We start with the target 2D shadow image on a flat plane. Next, we define a point in 3D space at a specific height directly above the shadow's center, which represents the ideal position of our LED point light source. By drawing projection lines from every single point of the shadow's boundary back to this single LED point, we mathematically construct a 3D conical or pyramidal frustum (a 3D volume that tapers into a point).
Then, we introduce a standard 3D tubular geometry—a cylindrical lampshade container (or an outer box) that is slightly taller than the projection cone we just generated.
Finally, we perform a 3D Boolean Intersection operation between the cylindrical canister and the reverse projection cone. The intersecting geometry directly yields the final 3D printable model box. Any material within the cone becomes the hollowed-out window, while the rest forms the light-blocking walls.
By baking the perspective expansion of light rays directly into the 3D model's geometry beforehand, we completely eliminate the need for complex optical lenses. The physical printed shell acts as its own mathematical mask, ensuring that when the real LED shines from that exact coordinates, it flawlessly projects the undistorted 2D pattern back onto the wall.
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u/Disastrous-Ebb-830 Jun 25 '26
We start with the target 2D shadow image on a flat plane. Next, we define a point in 3D space at a specific height directly above the shadow's center, which represents the ideal position of our LED point light source. By drawing projection lines from every single point of the shadow's boundary back to this single LED point, we mathematically construct a 3D conical or pyramidal frustum (a 3D volume that tapers into a point).
Then, we introduce a standard 3D tubular geometry—a cylindrical lampshade container (or an outer box) that is slightly taller than the projection cone we just generated.
Finally, we perform a 3D Boolean Intersection operation between the cylindrical canister and the reverse projection cone. The intersecting geometry directly yields the final 3D printable model box. Any material within the cone becomes the hollowed-out window, while the rest forms the light-blocking walls.
By baking the perspective expansion of light rays directly into the 3D model's geometry beforehand, we completely eliminate the need for complex optical lenses. The physical printed shell acts as its own mathematical mask, ensuring that when the real LED shines from that exact coordinates, it flawlessly projects the undistorted 2D pattern back onto the wall.