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@Lucodivo
Created July 31, 2021 23:23
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Oblique Projection Matrix for Portals
/*
* // 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;
}
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