed start and only extends forward, so backward projections must be clamped to the origin.
3. What happens when the projection parameter is negative?
A negative parameter means the perpendicular projection lies behind the ray origin. Then the nearest point on the ray is the starting point itself.
4. Can I use this for 3D geometry?
Yes. Choose 3D mode and enter z-values. The calculation uses all three coordinates, while the chart still presents an x-y view for clarity.
5. Why must the direction vector be nonzero?
A zero vector gives no direction, so it cannot define a valid ray. The calculator blocks that case to avoid division by zero.
6. Does the calculator require normalized direction vectors?
No. Any nonzero direction vector works. The formula divides by d · d, so normalization is optional.
7. What does the closest point mean?
It is the exact location on the ray nearest to your input point. The displayed distance is measured between that location and the point.
8. When would this be useful?
It helps in geometry homework, vector analysis, graphics, simulation, robotics, path modeling, collision checks, and directional measurement problems.