Flip a 3D point over a line defined by two 3D points

flip-point-over-line.js

export function flipPointOverLine(linePoint1, linePoint2, point) {
  // Calculate the vector that represents the line direction
  const lineVector = vec3.create();
  vec3.subtract(lineVector, linePoint2, linePoint1);
  vec3.normalize(lineVector, lineVector);

  // Calculate the projection of the point onto the line
  // relative to the start of the line
  const pointToLinePoint1 = vec3.subtract(vec3.create(), point, linePoint1);
  const dotProduct = vec3.dot(pointToLinePoint1, lineVector);
  const projection = vec3.scale(vec3.create(), lineVector, dotProduct);

  // Calculate the reflection of the point across the line
  const reflection = vec3.create();
  vec3.subtract(reflection, pointToLinePoint1, projection);
  vec3.scale(reflection, reflection, -1);
  vec3.add(reflection, reflection, projection);

  // Add the start of the line to the reflection to get the
  // absolute position of the reflection
  const absoluteReflection = vec3.add(vec3.create(), linePoint1, reflection);

  return absoluteReflection;
}