CHAPTER 5 — Visual Elements II: Volume
11-minute read
If enough planes act together in a specific, closed configuration, we perceive the appearance of Volume or Mass. The presence of mass creates a byproduct, the Void or Space surrounding the mass. The 3D Mass-Void relationship is equivalent to the 2D Figure-Ground relationship encountered with shape.
Beyond Kandinsky: Volume
Related terms: Extrusion | Mass-Void
1) top to bottom
2) left to right
3) front to back
Bauhaus Basic Course instructors tended to be painters. Kandinsky sets up a dimensional logic for purely 2D relationships. Klee, who sometimes toys with pictorial abstraction, extends that logic into 3D illusionist references in 2D pictorial space. 1 Such references are important when considering digitally rendered still images, but our discussion will extrapolate into dimensions that Kandinsky and Klee, as painters, only encountered pictorially. The Bauhaus aesthetic was rife with Modernist concepts of lightness and material standards from manufacturing, thus sculpture and architecture at the Bauhaus tended to shun a sense of mass.
With the Proun Room, El Lissitzky, a Russian Suprematist artist who was highly influential at the Bauhaus, attempted to take the almost exclusively 2D theorizing of early Modernism into a 3D context infused with this dematerializing, spatially ambiguous lightness.
We can see a direct sense of volume based on mass, rather than implied by planar relationships, in the work of Bauhaus protegé Max Bill. In many of his works, he revived mass (and void) in the Modernist vocabulary.
However, for an earlier iteration of mass, we can turn to the playful work of Alma Siedhoff-Buscher and her Bauspiel blocks. This deceptively complex toy embodies characteristic Bauhaus concerns. Note how the designer derives the various block forms from one mass, evocative of a slicing or Boolean intersection function (see Chapter 11).
Extrusion
We define the dimensional property of Volume as an occupation of space. It is the path of a plane in motion, perpendicular to its surface; It is a plane with depth. This kind of plane is Extruded. We push it through space like Play-Doh in a Fun Factory, a common action analogy found in digital modeling.
But planes can also be folded, twisted, bent, and closed to become a volume, an enclosed space. Volumes can be defined as Mass (a body occupying space) or Void (a space defined by adjacent masses or planes). Objects, bodies, and buildings are examples of physical manifestations of volume. Like planes, volumes can embody many materials and material properties. Like the global space they occupy, volumes can contain a local coordinate system, sometimes known as UVW coordinates. Analogous to the XYZ coordinates in the global Cartesian system we saw in Chapter 4, the UVW system generates surface texture and material, a topic we’ll explore in Chapter 12.
Mass and Void
A Mass and a Void are not phenomenologically equal, even if they displace each other in equal size or proportion. The quality of presence (exhibited by mass) and absence (exhibited by void) changes radically. Observe the variety among these essays on the primary form of the cube below. What qualitative attributes make the cube appear to be defined by mass, void, or some ambiguous hybrid of the two?
Mass and Void relationships occur in the context of Relief and Freestanding sculptural works. We’ll briefly discuss these, and their relevance to your 3D modeling efforts, with examples below.
Relief
Relief work is a kind of sculpture intended to be seen frontally, like a painting. It can be classified among three categories: Sunken Relief, Bas Relief,High Relief, illustrated here.
Sunken relief
A relief characterized by shallow mass-void carving under the primary manipulated surface. Often associated with Egyptian work, it can be found where strong sunlight can cast shadows and is common in carved environmental lettering in architecture.
Bas relief
The French word bas, meaning low, gives us to understand bas relief as a shallow carving emerging out of the primary surface. Distinguishing bas relief from high relief is the attachment of all elements back to the carved surface. Bas relief can be seen on most coins.
High relief
Protruding limbs, open forms, and detail more characteristic of freestanding sculpture are the hallmarks of high relief. Although intended to be seen frontally, much articulation can occur “in the round” and facing the primary surface.
Hybrids
As a practical matter, it is common to see types of relief combined into hybrid forms, such as can be seen in the East Doors of the Baptistry in Florence, by Ghiberti. Can you discern where high relief stops and bas relief begins?
The question above would be more than an academic exercise if it becomes our job to model these doors. Strategically, we would determine that the high-relief elements — mostly the figures — should be modeled. On the other hand, we could develop the low-relief elements — mostly the environment and architecture — using a bump map instead of polygon geometries. Here, a map is a means to develop texture or relief elements on simple geometry using a tonal-scaled bitmap image, where the lights represent one value ‚ raised, say — and the darks represent the opposite — in this instance, deeper areas.
Work sometimes acts like a hybrid or combination of relief and the freestanding type of sculpture discussed next. Is the Donald Judd work relief? It’s flat if seen from the front, but from the side it becomes animated, though it attaches to the wall like a relief. The Rachel Whiteread work is freestanding as we’ll read about below, but how would its meaning change without the strong presence of relief found in the reversed-out room elements — doors, windows, fireplaces, moldings?
Freestanding
Freestanding work, sometimes called “in-the-round” sculpture, is meant to be experienced spatially. That is, the viewer is active and in motion to perceive all sides. In one sense, the active viewer has 4D, kinetic implications. Thus, we’ll explore two object-oriented volume works — Closed versus Open compositions — alongside interior-oriented volumes that border on architectural expression in the world of Installation.
Closed volume
As it is with bas relief, closed volumes create mass-void relationships where the material maintains a sense of mass and does not develop interior voids.
Open volume
Mass melts away, opening voids deep inside the work. As with high relief, elements break away from the main mass and define these voids.
Consider: how would you model these two versions of The Kiss in Maya? Brancusi’s closed-volume version could be modeled out of one polygonal cube with a combination of geometric deformations and maps, analogous to how it was carved out of one block of stone. As an open-volume work, Rodin’s version would be better suited to working with composites of multiple polygonal forms.
Installation
As the scale of the work and the open void increases, a primary inversion in the perception of a 3D artwork can occur: instead of a viewer walking around an object, the object can wrap itself around the viewer as an Installation. Alongside El Lissitzky’s Proun Room above, Kurt Schwitters’ Hannover Merzbau is also a prototype for the installation work that was to become popular in the final quarter of the 20th Century. These works exhibit a fusion of painting, sculpture, and architecture not seen since the days before the Renaissance, and indeed relieve us of the need for these creatively stifling categories.
As the scale of the work and the open void increases, a primary inversion in the perception of a 3D artwork can occur. Instead of a viewer walking around an object, the object can wrap itself around the viewer.
Sensory engagement beyond the optical
The Merzbau was destroyed in a World War II bombing raid. Modeling was used to recreate it spatially and optically from photographic records. What, on the other hand, would be needed to recreate Ann Hamilton’s tropos, which only exists as a record now? The work uses a human figure engaged in a repetitive act you can read about at this link, so you’d need to incorporate a kinetic (time and motion) element as described in the next chapter.
But the model would only be a partial one. Impossible to model would be the haptic (feeling), auditory (hearing), and olfactory (smelling) sensory qualities that Hamilton considers part of the experience. She modifies the factory floor under the hair to undulate in a way only the feet can feel. Horsehair muffles sound, changing our understanding of the scale. She also intermingles smells of horsehair and burning paper that are as unforgettable as they are un-modelable.
For an interesting take on the relationship between modeling and installation art, read Richard Serra’s account of making a work like Band at MoMA. Turns out he can model the work but not the experience. Serra mentions the galleries of the Dia Foundation in the interview, and they house some of the world’s most compelling installations, including Serra’s work.
Mass-void reversal and Booleans
The phenomenon of mass-void reversal in the physical world is the key to understanding digital modeling practices such as Boolean operations. Named after the mathematician George Boole, the inventor of the algebraic logic underpinning computer science, these operations use set theory and interactions akin to Venn diagrams to create a more complex hybrid form out of simpler building blocks. Boolean operations can union two volumes, fusing their masses together; intersect two volumes, keeping only the volume shared by both; or subtract one volume from another, depending on the hierarchy of selection.
A study of Boolean operations from Antti Lehtinen at Polygonblog.
Clockwise from top left:
- Union of cube & sphere
- Intersection of cube & sphere
- Subtraction of sphere from cube
- Subtraction of cube from sphere.
In digital modeling, an object created through polygon modeling “acts” like a solid, while the same object created using NURBS modeling “acts” more like a thin surface. On the other hand, if a Boolean operation is desired, polygon modeling tends to do a better job. By analogy, one could say the plaster cast inside the balloon is a NURBS-like physical object, whereas the plaster surrounding the balloon voids is similar to a polygon-based Boolean subtraction of spheres from a cylinder. We’ll elaborate on polygon and NURBS modeling in Chapter 11.
In the studio
Volume work from 3D design studios:
At left: Creating a volumetric spherical shell using plaster and a balloon.
At right: Student exercise, inverting the relationship, the balloon creates a void in a cylindrical mass. All from a studio by the author.
3D design classes often use material exploration as a means of conceptual understanding. One student created a solution to an experimental material problem: reverse the relationship between cast material and mold. In his solution, he poured plaster into a balloon, sometimes creating heavy mass, sometimes creating a delicate shell as illustrated. Popping the “mold” for the shell version created a sense of a randomly broken sphere as the thin material resisted or gave way to the force of the pop. He next created a container filled with balloons, into which plaster was also poured. The plaster filled the void volumes and converted them into mass, and the balloons were then removed to create void volumes.
This same technique was employed by Andrew Kudless with Matsys Design. It is a physical means of creating a random array of void spaces generating a 3D version of a Voronoi diagram which Matsys then used as inspiration for 3D models of Voronoi-based structures. These digital models were then, in turn, output into physical structures for final installation. The process is reminiscent of Boolean Subtract functions.
- Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. p. 35.[↩]