OBB vs rectangle/quad/plane with bounds collision detection/response

Question

I am able to resolve collision between an OBB and a plane but can't get it to work when I introduce some bounds on the plane size. I want to have the plane of width and height dimensions defined by a normal and a position.

The code for detecting/resolving is fairly simple if the plane doesn't have any bounds:

function obbIntersectsPlane( obb, plane ) {
  let r = obb.size.x / 2 * Math.abs( dot( obb.right, plane.normal ) ) + 
          obb.size.y / 2 * Math.abs( dot( obb.up, plane.normal ) ) +
          obb.size.z / 2 * Math.abs( dot( obb.forward, plane.normal ) );
  
  let s = dot( plane.normal, obb.position ) - dot( plane.normal, plane.position );

  if ( Math.abs( s ) < r ) {
    return {
      overlap: r - s,
      vector: plane.normal
    };
  }

  return false;
}

Answer 1

Taking the plane as an obb with depth=0 works fine for me. I had to modify how I calculated overlap though to account for cases when the projection of one object was fully inside the other object's projection.

let overlap;

// check for cases when the projection is fully inside the projection of the other object

if ( a_max > b_max && a_min < b_min ) {
    overlap = Math.min( a_max - b_min, b_max - a_min );
} else if ( b_max > a_max && b_min < a_min ) {
    overlap = Math.min( b_max - a_min, a_max - b_min );
} else {
    overlap = Math.min( a_max, b_max ) - Math.max( a_min, b_min );
}