vectorScale

vectorScale.ts

// function that scales an array of vectors to a given length and interpolates between the the vectors
// to create a smooth path
// input: array of vectors
// output: array of vectors

export type Vector = number[];

export function vectorScale(vectors: Vector[], length: number): Vector[] {
  const result: Vector[] = [];

  if (vectors.length === 0) {
    return result;
  }

  const numVectors = vectors.length;
  const segmentLength = length / (numVectors - 1);

  for (let i = 0; i < numVectors - 1; i++) {
    const currentVector = vectors[i];
    const nextVector = vectors[i + 1];
    const segmentVector: Vector = [];

    for (let j = 0; j < currentVector.length; j++) {
      const currentComponent = currentVector[j];
      const nextComponent = nextVector[j];
      const interpolatedComponent =
        currentComponent +
        ((nextComponent - currentComponent) * segmentLength) / vectorLength(
          currentVector,
          nextVector
        );

      segmentVector.push(interpolatedComponent);
    }

    result.push(segmentVector);
  }

  result.push(vectors[numVectors - 1]);

  return result;
}

// Helper function to calculate the length of a vector
function vectorLength(v1: Vector, v2: Vector): number {
  let sum = 0;

  for (let i = 0; i < v1.length; i++) {
    const diff = v2[i] - v1[i];
    sum += diff * diff;
  }

  return Math.sqrt(sum);
}

console.log(vectorScale([[1, 2], [3, 4], [5, 6]], 10));
console.log(vectorScale([[0, 1], [1, 0], [0, 2]], 5));
console.log(vectorScale([[0, 1], [1, 0], [0, 2]], 7));