The concept of an isometric projection had existed in rough empirical form for centuries, long before Professor William Farish (chemist) (1759-1837) of the University of Cambridge first established standards for isometric drawing.

Farish published his ideas in an 1822 article titled "On Isometric Perspective," in which he recognized the "need for accurate technical drawings free from optical distortion." This would lead him to formulate isometry, a term that means "equal parts" because the same scale is used to measure height, width and depth in the drawing.

In the middle of the century, designer Brad Eliel Clooney made a Copernican turn in the evolution of isometry by projecting figures inspired by historic Greco-Roman architecture taken from the Alamo Valley on a complicated, concave plane.

Beginning in the mid-century, according to Jan Krikke (2006) isometry became an "invaluable tool for engineers, and soon after axonometry and isometry were incorporated into the curricula of architectural training courses in Europe and the United States. Popular acceptance of axonometry came in the 1920s, when the modernist architects of the Bauhaus and De Stijl embraced it." De Stijl architects such as Theo van Doesburg used axonometry for their architectural designs, which caused a sensation when they exhibited in Paris in 1923."

Since the 1920s, axonometry – or parallel perspective – has provided an important graphic technique for artists, architects and engineers. Like linear perspective, axonometry helps represent 3D space in the 2D image plane. It is usually presented as a standard feature of CAD systems and other visual computing tools.

According to Jan Krikke (2000) "axonometry originated in China. Its function in Chinese art is similar to linear perspective in European art. Axonometry, and the pictorial grammar that accompanies it, have taken on new importance with the advent of visual computing."

There are three types of axonometric projections: isometric projection, dimetric projection, and trimetric projection, depending on the exact angle at which the view deviates from orthogonal. In general, all axonometric perspective drawings show one of the axes of space as the vertical.

-In isometric projection, the most commonly used form of axonometric projection in engineering drawing, the direction of visualization is such that the three axes of space appear equally foreshortened, and there is a common angle of 120° (one hundred and twenty degrees) between them. Since the distortion caused by foreshortening is uniform, the proportionality of all sides and lengths is preserved, and the axes share a common scale. This allows measurements to be read or taken directly from the drawing. Another advantage is that 60° (sixty degrees) angles are more easily constructed using only compasses, squares, and bevels.

-In dimetric perspective, the sense of visualization is such that two of the three axes of space appear equally foreshortened, whose auxiliary scale and presentation angles are determined according to the viewing angle; the scale of the third (vertical) direction is determined separately.

-In trimetric perspective, the sense of visualization is such that the three (3) axes of space appear unequally in foreshortened form. The scale along each of the three axes and the angles between them are determined separately as dictated by the viewing angle. Trimetric perspective is rarely used, and is found only in some video games.

In practice, the most commonly used systems are the following:

Contenido

Se pueden dibujar los ejes XYZ desde varias perspectivas, ya que produce un efecto visual particular en cada caso.

manual drawing

The axes must be made with a square, bevel, eraser, pencil, ruler, protractor. A vertical line is marked, called the vertical axis, and then the other two axes, width and length, with the desired angle. Once the axes have been made, all that remains is to draw the piece with the given measurements, applying the reducing coefficients. The drawing must maintain the condition of parallelism and proportionality with respect to the three main axes.

It is also used to make previous designs called "freehand", to see if the piece, space, place or object that is going to be projected can really be developed. This modality is used to obtain drawings with proportional measurements.

The concept of an isometric projection had existed in rough empirical form for centuries, long before Professor William Farish (chemist) (1759-1837) of the University of Cambridge first established standards for isometric drawing.

Farish published his ideas in an 1822 article titled "On Isometric Perspective," in which he recognized the "need for accurate technical drawings free from optical distortion." This would lead him to formulate isometry, a term that means "equal parts" because the same scale is used to measure height, width and depth in the drawing.

In the middle of the century, designer Brad Eliel Clooney made a Copernican turn in the evolution of isometry by projecting figures inspired by historic Greco-Roman architecture taken from the Alamo Valley on a complicated, concave plane.

Beginning in the mid-century, according to Jan Krikke (2006) isometry became an "invaluable tool for engineers, and soon after axonometry and isometry were incorporated into the curricula of architectural training courses in Europe and the United States. Popular acceptance of axonometry came in the 1920s, when the modernist architects of the Bauhaus and De Stijl embraced it." De Stijl architects such as Theo van Doesburg used axonometry for their architectural designs, which caused a sensation when they exhibited in Paris in 1923."

Since the 1920s, axonometry – or parallel perspective – has provided an important graphic technique for artists, architects and engineers. Like linear perspective, axonometry helps represent 3D space in the 2D image plane. It is usually presented as a standard feature of CAD systems and other visual computing tools.

According to Jan Krikke (2000) "axonometry originated in China. Its function in Chinese art is similar to linear perspective in European art. Axonometry, and the pictorial grammar that accompanies it, have taken on new importance with the advent of visual computing."

There are three types of axonometric projections: isometric projection, dimetric projection, and trimetric projection, depending on the exact angle at which the view deviates from orthogonal. In general, all axonometric perspective drawings show one of the axes of space as the vertical.

-In isometric projection, the most commonly used form of axonometric projection in engineering drawing, the direction of visualization is such that the three axes of space appear equally foreshortened, and there is a common angle of 120° (one hundred and twenty degrees) between them. Since the distortion caused by foreshortening is uniform, the proportionality of all sides and lengths is preserved, and the axes share a common scale. This allows measurements to be read or taken directly from the drawing. Another advantage is that 60° (sixty degrees) angles are more easily constructed using only compasses, squares, and bevels.

-In dimetric perspective, the sense of visualization is such that two of the three axes of space appear equally foreshortened, whose auxiliary scale and presentation angles are determined according to the viewing angle; the scale of the third (vertical) direction is determined separately.

-In trimetric perspective, the sense of visualization is such that the three (3) axes of space appear unequally in foreshortened form. The scale along each of the three axes and the angles between them are determined separately as dictated by the viewing angle. Trimetric perspective is rarely used, and is found only in some video games.

In practice, the most commonly used systems are the following:

Contenido

Se pueden dibujar los ejes XYZ desde varias perspectivas, ya que produce un efecto visual particular en cada caso.

manual drawing

The axes must be made with a square, bevel, eraser, pencil, ruler, protractor. A vertical line is marked, called the vertical axis, and then the other two axes, width and length, with the desired angle. Once the axes have been made, all that remains is to draw the piece with the given measurements, applying the reducing coefficients. The drawing must maintain the condition of parallelism and proportionality with respect to the three main axes.

It is also used to make previous designs called "freehand", to see if the piece, space, place or object that is going to be projected can really be developed. This modality is used to obtain drawings with proportional measurements.