The 18th-century rise of descriptive geometry claimed to provide universal principles for representation, leading to the idea that representation and human vision must align.
The theory of parallel perspective, in particular orthographic projection, and the form known as primary projection, planar projection, multi-view projection, and descriptive geometry allowed for the development of plan/elevation methods, including first- and third-angle perspective drawings.
Such drawings have the key advantage that they are not optically distorted (in any way) and thus a complete and perfectly proportioned/scaled description of any 3-D object can be created.Whereby the prescription is logically complete and visually correct, and there is no ambiguity or falsehoods in what is being presented in the plan/elevation drawing.
Primary or Multi-View Projection
Primary or multi-view projection is a technique in which principal axes or the planes (or faces) of the object are also parallel to the picture/ projection plane to create the primary views.
Sub-types of primary views include plans (top-down/bottom-up view), elevations (front/side view), and sections or cutting planes through the object to allow viewing of internal structures. Multi-view projection is so-named because the draftsman can completely define the 3-D geometry of a 3-D object by creating a drawing that shows three separate, or orthogonally related views: plan, front elevation and side elevation.
Primary projection is synonymous with the drawing technique named as descriptive geometry. It may involve first-angle projection (termed first quadrant), commonly used in Britain, where one looks out at the projection, or third-angle projection, commonly used in the United States, where one looks in at the projection as if it were in a transparent glass box.
Primary projections are often used in technical and engineering drawings and plans, as well as in architectural drawings, etc., and because the representation has a uniform scale that enables accurate, precise measurements to be taken directly from the drawings so constructed. Such orthographic/orthogonal drawings are the fundamental method and the cognitive foundation for producing accurate and precise manufacturing plans for all human-made spatial objects, machines, built environments, etc.
Descriptive Geometry
We can now summarise what we have learned about descriptive geometry,
Descriptive geometry is the branch of geometry that allows the representation of three dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are employed for engineering, architecture, design, and art. All geometric aspects of the imaginary object are accounted for in true-size/to-scale and shape, and can be imaged as seen from any position in space. All images are represented on a two-dimensional surface.
Descriptive geometry uses the image-creating technique of imaginary, parallel projections emanating from an imaginary object and intersecting an imaginary plane of projection at right angles. The cumulative points of intersections create the desired image.
Explore Theory
Explore the principal theories, classifications, types, forms, geometries, spatial concepts and visual phenomena of perspective.
Theory Hubs
Foundations of Perspective Theory · Perspective Category Theory & Classification · Perspective Types and Forms · Perspective Geometry & Projection · Vanishing, Horizons & Directional Reference · Form, Space & Perspective Images · Perspective Phenomena, Vision & Problems · Advanced & Additional Perspective Concepts
Foundations & Classification
Theory of Perspective · Functions of Perspective · Perspective Process · Perspective Principle · Perspective System · Perspective Category Theory · Perspective Category · Perspective Type · Categorical Ambiguity · Combined Perspective
Perspective Types & Forms
Types of Perspective · Central Perspective · Parallel Perspective · Linear Perspective · Curvilinear Perspective · Axonometric Perspective · Camera Perspective · Digital Perspective · Artificial Perspective · 360-Degree Perspective · Panoramic Perspective
Geometry, Vanishing & Spatial Reference
Perspective Projection · Perspective Geometry · Projective Transformation · Picture Plane · Station Point · Vanishing Point · Horizon Line · Viewpoint · Vanishing Structures · Optical Versus Geometrical Vanishing
Form, Space & Perspective Images
Perspective and 3-D Space · Object Space · Image Space · Perspective Image / View · Optical Image Chain · Linear Perspective Images · Perspective Product
Vision, Phenomena & Problems
Perspective Phenomena · Foreshortening · Depth Cues · Field of View · Binocular Vision · Scale–Shape–Size Problem · Equivalence / Correspondence Problem · Perspective and Illusion · Perspective and Spatial Immersion
Further reference:
Dictionary of Perspective ·
Perspective Research Centre
Major discipline hubs:
Fine Art, Illustration and Visual Design ·
Architecture and the Built Environment ·
Photography ·
Cinema, Television and Visual Effects ·
Computer Graphics, Games and Extended Reality ·
Cartography, GIS and Spatial Mapping ·
Science, Engineering and Technical Imaging ·
Medical Imaging ·
Perspective in Professional Practice