Posts Tagged ‘Perspective’

Week2_Mathematics,Perspective,Time&Space by Dennis Yeh

Monday, January 19th, 2009

Throughout history, humans have attempted to explain the universe with mathematics.
Einstein managed to relate two facets of life: Energy and Mass with the equation E=mc^2. This demonstrates a law that is obeyed by everything in the universe, with just a simple mathematical equation. In fact, his equation was not proved until last year, by scientists that “envisioned space and time as part of a four-dimensional crystal lattice, with discrete points spaced along columns and rows.” I am unable to find a sketch or model of their work, but I’m sure that if it were to be drawn or modeled with a computer, it would be fascinating to see how energy and mass are equivalent.

What is the universe? When Professor Vesma discussed perspective and dimension, it reminded me of a video that demonstrates what all of the theoretical dimensions are, and where our universe lies in that scale.
-Theoretical Dimensions: http://www.youtube.com/watch?v=HvgwR9ERCBo
Professor Vesma talked about how all early paintings were simply 2-D sketches until artists experimented with the mathematics of perspective and lines that illustrate a third dimension when your medium (canvas, computer screen, paper, etc.) has only two dimensions. These techniques, such as the idea of a vanishing point, or transforming from higher dimensions into lower ones were covered extensively by my linear algebra class last quarter. Using vectors and matrices that represent linear spaces, it is possible to use math to calculate and model linear transformations to the linear spaces, and convert 3-D images into 2-D images easily and mathematically accurately using a computer.

Another interesting example of how math is found in art is with photography. A photograph is simply a 2-D image of how a certain 3-Dimensional setting appeared at a specific point in time. Math is involved with many aspects of photography:
-Single Lens Reflex cameras use math to calculate how the light will travel through the lens and inside the camera (as well as the positioning and angle of the mirrors inside the camera)
-Aperture size and shutter speed is used to calculate how much light will enter the camera as well as how long the light is exposed to the film.
-Photographers usually try to obey the rule of thirds: that is, an image is divided equally into 9 squares, and important compositional elements should be placed along the lines.

A demonstration of the Rule of Thirds.

When I thought about how artists these days almost always use techniques to give their paintings three dimensions, I realized that these days our technology is able to replicate 4-Dimensional images on a 2 or 3 Dimensional screen. Movies and video recording are now a cheap technology that everyone can afford and use.  Like photography, video recording is also related heavily with math.  Cinematographers deal with several variables when they compose their shots, which they have to get perfectly right every time.

Some of the variables cinematographers deal with:
-Film
frames/second: how many images are shot every second.
film gauge: thickness of the film emulsion.  Thicker emulsion = better quality = more expensive.
film speed: how sensitive film is to light.  Lower speed = less sensitive to light; higher speed = more sensitive to light.

-Lens
filters: Manipulate the light entering the camera to create emotions or moods (ie. colored filters, polarizing filters, diffusion filters, etc.)
focal length: Changes the angle of the shot and the field of view.
aperture: Used to control the exposure of the image.  Affects image quality and depth of field.
depth of field: How much the background, midground, and foreground are in focus.
Framing:
aspect ratio: the ratio of width to length of the shot.  Standard ratio = 4:3 (4 units wide, 3 units high).  Widescreen ratio = 1.85:1 (1.85 units wide, 1 unit high).  In the 1990s, with the advent of high-definition video, television engineers created the 1.78:1 (16:9) ratio as a mathematical compromise between the theatrical standard of 1.85:1 and television’s 1.33:1, as it was not physically possible to safely create a television tube with a width of 1.85:1. Until that point, nothing had ever been originated in 1.78:1. Today, this is a standard for high-definition video and for widescreen television.
movement: The video camera has a fourth dimension: time.  Therefore, cinematographers have to consider if and how the camera will move while it is recording.
Lighting:
mood: The “art” part of lighting.  Creating an effective mood in a video composition is greatly affected by how the set is lit.  The quality of lighting affects how effectively the mood is conveyed
video camera technology: Gives the cinematographer more options when considering how to light the set.  The quality of technology affects how effective the lighting is.