Curvilinear Perspective Grid: Fisheye, 5-Point and 6-Point
Straight lines curve when the field of view is wide. Rotate the view, push the angle past 180°, export.
How to use this grid
Linear perspective breaks its own first rule the moment you look along a very long wall: the parts far to your left and right should get smaller, but a flat picture plane makes them get bigger. Curvilinear perspective fixes that by projecting the world onto a sphere. Straight lines become arcs, and the picture can hold 180° or even the full 360° around you.
Drag to rotate the view. Move the angle-of-view slider: at 120° you have a very wide lens, at 180° a classic fisheye (five-point perspective), and at 360° the whole sphere is squeezed into the disc, with the point directly behind you at the rim (six-point perspective).
Reading the grid
The six vanishing points are labelled: VP1 and VP1′ for the two ends of one horizontal axis, VP2 and VP2′ for the other, Zenith above and Nadir below. With the angle at 180°, four of them sit on the rim and one in the centre. The dashed inner ring, visible above 180°, marks the 90° circle: everything inside it is in front of you, everything outside is behind.
The dashed curve through the middle is the horizon. Notice that it is only straight when the view is level; tilt the camera and it bends, exactly as it does in a fisheye photograph.
When to use it
Wide interiors, cockpit views, dream sequences, anything under 20 mm, and any scene where a linear grid would stretch the edges into nonsense. Comic artists use it for panels that need to show a whole room; concept artists for establishing shots; anyone drawing a 360° panorama needs the 360° setting.
Getting the grid into your app
Export a transparent PNG (2× or 4×) or SVG. In Procreate, Copy to clipboard and paste. In Clip Studio, import as a layer; Clip Studio's fisheye ruler is a separate feature and does not go past 180°.
Read curvilinear perspective explained for the theory, with this grid embedded.
Questions
What is the difference between 5-point and 6-point perspective?
Five-point is a 180° fisheye: four vanishing points on the rim (left, right, up, down) and one in the centre. Six-point extends the view to the full 360° sphere, adding the point directly behind you. Set the angle to 180° for five-point and 360° for six-point.
Why do straight lines curve?
Because the picture surface is a sphere flattened onto a disc, not a flat window. Any straight line in the world becomes a great-circle arc. Only lines that pass through the centre of view stay straight.
Which projection does this use?
Equidistant (r = f·θ): the distance of a point from the centre is proportional to its angle from the line of sight. It is the standard for drawn curvilinear perspective and matches most fisheye lenses closely.
Can I export this as SVG?
Yes. The curves are exported as vector polylines you can edit in Illustrator, Affinity Designer or Inkscape.