Indirect Techniques

Purely direct carving means attacking the stone directly, rather than mechanically copying a form that originates in some other medium, such as clay or wax. Indirect carving, the opposite, means copying into stone a shape that has been fully worked out in advance. Some sculptors are extremely direct, working without so much as a sketch, while others work entirely in clay, and may not even decide whether the finished piece will be stone or bronze until after the plaster casting is completed. The aesthetic issues around indirect carving are many, and are covered in Direct v Indirect. In this section we discuss practical techniques.

The basic problem solved by all indirect methods is that of measuring the location of a point on the surface of a model and transferring it to a corresponding point, either in empty space in the case of modeling, or to a point inside a stone block for carvers. Artists did, and still do, accomplish remarkable things with the traditional mechanical methods, but the old tools are now evolving rapidly because these measurements can now be done more far more quickly and accurately with lasers.

The techniques described below will probably remain in use by amateurs and artists for years to come, but professional and commercial carvers, and art restorers are already moving to laser measurement, and in some cases even to computer controlled machine tools driven by such data.

But the technology available in the fine arts studio is still considerable. Laser measuring tools for tradesmen, accurate to within a millimeter, are already available in the $50 to $100 range, can greatly enhance the pointing process as seen below).

Copying Frame

Enlarging frames have been used since at least the Middle Ages to guide the sculptor in reproducing models, either in the same size or scaled. Frames are applicable to both relief sculpture and to sculpture in the round. Although the technique is more often applied to modeling, it can be used with reductive sculpture as well. A stone sculptor would usually use the copying frame to enlarge a small original to a full-sized plaster model suitable for use with a pointing machine.

The basic idea is that similar rectilinear frames surround both the model and the space in which the reproduction will be executed, allowing points on the original to be located in three dimensions with X,Y,and Z coordinates. The same three measurements are then located on the frame surrounding the work piece. One great advantage of this system is that scaling is easy, because the frames can be made in different sizes, and ruled with proportional measurements. The following is an example of how the frame can be used.

• A ruled batten is clamped to two opposite top rails, parallel to the adjacent side.
• A plumb line is dropped from ruled batten to some feature of the model.
• The rules on the two rails give the X coordinate, the rule on the batten gives the Y coordinate, and the length of the plumb line gives the Z coordinate.
• When enlarging a model in clay, the same basic idea can be used to scale up the armature. Battens can be fastened on the sides and top, to allow supports to be clamped in a precise location to hold an armature while it is being attached.
• Battens locked into fixed positions can also be used as a location for "mother" points, from which precise locations can be determined using the three-compasses method (see below.)

Antonio Canova Cupid and Psyche⁴⁹.

Antonio Canova Cupid and Psyche detail of right arm.⁵⁰.

The Metropolitan Museum, in New York has on display a late 18th Century example of a plaster model for Cupid Reviving Psyche With a Kiss (see above) by Antonio Canova, which was used to produce numerous instances in marble using the copying frame and plumb bob method. This piece is particularly interesting because still in place are numerous iron pins projecting from the surface to identify the precise locations of the reference points. The pins stick out from the surface approximately an eighth of an inch, and are very irregularly spaced, some regions having pins separated by only an inch or two, and other regions containing few or no pins. In general, more pins appear in complex areas, such as Cupid's hand on Psyche's breast.

Note that one can only locate positions on the top surfaces of the model in this way. Canova and his assistants supplemented the copying frame with calipers as described below. More about Canova's methods can be found in the Miscelaneous Issues section.

Alberti's Method

The Use of Three Compasses

It always takes three quantities to uniquely describe a point in space: copying frames use distances along three lines, and Alberti's method uses distances on two lines, plus a radial angle. The method of three compasses relies on the geometric principle that the location of any point is also uniquely determined by its distance from any three distinct points that are not on the same line. Note that for this statement to be true, you need to allow negative distances as well as positive.

In this method, three fixed reference points, called mother points, are marked on the model, as far apart from each other as is convenient. Three corresponding points are located in the target block in precisely corresponding positions Because the block is larger than the model, these points will almost always be on surfaces that have been cut into the block.

Given these starting points, any point on the model can be mapped to a point within the volume of the block, using three pairs of compasses. Putting aside for the moment the problem of transferring the first three points, the rest of the points are transferred from the model to the block using the following procedure.

• Three pairs of compasses, A, B, and C, are used, one for each mother point.
• The compasses have curved legs so they can reach around the model easily, and a wing-screw to lock the legs in positions after a measurement is taken.
• The point on the model to transfer is marked with a dot.
• After compass A is set to the precise distance from mother point A to the dot, one its feet is placed on mother-point A of the target block, and a small line marked on the stone where the swing of its other foot reaches closest to the approximate location of the target point in the stone. The procedure is repeated for compasses B and C.
• If all is set up correctly, the point we seek will be somewhere below the surface of the stone, within the region bounded by the three lines we have marked on the block.
• Some stone is chiseled away, and the three marks redrawn. The triangular region between the lines will be smaller than before, and the surface closer the point we are seeking. The divergence of the triangle from equilateral tells the carver how to adjust the angle of the plane from which the stone is being carved, so that will end up tangent to the final surface.
• As the triangle bounding the location converges to a single point, the depth of the target point below the surface goes to zero, and the target has been precisely located.

The only problem is, how do we find those three points on the target block? One of the ways this can be done follows:

• A rigid wooden frame is constructed that fits exactly around the target block on three sides. It should be snug, but easily removable.
• The model is fixed in position so it cannot move while the points are being determined.
• The frame is removed from the block, placed over the model and fastened down rigidly, but temporarily, in place.
• Points on the model are chosen at widely separated points that are will be reasonably close to the surface of the block, as indicated by the position of the wooden frame.
• A thick piece of wood with a 1/4" hole drilled through it is fastened to the frame in such a position that a 1/4" drill bit stuck through the hole will exactly touch the desired location of a mother point. The exact depth of the bit through the hole is marked, and the procedure repeated for the other three mother-points.
• The frame is now transferred back to the block, and the holes used to guide the drilling of holes to the precise measured depth, less say, 1/32". In most cases, it will be necessary to chisel the stone where the drill enters, so that it is exactly perpendicular to the direction of the drill bit. This prevents deflection of the bit as it enters the stone.
• After the holes are drilled, remove the frame, and chisel down almost to the bottom of the drill holes, leaving intact the slight dent made by the drill tip.
• Mathematically, only three points are strictly necessary, but you will want to drill more than three mother points so that there will always be a set of three at a convenient distance from the point to be transferred.

Alternate Method

The mother points do not actually have to be on the original model, so long as their locations with respect to the model are unchanging. A fixed frame constructed around the original can also serve as the location of the mother points, and may in fact be more convenient. If this technique is used, it is best to construct the frame so that the mother points can will all correspond to points inside the target block. If this is not done, an identical frame must also be constructed around the block and fastened to it, to prevent any relative motion between the block and frame.

In this way, the three compasses method and the copying frame method can be combined. The copying frame can be reserved for the coarse blocking out, and the three compasses used for the more exacting details.

Pointing Machines

Pointing is the most commonly used of the traditional techniques. The model is usually plaster, but wood or any other rigid material can be used.

A pointing machine is an adjustable armature attached to rigid frame, which rests, during use, either on three fixed points on the original, or on three corresponding points on the work-block.

The adjustable armature terminates with a steel or brass block drilled through to allow a long pin, like a knitting needle, to slide through. The armature is articulated with several degrees of freedom to allow the block to be positioned above any point on the model.

The adjustable pin can slide in and out freely. It is inserted so that it almost touches the stone, and a locking collar around it is tightened, so that it can be withdrawn and replaced later to exactly the same depth.

To take a point, the frame is mounted on the original, and the armature is adjusted so the pin will be perpendicular the desired point on the model. The pin is inserted until it almost touches the model, and the collar locked in position. After everything is tightened down, the pin is removed and the frame transferred to the work-block.

The pointing machine in place on a plaster model in-the-round.

Before you start carving, you should be absolutely sure of two things: that the frame is in the same relative positions with respect to the model and the block, and that the finshed carving will be completely within the block.

If you have made the main members of the frame plumb and level on the model, they should be the same when the frame is on the block. If they are not the same, the piece will be carved at an angle. You can check this with small spirit level or a carpenter's square.

To be sure that the block will contain the piece fully, check the key, outermost points by setting up the armature and the pin, and checking that in each case, the pin bumps into stone when you try to replace it. If it does not, some of your points will be outside the block!

There are two approaches to removing the stone that covers the reference point:

• Drill a hole in the indicated direction to the measured depth. The bottom of the hole is the desired point. Remove the frame and chisel away the waste stone down to the bottom of the hole.
• Estimate by eye the amount of stone to remove, withdraw the pin, or remove the entire frame, and use the point chisel, perhaps followed by the claw, to directly remove most of the waste stone. The pin may be replaced as removal progresses to check the amount being removed. This approach works best to remove a lot of stone on convex curves at the early stages of carving.

The number of points you will use to copy a piece depends upon the desired accuracy--a highly accurate copy can require thousands of points. To reduce the amount of work, a few key points should be chosen first so that the largest amount of stone can be removed quickly, leaving only a thin layer to go through to establish the final points.

Start with outermost spots where a tangent plane will not bump into any other parts of the finished sculpture, and set the armature well away from the piece-say, half an inch. Several points like this will let you strip off huge amount of stone, and greatly reduce the total depth you will have to cut through for the rest.

There is no need for drilling at this point. Pick the point that will put the maximum amount of stone outside the tangent line and start there. Use the punch to cut off all the excess, then move to the next point. when you have completed this stage you will have a shape that is as if you had stretched a covering over the original.

If there are large hollows that will not weaken any part of the piece, you can now proceed to rough them out. This is a good place to start using the drill, expecially if the hollows go all the way though. The hole gives you an indelible marker about how deeply you can chisel. Don't forget that in a hollow, the sides of the drilled hole can be the significant part, not just the bottom. If it's a through-hole, there won't even be a bottom.

Be careful to leave plenty of stone anywhere the piece narrows, such as the neck. In such a spot, you can either leave the entire area thicker, or you can leave bridges of stone in a limited area.

When only a thin layer of stone--1/4 to 1/2 an inch--is left, you are ready to start establishing the real points. You are going to choose points that divide the surface into little regions, like the triangles on a computer-graphics wireframe. Each of the little regions will be very close to flat. The size of these regions is a function of how accurate you want to be. If your points are to be, say, 1/16 of an inch from the finished surface, the curvature of one of these regions must be within 1/16 of an inch of being flat. Therefore, for big gently curving surfaces, the regions can be bigger, and for more tightly curving surfaces, the regions must be smaller.

You want all your points exactly the same distance from the finished surface. Cut a small measuring thickness guage that from a piece of material that is the exact thickness of the distance you want for your points, in this case, 1/16 inch. Plastic, brass, etc. are good for this. It should have a narrow end and a wider end, and be long enough for convenience--say, six inches long, an inch wide at one end, and a quarter inch at the other. Each time you take a point, you will slide this guage between the pin and the surface, so that your points will stand off the model by a uniform amount.

To mark a point, first set the pointer from the model with the spacer in place. Then transfer the frame to the roughed out carving, and reinsert the pin. Use a chisel to shave away the patch of stone until the pin slides in to within at most 1/8. Then mark the spot with a pencil and carefully drill until the pin inserts exactly. This point will be exactly correct, minus the thickness of your gauge.

You can now shave most of the 1/8 inch away, just leaving a small amount above the marking hold.

If you are working to within 1/16, when you have all the points drilled, you will only have about 3/32 of an inch of stone left, with the holes down to 1/16 of perfect. At this point, the rest is done by eye. Shave the stone away over each little region until you reach the bottom of the holes, leaving only the pencil mark, so you can shave away the adjacent regions.

When you are down to this level, there should be nothing left but rasping and other final finishing work.

Working to 1/16 inch would actually be fairly crude. Sculptors frequently copy to an accuracy of 1/32 of an inch.

Note that the machine pictured here is quite heavy for a sculpture of this size. Most machines are of lighter construction. This particular machine is unusually heavily built. This is because it is designed to allow a drill bit to be substituted for the pointer. The armature itself then serves as a drilling guide, to accelerate the roughing out stage as described above. When used this way, the drill bit is inserted into drill after the frame is placed on the block, and the hole drilled to the correct depth in one step. This process is only for roughing out, and is not accurate enough for the finished holes. It is necessary to flatten the surface where the drill will enter the stone with a chisel, so that the bit does not tend to shift before it bites into the stone.

Considerations for Pointing Sculpture in the Round

So far, this description of the the pointing process has been described as taking place from one side of the original only, as if it were a relief. Theoretically, a single machine could reach every point all the way around, but in practice, multiple sets of mounting points, and often, multiple machines are used, both for convenience and to allow multiple carvers to work at the same time.

The primary reference points are used to defined any number of alternate sets of holes. Bolt heads for the alternate mounting points can be installed in any convenient positions on the model, and transferred to the block using the pointing machine. As with the originals holes, these must be outside of the surface of the model. Leave 1/4" to 3/8" of stone above the bottom of the drilled holes, so there will be a stone for the frame's points to seat in. Because the secondary holes are fixed relative to the originals, there is no need to be concerned about getting the copying frame plumb and level.

For large work it is common practice to use a large machine to set up mount points for smaller smaller machines, to avoid having to shift an unwieldy machine frequently.

The Pointing Machine Updated

A typical laser measuring device for contractors costs between fifty and two hundred dollars, and is capable of measuring distances to within plus or minus one millimeter. This tolerance means that the average error is only about 1/32 of an inch, and worst case about twice that, which is pretty tight. Mounted on an auxiliary attachment to the pointing machine, this device can replace the need for the removable pointer, while allowing the armature to be far from the workpiece, leaving room to work without moving the machine.

Once the machine has been adjusted to place the laser dot on the desired location, the distance to the model noted, and the machine transferred to the block, the carver knows the precise amount of stone to remove from beneath the laser dot in order to reach the correct depth. By conservatively removing a little less, and iterating the procedure, it is possible to quickly converge on a perfect depth with chisel alone.

Combined with the standard armature for areas where drilling is required, this can greatly speed up the roughing out phase of carving. Make sure you have a heavily padded, but easily removed cover for the laser device to protect it while carving.

Computer Numeric Control (CNC) Carving

Milling machines controlled by computer, called CNC milling machines, have been used extensively in industry for many years for machining complex shapes from metals and plastics. When used on metals and plastics these technologies are often called five-axis machining because of the number of points at which the arm holding the cutting head can be rotated. A YouTube search on this term is a good way to check out the state or the art. Since the 1980's, the same techniques have been extended to controlling tools for stone shaping. Such machines are available commercially, and can be used to reproduce an original to almost microscopic accuracy. Objects as small as a figurine, or twenty feet tall can be carved in this way.

The picture below shows a piece from the Captives series, by the artist Quayola⁵¹, being carved by a huge CNC carving machine. This piece is not actually stone, but high density expanded polystyrene (EPS) similar to the blue slabs used for insulation. However, the machinery and techniques used for CNC carving of stone are almost identical, except that with stone, a water hose is run continuously on cutting point to cool it and clear the waste.

Captives 2012, EPS, by Quayola. CNC driven carving machine on the left, and the finished piece on the right.

The technology for defining complex three dimensional shapes as lists of number is fantastically advanced, and continues to evolve rapidly, in part because cinematic CGI and computer games use it extensively.

A set of numeric coordinates defining the surface of the piece to be shaped can be prepared in many different ways, but however the data is prepared, it consists of a set of locations on the surface, together with information defining how they are related. Usually, the numbers are represent the apexes of triangles as X,Y,Z coordinates. Triples of these coordinate points define a triangle in space, and the full set of triangles together define a wireframe model of the surface, but other systems can be used. The machine need not mindlessly carve out the triangles as flat planes--smooth curves can be interpolated even though the raw numbers actually define an angle.

One of the most common ways to get coordinates for an existing object is to use a laser scanner, either hand held or mounted on a tripod or scaffold. First, a few colored dots for reference points are stuck onto the original, for the sensor to use as fixed reference points. A laser beam, similar to the red beam of a bar-code reader, is played over the surface of the object being scanned, and the linear distances from the scanner to the reference points, and their angles with respect to the scanner are measured. These defined points providing a framework for computing the spatial locations of the innumerable surface points that will be the apexes on the wire frame, using the same trigonometry we all sit through in high school. The process is very fast and improves all the time. Not long ago, this process required rigid scaffolding for the scanner, but a modern hand-held scanner about the size of a highway patrol radar-gun works just as well.

The raw data is exported directly to a computer, where specialized programms turn it into models that can be used by the specialized Computer Aided Design (CAD) programs designed for CGI or other use. These programs can be used to manipulate the model in many ways, stretching, deforming, changing the surface texture, or even stitching multiple models together.

A CNC stone carving systems that use this data are scaled-up versions of CNC five-axis milling machines. They are basically a robot arm with a cutter on the end, and a sensor to tell exactly where in space the tool tip is. The computer intelligently plans the cuts, allowing it to grind away the surface in such a sequence that only the cutting head ever contacts stone.