Mass and Void
Space can be either full or empty
A void is an empty volume, while a mass is a filled volume.
Voids and masses can be referred to as:
Negative space/ Positive space
Negative form/Positive form
Volume/Solid or Space/Form
Mass/Void Interaction
When a void occurs, the space between two solids it is passive.
When it occurs as a removal, or subtraction, from a solid, the void is active.
Penetration of space can be regarded as empty space entering into a solid form.
Penetration is a deep incursion of space into a mass, where as concavity refers to slight indentations.
If space completely passes through a solid form it is a perforation.
Isamu Noguchi
Subtraction and Addition
Carving is an example of a subtractive process where sections of simple mass are removed (or voided) to create a more complex mass.
Subtractions should create distinctively shaped voids that interact visually with the mass to create strong positive/negative relationships and open up the space of a form.
Additive processes build form up and out into space.
Addition suggests growth.
Surface and Volume
A closed surface defines volume
The surface may be curved, like an egg, faceted, like a cube or a combination of both, like a cylinder.
Volumes enclosed by continuously curving surfaces are integrate volumes.
Integrate volumes have no sharp corners, straight line, or flat planes
All organic volumes are integrate volumes
Volumes enclosed by faceted surfaces are called polyhedrons
Enclosing Volume
A cube constructed from six square plates of steel will read as a solid even though it is an empty volume.
The most common method of fabricating closed volumes is pattern construction
Geometric Volumes
Polyhedrons
Polyhedrons
are geometric solids whose faces are polygons. The prefix poly
means "many" and hedron means "face".
A face (or facet) of a solid is by definition a flat plane. A
polygon is a plane figure demarcated by straight sides. As part of a polyhedron
the sides of the polygon become the edges of the polyhedron and the
corners of the polygons meet to become vertices of a polyhedron.
Types of Polygons
Geometers name polygons according to the
number of sides enclosing them. Triangles have three sides and quadrilaterals
have four sides. Beginning with five sided figures polygons are named according
to the Greek name for the number of sides: pentagons, hexagons, heptagons and
octagon, for example, feature 5, 6,7 and 8 sides respectively.
The sides and corner angles of
regular
polygons are all equal. Most polygons tend to be convex, meaning that all
of their angles point outward, but should a corner turn inward, the polygon is
labeled as concave.
Types of Polyhedrons
The simplest and most common polyhedrons
used in constructive modeling are prisms, pyramids and the truncation, or frustum,
of a pyramid.
These three categories of polyhedrons
constitute the vast majority of constructive modeling and are the subject of
this tutorial. A particularly elegant, but less common, family of polyhedrons is
the spherical polyhedrons. These tend to have many, many faces deployed
around the center as if on a ball.
Spherical Polyhedra
Polyhedrons whose vertices fit evenly into a sphere
Form in Nature
Biomorphic Form
Jean Arp
Rather than depict a particular form of life, Arp sought to express a vital force to which he believed inhabits all life.
In order to do so, he shaped marble into a sleek, continuous surface that appeared to have expanded or contracted from an inner force.
Generated Form
Stacking
Wendell Castle
- Wendell Castle, 1996
John Cederquist
Cross-Sections