Elements of Three-Dimensional Design: A Comprehensive Guide

Posted on Sep 17, 2024 in Physics

Three-Dimensional Elements

Conceptual Elements

These elements do not physically exist until they take shape in mind:

• The conceptual point indicates a position in space. It has no length, width, or depth.
• The line is formed by moving a point in space. It has length but no width or depth. Lines serve two roles: as a visual element and a conceptual one. They can be seen visually and also represent something three-dimensional.
• The plane is formed by a line deployed in a direction other than its own. It has two dimensions: length and width (no depth). It is assumed to be limited.
• The volume is the path of a plane in space in a direction not within the plane. It has length, width, and depth, but its weight is not physical.

Visual Elements

These elements determine the final appearance of forms as seen from different angles, distances, or under different lighting conditions. These elements are independent of variables and belong to the object itself.

• The contour is the set of lines that define a figure or composition. It is characteristic of the forms and is given by a specific configuration of the surfaces and edges of the forms. It is the first thing we see when observing an object. There are three basic contours: square, circle, and triangle.
• The size refers to the specific measures of a design in terms of volume, length, width, and depth, from which we can calculate its volume.
• Color: We define two types of color: natural color, which is the color of the material the object is made of, and artificial color, when its properties have been altered. Color has special features such as value (the degree of darkness or lightness), hue (the quality that distinguishes one color from another), and intensity (the difference between a pale and intense color).
• Texture is the surface appearance of the exterior. It tells us the material the object is made of. There are two types of visual textures: those that we can see directly (often evoking real objects or materials in a two-dimensional way to seem realistic) and touch textures, which can be felt through touch.

Related Elements

These elements encourage interaction with one another.

• Position: The spatial location of a point or element, given by a reference system. One way to position a point may be using x, y, and z axes.
• Direction: The orientation of a line in a plane, always set in relation to something, usually the observer. It can be vertical, horizontal, diagonal, oblique, parallel, or perpendicular relative to another element.
• Space: The three-dimensional reality that can be seen and occupied by solid material or unoccupied. Materials help us define and discuss space.
• Gravity: All 3D structures depend on gravity and their weight. This depends on whether the material is light or heavy. The center of gravity of an object is the point where it is balanced.

Constructive Elements

These elements give shape to conceptual elements. They have the following structural qualities:

• Vertex: The point where two edges or corners meet (e.g., the corners of a cube).
• Edge: The intersection of two faces (e.g., the edges of a cube).
• Surface: The plane faces of a volume or solid figure bounded by straight or curved edges.

Practical Elements

These elements underlie the content and scope of design.

• Representation: When a form is designed based on nature or the human-made world, it is representative. It may be realistic, stylized, or semi-realistic.
• Meaning: Present when the design conveys a message.
• Function: Present when the design serves a purpose.

Relationship of Forms

Flat and 3D shapes can be joined to create new forms. They can interact in various ways.

Volumetric figures can also be grouped in the following ways:

Classification of Forms: Planar, Geometric, and Volumetric

Geometry

Geometry studies the mathematical relationships between elements in a plane or in space.

Basic Shapes:

• Closed polygons formed by straight lines:
  • Irregular: Sides and angles have different measures (e.g., trapezoid, rectangle, rhombus, parallelogram).
  • Regular: Sides and angles are equal (e.g., equilateral triangle, square).
• Stars: Formed from regular polygons by joining the vertices alternately.
• Regular curves:
  • Circumference: Consisting of all points equidistant from a center.
  • Spirals: Curves that develop continuously around a central point according to different patterns (e.g., 2 or 3 or more sites, some based on the golden section).
  • Parabola, hyperbola, ellipse: Conic curves resulting from the section of three-dimensional tapers.

Volumetric Shapes

• Geometric shapes formed by three-dimensional shapes with flat or curved surfaces.
• Prisms: Have two parallel faces called bases and three or more sides.
• Pyramids: Consist of one base and triangular faces that form a vertex at the top.
• Regular polyhedra (Platonic solids): Have equal faces, edges, and angles. Archimedean solids have two or three different types of faces.
• Bodies of revolution: Curved shapes formed when a generating line (e.g., a line in a cylinder or cone) revolves around an axis called the axis of revolution (e.g., cone, cylinder, sphere, torus, hyperboloid).

Symmetry in the Plane and Space

Mathematically defined as the relationship between two elements whose distances from a point, a line, or a plane are equal. Three kinds of symmetry are found in nature. Symmetry is based on the principle of superposition, where two symmetrical figures can be superimposed by rotation and/or translation.

Symmetries in a Two-Dimensional Field:

• Axial symmetry: Two elements are symmetrical about an axis.
• Radial symmetry: Two or more elements are arranged around an axis of symmetry with angular order and distances.

Symmetries in Space:

• Radial symmetry: About an axis of symmetry.
• Axial symmetry: With respect to an axis of symmetry.
• Specular symmetry: When the reference point is a plane.

Concepts and Ideas on Space

Lao-Tse and the Tao

Lao-Tse’s philosophy centers on the Tao, or “the way.” He believed that nothing is permanent in a constantly changing world. Unlike Confucius, Taoists believe that everything is in flux. Lao-Tse proposed flexible thinking that reflects the changing nature of humans and space. He established the philosophical principles of polarity, joining Being and Non-Being, matter and space. Matter is tangible, while space is a vacuum. This unity of opposites is vital to contemporary spatial aesthetics. Lao-Tse saw architecture and interior space as equally important, distinguishing exterior, interior, and transitional spaces (doors and openings that link inner and outer space).

Plato’s Concept of Space

Plato’s philosophy contrasts with Eastern metaphysics and is a significant influence on Western thought. In Timaeus, Plato described space as the mother and receptacle of all creation. He considered it the entity that receives all bodies without changing, a natural container of impressions that is shaped by them. Space, for Plato, was finite within a finite world. His concept of space was based on rational and finite geometry. He distinguished four elements that comprised the world: fire (tetrahedron), earth (cube), air (octahedron), water (icosahedron), and the cosmos (dodecahedron), which represented the set of all.

Aristotle’s Theory of Place

Aristotle developed the theory of place (topos), where every object has or occupies a space. Place is the container of a body (movable for transport) and its limit. Place is not part of the thing it surrounds and is not material. Aristotle’s concept of place implies a system of receptacles where smaller objects have a place within larger ones. He developed a theory of positions in space but not a concept of space in general.

Descartes’ Cartesian Space

René Descartes considered space an extension of objects, as extension in length, width, and depth is space. Space is identical to extension, but extension is connected to material objects, so there is no space without objects and no empty space. According to Descartes, space and matter were one, and space was the same as the extension of matter. This concept of space should be interpreted as an existential and three-dimensional expansion of physical reality. Cartesian space refers to a coordinate system where each point in space is linked. This system is based on Euclidean geometry and Euclid’s five postulates.

Euclidean Space

Euclidean space is a real vector space with a finite-dimensional inner product. A vector space is a set of objects (vectors) that can be scaled and added.

Newton’s Absolute Space

Isaac Newton believed that absolute space could only be perceived by the senses and measured by relative space. Absolute space is homogeneous, infinite, and independent of the objects or events within it. Newton assumed the existence of space as a substance in which material objects float motionless and intangibly.

Einstein’s Space-Time Continuum

Newton’s concept of absolute space was long considered infallible, but it gradually gave way to more sustainable theories (aided by Faraday’s experiments on electromagnetism and the emergence of non-Euclidean geometry). For Einstein, space is a field, not an empty space as Newton proposed. It depends on four parameters: the three dimensions of space plus time. This assumes a non-Euclidean geometry where curved space is possible, but this is only valid at vast, interplanetary distances. At the human scale, Newton’s theory remains valid. Einstein’s theory was influenced by Maxwell and Faraday.

Space Perception: Two-Dimensional Figure-Ground

Several conditions determine whether a contour in an image is seen as the figure or the background. Size is one such condition; the smaller area is usually perceived as the figure, and the larger area as the background. Color and texture can also influence perception. A textured area tends to be seen as the figure, while a solid color is perceived as the background. Convex shapes are often seen as figures because they appear to be taking an active role and expanding.

If a field consists of two areas separated by a horizontal division, the lower area tends to be the figure.

Summary of Space Concepts

• Aristotelian space: A small portion of land identified by a name or arrangement of objects.
• Space as a container: A volume of empty space that can be replaced, existing independently of material objects (Newton’s absolute space).
• Space as a four-dimensional field: Einstein’s concept, influenced by Maxwell and Faraday.

These three conceptions of space have shaped science and philosophy, coexisting and remaining valid and synchronous aspects of Western culture.