Linear Interpolation (lerp)

Method: point.lerp(that, t)

Parameters:

• that — the end point

• t — a number in the range \([0, 1]\)

Returns: Point

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Description

Linear interpolation (lerp) finds the point that lies a fractional distance \(t\) of the way from this to that along the straight line between them:

\[P(t) = A + t\,(B - A) = (1 - t)\,A + t\,B\]

where \(A\) is this and \(B\) is that.

Evaluating the formula at the boundary values and midpoint:

t	Result
0	\(A\) — the start point
0.5	Midpoint between \(A\) and \(B\)
1	\(B\) — the end point

Values of \(t\) outside \([0, 1]\) extrapolate beyond the segment.

Relationship to midPoint

The built-in midPoint() method is a special case of lerp with \(t = 0.5\):

\[\text{midPoint}(A, B) = A.\text{lerp}(B,\ 0.5)\]

Implementation

lerp(that, t) {
  return new Point(
    this.x + (that.x - this.x) * t,
    this.y + (that.y - this.y) * t,
  );
}

Usage in Design

lerp is used whenever a point at a known fraction along a segment is needed — for example, generating intermediate sample points along a line or polyline segment for snap calculations, or computing a position part-way between two geometry points during drawing operations.

See Also

Project | Development