# How can I create diagonal cross sections for complex forms?

I have Scott's "How to Render" and am stuck with how to create diagonal cross sections for complex forms. I can figure it out when it's a geometric form because the diagonal cross sections are easy to connect from point to point.

But when it's a rounded form I can't do that and have trouble figuring out what the round shape is and how to solve for it.

Here is what I mean by a complex form's diagonal cross section that I have trouble constructing:

• Okay so you dont start with a form, you start with the cross sections, that then make the form. Commented May 20 at 19:57
• A cross-section of a primitive, cylinder is predictable an ellipse. The second example does not expect you to make the cross-section, only to have a basic reference on where the shadow could be. Commented May 21 at 16:44

## 1 Answer

The linked examples look like they are inherited from the construction examples in previous lessons by the same writers. Nobody can construct the right plane intersections by starting only from the 2D outline image of a 3D shape. There needed information simply isn't included. The geometry either must be known or be magically guessed before the plane intersections can be drawn. The examples in the book contain the needed geometry information as wireframes.

The image captions in your linked examples say that a full construction is recommended. I guess it means constructing the plane intersections like one draws a perspective image of an already known and well defined 3D structure. It's useless to open the book for the first time just at the linked pages.

Building the 3D shapes in a 3D modelling program can give all wanted outline images and plane intersections in wanted views virtually effortlessly. To make a 3D model one must at first construct the wireframe or otherwise define the exact 3D structure. Several geometry defining methods are commonly available. The program generates the outline surface and all intersections with all planes that one bothers to ask. But that's not drawing, it's using an automate. The same automate (if you have purchased an advanced enough version) inserts also the lights and shadows i.e. renders the image in the wanted light environment. That approach may save an year of practicing and greatly reduces the need of the things called skill and talent. But if you want to be able to learn to construct it manually restart from a thick pile of pages or book volumes earlier.

When one has understood the ideas of the manual construction and developed some confidence he finally can draw plausible lights and shadows intuitively. A skilled artist knows exactly what he is going to draw. Inserting the right lights and shadows is the way how he presents his imagined geometry to others. Getting to that level unfortunately may need thousands of practicing drawings. Many of us never reach it.

Added later

It's tempting to try how difficult your problem actually is. I have this 3D shape, which is quite as complex as your examples:

As you see, having only the outline of the 2D image doesn't tell what's the actual form. But I have constructed it properly in a 3D program and know what it is. I can let the 3D program to insert a sparse wireframe skeleton to supplement the outline:

The shape resembles a boat turned upside down and it has planar bottom face. It makes everything 50% simpler.

Maybe not interesting, but the skeleton was made in the 3D program by splitting the "boat" body with one longitudal and three transversal planes. As a plus the centerline height of the body became easily visible.

In the next image I have a vertical plane which intersects the shape diagonally (as you call it):

The skewed rectangle gives no info how far away the plane actually is nor does it intersect the 3D shape at all. In the 3D program the plane is a separate element, in this simple line-only display mode there's given automatically no hint of the possible intersection before the plane is actually used to split the boat.

To show where the plane intersects the flat bottom face I inserted onto the plane manually an extra line just at the elevation of the flat bottom face:

If I worked only in a 2D drawing this would be the way to tell where the plane actually is.

Next we try to draw manually the approximate intersection curve to the screenshot in Inkscape. The cross-section profile of the 3D shape changes smoothly along the length axis of the "boat". We can guess the tangential direction of the intersection curve at three points which are in the middle of the red circles in the next image:

The tangential directions are drawn as blue. They are pure guesses based on assumption the form is smooth, so the wanted curve must resemble the nearly elliptical curves in the skeleton. The red dashed line is an insertion to the skeleton. It's the guessed height of the "boat" left-right vertical symmetry plane.

In the next image the purple curve is drawn with the pen. The tangent handles are drawn along the guessed tangent lines so that the result resembles an ellipse visually as much as the adjacent skeleton curves and the curve touches tangentially the shape outline in one point. Unfortunately one cannot see beforehand where it happens, but one such point should exist because this is a smooth and convex 3D shape:

Looks fine, but is it any good? The only way to find it is to move the purple curve onto a new screenshot which presents the actual intersection of the boat and the inserted plane. The 3D program creates the intersection with 3 clicks:

As you see, it's off about as much as the used line width which is far from the thinnest possible. That's trashcan stuff in engineering, but it can be accurate enough for constructing lights and shadows.

• The construction is in the image itself Commented May 20 at 16:57
• Sure, but doing the same without having the perpendicular wireframe and without knowing how to proceed from it is not easy. But it's possible to end to the same result by making successful guesses. Commented May 20 at 18:23
• Well obviously you cant draw with this method that which you cant construct. But then you cant draw much anything without construction. I mean even if you do 3d your still stuck with the same problem, no construction no 3d model. Don't know how to construct means no solution. In nearly all cases too. Every complex case can obviously be approximated with a simpler shape which is how much of 3d works. Commented May 20 at 18:54