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Curvilinear perspective is a result of an abnormally wide field of vision, such as you see when you look through a security camera, or any camera with an extreme wide-angle lens. Compare the diagram of the cone of vision for the normal human eye verses the cone of vision for the fisheye camera lens. A curvilinear view opens up our cone of vision beyond the normal range of the human eye. If we open up the cone of vision wide enough, it can be like looking in multiple directions at once.
If taken to the extreme (i.e.: we open up the field of vision to about 180 degrees or so) we could be looking up and down at the same time, producing an extreme fisheye view like the sketch shown here.
A Curvilinear perspective view, also known as a "fisheye view", or "fisheye perspective", is really just like regular perspective, but with fisheye effect added. In the examples below, I add fisheye effect to a 1pt-perspective view and a 2pt-perspective view. In curvilinear perspective, the 1pt view becomes a 5pt-perspective view, while the 2pt-perspective view becomes a 4pt-perspective view. Further down this page, you will find the grids I used to construct these 5pt and 4pt curvilinear perspective views.
Step-By-Step Demo
Step-By-Step Demo
Below is a step-by-step 5pt-perspective demo which I created for my online classes at AAU. Some years ago, I posted the last step of this demo on Pinterest, and my drawing was widely copied (without attribution to the original creator). Many people have done their own version of my drawing (which is fine by me), while others just swiped my drawing and posted it as if it were their own work. Unlike all the copyist out there, I have all the steps in my original demo. I post them here so you can see how the drawing was constructed starting with the 5pt curvilinear grid.
Scott Caple, an accomplished artist and veteran of the animation industry, demonstrated the "Universal Grid" in his "Layout for Animation" classes at Associates in Art (a popular commercial-arts school in the Los Angeles area back in the year 2000). This Universal Grid can be used to setup almost any kind of camera angle or perspective view. Scroll through the image carousel to see examples.
This Universal Grid can also be used for setting up 5pt curvilinear perspective views, using the center of the grid as the central vanishing point, with the other four vanishing points placed at the left/right, top/bottom edges of the grid. In the example below, I plotted my 5pt drawing on the grid. When I finished the drawing, I cropped out the grid and rotated the frame so the sides are vertical. This creates a tilted view, known in filmmaking as a "Dutch Angle".
In curvilinear perspective, a 2pt perspective view becomes a 4pt perspective view, and for this we need to use a 4pt grid. Keep in mind that the vanishing points for an object rotated in 2pt perspective are based on a 90 degree angle, whereas a curvilinear view can open up the field of vision beyond 90 degrees, hence the left/right vanishing points must be closer together, rather than at the edges of the grid, as you see in the example below.
Additionally, we can use the 4pt grid to create up or down shots, by constructing our drawing within either the top half or bottom half of the grid, as illustrated in this next example.
Finally, we can rotate the grid to create a 4pt curvilinear version of a regular 2pt-vertical perspective view, as shown below.
In his book, Extreme Perspective!, author David Chelsea demonstrates how to create a 4pt grid for an environment rotated 45 degrees to viewer's line of sight. I followed his steps to create the 4pt grid used in the examples above. The diagram below shows how the various cross-sections, plan and elevation views come together to create the 4pt grid. For environments at other rotations (other than 45 degrees), I highly recommend you check out David Chelsea's book. The book includes a DVD-ROM with many grids, including fisheye grids for practically every rotation.
Finally, I am posting some curvilinear grids which I made in Illustrator+Photoshop. Feel free to use these in creating your own fisheye perspective drawings. To download, "right click" on each image and click "Save image as".
5pt Curvilinear Grid
4pt Curvilinear Grid
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