Oblique Projection Matrix for Portals

ObliqueProjectionMatrix.cpp

/*
 * // NOTE: Oblique View Frustum Depth Projection and Clipping by Eric Lengyel (Terathon Software)
 * Arguments:
 * mat4 perspectiveMat: Perspective matrix that is being used for the rest of the scene
 * vec3 planeNormal_viewSpace: Plane normal in view space. MUST be normalized. This is a normal that points INTO the frustum, NOT one that is generally pointing towards the camera.
 * vec3 planePos_viewSpace: Any position on the plane in view space.
 */
mat4 obliquePerspective(const mat4& perspectiveMat, vec3 planeNormal_viewSpace, vec3 planePos_viewSpace, f32 far) {

  mat4 persp = perspectiveMat;

  // plane = {normal.x, normal.y, normal.z, dist}
  vec4 plane_viewSpace = Vec4(planeNormal_viewSpace, dot(-planeNormal_viewSpace, planePos_viewSpace));

  // clip space plane
  vec4 oppositeFrustumCorner_viewSpace = {
          sign(plane_viewSpace.x) * (1.0f / perspectiveMat.xTransform.x),
          sign(plane_viewSpace.y) * (1.0f / perspectiveMat.yTransform.y),
          -1.0f,
          1.0f / far
  };

  vec4 scaledPlane_viewSpace = ((-2.0f * oppositeFrustumCorner_viewSpace.z) / dot(plane_viewSpace, oppositeFrustumCorner_viewSpace)) * plane_viewSpace;

  persp[0][2] = scaledPlane_viewSpace.x;
  persp[1][2] = scaledPlane_viewSpace.y;
  persp[2][2] = scaledPlane_viewSpace.z + 1.0f;
  persp[3][2] = scaledPlane_viewSpace.w;

  return persp;
}

/*
 * // NOTE: Oblique View Frustum Depth Projection and Clipping by Eric Lengyel (Terathon Software)
 * Arguments:
 * vec3 planeNormal_viewSpace: Plane normal in view space. MUST be normalized. This is a normal that points INTO the frustum, NOT one that is generally pointing towards the camera.
 * vec3 planePos_viewSpace: Any position on the plane in view space.
 */
mat4 obliquePerspective(f32 fovVert, f32 aspect, f32 near, f32 far, vec3 planeNormal_viewSpace, vec3 planePos_viewSpace) {
  const f32 c = 1.0f / tanf(fovVert / 2.0f);

  // plane = {normal.x, normal.y, normal.z, dist}
  vec4 plane_viewSpace = Vec4(planeNormal_viewSpace, dot(-planeNormal_viewSpace, planePos_viewSpace));

  // clip space plane
  vec4 oppositeFrustumCorner_viewSpace = {
          sign(plane_viewSpace.x) * (aspect / c),
          sign(plane_viewSpace.y) * (1.0f / c),
          -1.0f,
          1.0f / far
  };

  vec4 scaledPlane_viewSpace = ((-2.0f * oppositeFrustumCorner_viewSpace.z) / dot(plane_viewSpace, oppositeFrustumCorner_viewSpace)) * plane_viewSpace;

  mat4 resultMat = {
          (c / aspect), 0.0f, scaledPlane_viewSpace.x, 0.0f,
          0.0f, c, scaledPlane_viewSpace.y, 0.0f,
          0.0f, 0.0f, scaledPlane_viewSpace.z + 1.0f, -1.0f,
          0.0f, 0.0f, scaledPlane_viewSpace.w, 0.0f
  };

  return resultMat;
}