The Scaling FAQ—Pointing Up: Making Big Ones from Little Ones

For many years, since at least the Renaissance, sculptors have built small macquettes or models of sculptures they wished to realize on a larger scale. Simple methods have been devised to accurately produce a large model based on a small one. This is called “Pointing Up”, because points on the surface of the original must be transferred to corresponding points on the larger model. Old fashioned pointing can be done with just a few simple tools. Say you want to point up by a factor of 4. Mount your maquette on a flat board twice as wide as your maquette. Use a square set perpendicular to the board to transfer the widest points of your maquette to the surface of the board, and marking them on the board . Do this on all four sides. Screw to the board 4 lengths of 1″ angle iron or aluminum, cut at 45 degrees so that they form a square frame or “rail” around your piece. Line it up so that the angle iron runs outside the marks on the board. The flanges you screw through should be on the inside of the frame so that the outside perimeter forms a clean corner with the board surface. Make sure the frame is very square. The corners do not have to meet perfectly, though.

You now have a ‘reference plane’ (the board) and a ‘reference frame’ (the vertical faces of the angle irons). You will need to measure the dimensions of this frame precisely, multiply them by 4, and create another, precisely-calculated larger frame. Do this on a level table, floorspace or platform made to be level. You will build the large model on this, and just the way your maquette fits in its little frame, your big version will fit in its larger one.

Pick a corner on both frames and drive a finish nail into its absolute apex. This is your zero point. With a marker—label the corresponding four sides of each frame A, B, C, and D. With a file or engraving point, scribe the edges of the maquette’s rails at every half inch (if you’re not American, use a centimeter) of length starting with the nail as zero-basically turning the rail into a ruler. This is called a “ruled reference rail”. You want to scribe both rails running away from the corner nail, then, make the opposite and parallel rails match them, so that each pair of parallel rails has a zero starting at the corner nail.

Now do the same for the large frame, only, scribe its rails every 2 inches. (½″ times 4—or 4 centimeters, if you started with them) Be precise—the accuracy of your scaled model will be determined by the accuracy of your reference rails and plane.

Now you will have to fabricate a tool (or buy one if you can afford to) You need to make a pair of “surface gauges”. One will need to be a little taller than your maquette, the other four times taller than that. Basically, a surface gauge is three perfectly perpendicular planes coming together at one perfect corner. Like 3 sides of (an ideal) cardboard box. Two of the planes are very long and narrow (forming the vertical sides) and one is small and square (forming a base just wide enough for stability) I have made them in a hurry out of plaster, or used ultracal and burlap, making a 3-sided corner into which I could hand cast the plaster. You can make them out of wood, but use particle board or some other material that will not warp over time. The very best are just 3 steel plates welded along 2 edges to each other and with the outside faces machined perfectly square.

In any event, what you want to end up with is a stable, vertical tower-like thing where the vertex or edge formed by the two vertical perpendicular faces is dead straight and also dead perpendicular to the reference plane it stands on. When you butt one flat face up against the reference rail, the other vertical face forms a plane perpendicular to both the rail and the board. This face is what you line up with the scribed rule marks on the rails. You can rotate it 90 degrees to switch to the other face against the rail to line up when you get to the end of a rail. You should scribe the two vertical faces of the surface gauge—at ½ inch (or 1 cm) for the small one and every 2 inches (or 4 cm) for the big one.

Now you will need a tool to measure from the reference edge of the surface gauge to the surface of the sculpture. For a moderately sized piece you can use a combination square, a tool with a steel ruler running thru a machined block of metal that forms a kind of T-square head. The ruler can be slid through the head while the head is held against the reference edge of the surface gauge. Doing this will hold the ruler parallel to the board (reference plane) You can use anything you can rig up that will hold the ruler perpendicular to the reference edge and parallel to the reference plane. I ground the end of my steel ruler to come to a point for getting into tight spots. You can even use a steel rod, marking the length with your thumb and then measuring it.

Then get 8 pieces of paper, label two of them “A”, two “B”, two “C”, and two “D” and draw matching grids on each pair with a vertical line for every scribed mark of rail length and a horizontal line for every scribed mark of surface gauge height. Now it’s just a matter of lining up the surface gauge against the rail at the first mark and, starting at the top, write down the distance between the surface gauge’s reference edge and the sculpture at each scribed mark on the gauge. Write it down at the corresponding grid point on one of the papers marked for that side—making a sort of numeric map. Leave a blank at any coordinate that doesn’t line up with the sculpture. Slide the gauge down the rail to the next scribed mark and repeat.

Once you have done that for all 4 sides—multiply every measurement by 4 and transpose them to the second set of grids for each side. Use this second set to transpose the measurement to the large model, using the larger surface gauge and reference frame. Build up or carve away to match the numbers. You can also use this technique to make left and right matching sides on a sculpture—like say a car body, by transferring the measurements from one good side to the other you’re trying to make conform to it.

If you want to know more about this and other traditional sculpture techniques, get both books on sculpture written by Eduoard Lantieri, from about 1900. It is the best work on sculpture techniques ever written, and in it he describes a similar technique for very large pieces using an overhead reference frame and plumb lines instead of surface gauges.

Here’s a quick way to get an accurate foam armature, using some computer shortcuts. Make a robust mold from your maquette and use it to cast a urethane foam pattern. You will have to be able to seal the mold closed to build foam pressure when the two-part compound expands, shortly after being mixed. Once that’s made, using a drill press, drill two parallel holes down the long axis of the foam casting. The bit should be one fourth the outside diameter of a ¾″ galvanized pipe. (for the above example of a 4× point-up) Take the foam casting to a big bandsaw (or use a hand saw, but be accurate) and slice it like a loaf of bread—perpendicular to the holes you drilled, cutting it into half inch thick parallel slices, less the kerf of the blade. As you cut, number the ‘down’ side of each slice consecutively. Spray paint the up sides a dark color for contrast.

Place each slice upside down on a scanner and scan it in as a bitmapped image. Import the scanned profile images into a vector graphic program like Adobe Illustrator as a template and trace them as vector graphics. Label each file to match the numbered slices. Be sure to trace the two holes in each slice accurately. For each traced vector profile, set the fill to black and set the stroke width to ¼″ and stroke color to white. Set the fill on the traced holes to white with no stroke. Scale the resulting graphic by 400%—so that the line widths are scaled, too. The scaled white line will give you a black profile a half inch shy of the surface of the model. (for a 4× point-up) Print them out. Use a service bureau to do this work if needed.

Go to the home improvement store (or wherever you can find it) and buy sheets of urethane or styrene foam in 2 inch thickness. Be sure they are precisely 2 inches thick—remember, a 2 × 4 is neither 2 nor 4. Cut out the black profiles and the white holes out of them and pin the paper profiles to the foam sheets—mark the foam UNDER each profile with the slice number. Spray paint around the edges of each paper profile to transfer the outlines to the sheet foam. Cut the foam profiles out and cut out both the ¾″ reference holes in each slice. Then slide the slices, in order, onto a pair of ¾″ pipes to align them. Glue the slices together with a spray adhesive, keeping the adhesive an inch or two away from the edge.

This will give you a very accurate foam armature that you can further refine by shaping the foam. It will be approximately ½ inch shy of the actual surface you want, so you can paint the shaped foam with molten beeswax and apply your plastilene over the wax to finish the piece. This works best if you mount the alignment pipes to your pointing platform. You can also use the alignment holes to hold the foam slices in position while you drill them to install additional reinforcements, which may be needed to increase the load-bearing ability of the foam.

Keep in mind that to make an 8 inch figure one inch taller requires twice as much volume—twice as much plastilene. To make it 16 inches tall (twice as big) will increase volume 8 times. Volume increases as the point-up factor, cubed. Length × width × height (E.G. for the above example of a 4× point: 4 × 4 × 4 = 64 × the volume of the maquette)

In today’s world, pointing up from a maquette to a life, heroic, or monumental size is best done digitally. Companies like CyberFX in Glendale California can take a maquette, scan it into their computer, and output it to a CNC foam cutter, creating a scaled-up replica in high density urethane foam. The accuracy they achieve is astonishing, (far better than any manual pointing technique) and the urethane can be easily tooled to refine the model as desired. You can have them output it at final size and finish the surface with resin, or have them output it ½ inch shy of the actual surface so that you can put beeswax on it and cover it with ½ inch of plastilene, allowing you better control of the final texture. I had CyberFX do two jobs for me with models I created digitally on the computer, and their price was competitive with what I would have had to charge to do it the old fashioned way. If they are not convenient geographically, do a web search, I know there are similar companies, like Bill Kreysler and Co. in Petaluma CA and the Johnson Atelier in New Jersey—609-890-7777 (ask for Jon Lash).

It is also now routine to take a given work and scale it down—outputting the final model in wax or resin on a Rapid Prototyping machine. Many toy action figures featuring likenesses are done in this manner. These machines, while limited in size, can produce extremely detailed reproductions by various strategies which build up layers of material which accrete to produce a solid replica of the scanned or computer-generated model.

by Christopher Pardell

With contributions by Andrew Werby