Perspective explorer

Drag a box or tilt the camera and see where its vanishing points really land — computed from true central projection, not drawn by eye.

Set-ups

Face the box straight on: only the depth edges converge — a single VP at the center of vision.

Box rotation (yaw)0°Camera tilt (pitch)0°Viewing distance (eye → picture plane)1.40 · FOV 71°Box distance4.0Show the depth row — equal posts marching away

Result

One-point perspective

1 of 3 edge families converge — the count of vanishing points isthe “mode”.

width edgesparallel — no VP

depth edgesVP at 0.00 fw R, 0.00 fw up

vertical edgesparallel — no VP

Horizonat eye level (frame center)

The picture plane — and where the VPs really land

Solid lines are the box; dashed lines extend each edge family to its vanishing point. Distances are in frame widths (fw) from the center of vision. Drag to look around.

How is this calculated?

Using the tool

One-point, two-point, three-point are not drawing styles you pick — they are what central projection does to a box depending on how it faces you. Drag the box (or tilt the camera) and watch each family of parallel edges either stay parallel or converge to its vanishing point, plotted exactly where the math puts it — usually outside the picture frame, which is why your VPs never fit on the paper. The viewing distance slider shows the other secret: the two horizontal VPs can't move independently — push one in and the other flies out.

The math

A vanishing point is not a drawing trick — it is the projection of a direction. Every family of parallel edges shares one direction, so all of its lines meet at one point on the picture plane: where a ray from your eye, parallel to those edges, punches through the plane. If the edges run parallel to the plane itself, that ray never crosses it and the family keeps its lines parallel on paper. Face the box and two families are parallel to the plane — one VP. Turn it — two. Tilt the camera so verticals lean into the view — three. The “mode” was never a choice; it is the count.

The two horizontal VPs are chained by an exact rule: their distances from the center of vision multiply to the square of your viewing distance (x₁ · x₂ = −d²). Rotate the box and one VP slides in while the other slides out — you cannot bring both close. Only shrinking d(eye closer to the window, wider field of view) pulls them together, and that is exactly when drawings start to look warped. The workshop advice “put your vanishing points far apart” is really “draw as if standing farther back”.

Proportion falls out of the same division: an object of height h at distance z projects to d·h/z. Double the distance, half the size — no judgment calls. The depth row shows it: equal posts shrink along 1/z, and their tops and bases both run to a single point on the horizon.