Fragment shader w/ perspective camera - How do I convert from clip space to world space? (for volumetric rendering)

To convert from clip space to world space, I am simply multiplying my clip space point by the matrix `mat4 clipToWorldMatrix = inverse(projectionMatrix * viewMatrix * modelMatrix);`. This strategy works for orthographic camera, but does not work for perspective camera.

A bit of background on what I am trying to do:
Overall, I am using a fullscreen quad as a “window” into a volumetrically rendered world. ie, from each fragment of a fullscreen quad I raycast into my data structure, and render collisions. The start and end of each fragment’s ray are two points located on the near and far clipping planes: variables `worldCoordNear` and `worldCoordFar`, respectively. In the vertex shader I calculate `worldCoordNear` and `worldCoordFar` and pass them to the fragment shader. Then in the fragment shader, I raycast between those points, and color the fragment based on intersection with my data structure (a single cube for now).

I’ve created a working implementation of this strategy using an orthographic camera: [done] three.js volumetric rendering onto fullscreen quad with orthographic camera - JSFiddle - Code Playground . You can see the volumetrically rendered cube (solid red) is the same size as the mesh cube (green wireframe).

However, this strategy does not work with a perspective camera: [bug] three.js volumetric rendering onto fullscreen quad with perspective camera - JSFiddle - Code Playground. I see a few indications that my raycast positions are wrong (cube looks big and orthographic). So where am I going wrong with my perspective camera to make the cube the wrong size?

After a bit more digging, I’ve found that clip space is not the same as “frustum space” when dealing with perspective camera projection. I’ve cobbled together this function to solve my problem:

``````  vec4 frustumToWorld(vec3 viewportPoint) {
vec4 worldCoord = inverse(projectionMatrix * viewMatrix) * vec4(viewportPoint.x, viewportPoint.y, 1.0 - viewportPoint.z, 1.0);
worldCoord.x /= worldCoord.w;
worldCoord.y /= worldCoord.w;
worldCoord.z /= worldCoord.w;

return worldCoord;
}
``````