The camera pitch that fits a ground plane to a frame is asin(footprintAspect / canvasAspect)
Fact
A flat board of width W and depth D viewed at pitch p above the horizon projects to W by D·sin(p), so its projected aspect is
projected = (W / D) / sin(p)Setting that equal to the canvas aspect A and solving gives the pitch that fits the board to the frame with nothing left over:
sin(p) = (W / D) / A p = asin(clamp((W / D) / A, lo, hi))A 20x13 board in a 2:1 canvas wants p = 50°; in a 1.7:1 canvas, 65°. The clamp is what keeps it usable: an A near the board's own aspect drives the solution to 90° — straight down, with the perspective thrown away — and a very wide A skims the camera along the ground.
Why it matters
Pitch is otherwise picked by eye on one window size and then quietly wrong everywhere else, because the mismatch does not look like a camera bug. It looks like wasted space, which invites tuning the canvas, the field of view, or the zoom — three knobs that cannot fix an angle.
The same relation also says which canvas shape to choose: measured against a 20x13 board, going from a canvas at the board's own 1.54 aspect to one at 2.0 raised the fraction of frame height the board covered from 0.65 to 0.81. Sizing a 3D viewport to the subject's 2D footprint is the reflex to avoid — the projection is always wider than the footprint.
How to apply
- Derive the pitch per layout from the measured canvas aspect; never store it as a constant.
- Clamp it to an angle range that still reads as a 3D view, roughly
sin(p) ∈ [0.6, 0.97], and treat the clamp as the design decision. - Shape the canvas to the projected aspect, not to the subject's footprint.
- Solve the distance separately, per corner of the bounding box.
- A pitch the viewer has since changed by dragging must not be overwritten on the next resize; keep a flag for it.
Related: [[framing-a-box-is-a-per-corner-solve]], [[auto-framing-collapses-to-face-on]].