OpenGL Placing billboards at height of a terrain

Question

I'm working on some simple terrain generation in OpenGL and I have it so I render the terrain first and then I render billboards. The billboards are created by generating random points in my world which are then transformed into quads through a geometry shader, and textured in a fragment shader.

I'm wondering how I might extend this and have billboards spawn at some point on the terrain based on the height of the terrain.

Currently my terrain uses a height map but all the terrain rendering is handled in one pass and then in another pass, the billboards are rendered. I'm not sure how to place the billboards using the height of the terrain.

This is some code of my terrain rendering vertex shader:

layout (binding=1) uniform sampler2D HeightMapTexture;
vec3 heightRGB = texture( HeightMapTexture, vec2(vertexUV.x,vertexUV.y)).rgb;heightRGB *= 255;

int height = int(heightRGB.r) << 16 | int(heightRGB.g) << 8 | int(heightRGB.b);
float scale = ...;
float scaledHeight = float(height) * scale;
vec4 new_position = vec4(vertexPosition.x, vertexPosition.y + scaledHeight, vertexPosition, 1.0);
gl_Position = MVP * vec4(new_position.xyz, 1);

I've put the billboard vertex, geometry and fragment shader's on pastebin since the geometry shader is quite long. Billboard_vertex_geometry_fragment_shaders