1. What is the Directed Line Segment Ratio?

The directed line segment ratio calculates a point that divides a line segment between two points (Start and End) in a given ratio t. When t=0, the point is at Start; when t=1, it's at End; when t=0.5, it's the midpoint.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

Where:

• \( t \) — Ratio parameter (0 ≤ t ≤ 1)
• \( \text{Start} \) — Starting point coordinates (x₁, y₁)
• \( \text{End} \) — Ending point coordinates (x₂, y₂)
• \( \text{Point} \) — Calculated point coordinates

Explanation: The formula computes a weighted average of the start and end points based on the ratio t.

3. Applications of Line Segment Division

Details: This calculation is fundamental in computer graphics, animation, geometric modeling, and physics simulations for interpolating between points.

4. Using the Calculator

Tips: Enter the ratio t (between 0 and 1), the start point coordinates, and end point coordinates. The calculator will compute the point that divides the segment in the given ratio.

5. Frequently Asked Questions (FAQ)

Q1: What happens if t is outside [0,1] range?
A: The calculator restricts t to [0,1]. Values outside this range would extrapolate beyond the segment.

Q2: Can this be used in 3D space?
A: Yes, the same formula applies by adding a z-coordinate calculation.

Q3: How is this different from midpoint calculation?
A: Midpoint is a special case where t = 0.5. This calculator works for any ratio.

Q4: What's the geometric interpretation?
A: The point divides the segment into two parts whose lengths are in ratio t:(1-t).

Q5: Can this be used for vector interpolation?
A: Yes, the same formula works for interpolating between vectors in any dimension.