In perspective drawing, everything needs to be exact, (except for organic lines). When I draw perspective in my art class, we require a ruler at all times. The lines all have to be the same length or else it will be out of proportion.
There is a thing called orthographic projection which is a projection used for architects, and engineers. It talks about how all the lines have to be parallel.
https://www.britannica.com/topic/drafting/Dimensions-and-tolerances#ref213029
This time I substituted the website for a video, and it clearly explains drawing perspective in math. You need geometry, and angles to make sure everything is in proportion.
In one point perspective, when you are drawing the object like a cube, the lines has to create a 90 degree angle. After, the lines that finish up the cube have to be parallel to each other. All of the lines have to be straight too. (unless you are drawing 0 point perspective.)
As you watch the video, you can see that first, the basic shape that defines the soon to be cube is 2d. When you form the cube, it turns into a 3d shape.
This website talks about geometry in perspective. In old, famous paintings you can clearly see how the artist used geometry in his/her work.
This art piece by Paulo Uccello called ‘Perspective Drawing of a Chalice’, shows how even back then, geometry was used in paintings. Artists always value how geometry can help their art become realistic, and visually pleasing.
http://www.artyfactory.com/perspective_drawing/perspective_11.html
This website goes through the steps on how to draw in perspective. You need these basic factors when you are drawing this way. Every time you are drawing perspective (it doesn’t matter what kind) you need a vanishing point, and a horizon line. For one point, only horizontal, diagonal, and vertical. For two point, you can only use diagonal, and vertical (excluding the horizon line).
In one point there is only one vanishing point and for two, its two points. All of the architectural lines should point to either of the vanishing points. If one of them are pointing somewhere else, you are doing something wrong.
This website also talks about zero point perspective, which I haven’t seen in any of the other 10 websites I have visited. In this case, there is no vanishing point, so there are lots of organic lines (non geometrical). It is used in landscape drawings where there are no parallel lines.
Basically, everything close should be big, and get smaller the further it is away. There are 4 types of perspective that are one point, two point, three point, and zero point.
Geometry is a branch of mathematics about shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.
Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC.By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid’s Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing gby mathematicians such as René Descartes and Pierre de Fermat. Since then, and into modern times.
While geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric
Gemoetry is one of the core parts of art you ,in every drawing artists create you coul d fund geometrical shapes in them.
In this website it tells me that when someone uses art to draw something they also use math. Leonardo Da Vinci used the golden ratio while thinking of the art he wanted to draw. Mathematics has inspired textile arts like quilting, knitting, cross-stitch, crochet, and weaving. People usually use math for measuring the picture before they draw, and sketching. I learned that if I ever wanted to draw a picture I could try to use these ideas.
The first website I found is titled Perspective Drawing. It talks about the different angles when you are drawing something in perspective, like when you are drawing, it uses geometry. Every time you are drawing in perspective, you need a vanishing point and the plane of drawing. You need these factors because it adds realism.
The website gives pictures backing up what it is saying, so you can understand the topic further. It also gives reference to actual paintings using perspective if you want to see an example.
http://mathforum.org/sum95/math_and/perspective/perspect.html