Geometry is used to automatically generate graphics.
Geometry is central to the development of computer graphics software. Scientists and computer programmers study fractal geometry, descriptive geometry and linear perspective, that is 3D geometry, to develop mathematically draw objects instead of drawing them with a mouse or pen and pencil.
Two-Dimensional Coordinate Geometry
Two-dimensional coordinate geometry, the use of algebraic equations to represent two-dimensional geometric shapes such as lines and polygons, is the basis for the design of computer graphic software. Popular illustrations programs let graphic designers quickly create two-dimensional geometric figures through simple point and click operations. The computer code that generates the two-dimensional object on the screen is based on coordinate geometry formulas, such as the distance and midpoint formulas.
Three-Dimensional Coordinate Geometry
Three-dimensional coordinate geometry principles are also used in computer graphic programs. Many of the geometric formulas used in three-dimensional graphics computer programming are extensions of two-dimensional coordinate geometric formulas. For the rotation of a 3D geometric object in a computer graphic program, geometric point transformation procedures are used that rotate all the vertexes of the 3D object.
Fractal geometry is the study of automated drawing methods that are based on a specific geometric shape or set of specific geometric shapes. Often fractal methods involve the repeated inscription of a geometric shape within a geometric shape. One example, is when an equilateral triangle is inscribed within an equilateral triangle, repeatedly, such that each successively inscribed equilateral triangle is smaller than the previous. When computer code is written to perform this procedure, successively smaller equilateral triangles can be continually constructed without end and without human intervention.
Linear perspective is a geometrical drawing method that is used in computer graphics programs to construct a three-dimensional object on a two-dimensional computer screen. In effect, linear perspective is a geometrical system that lets one construct a true photo like image of an object from the three-dimensional coordinates of an object. Fundamental to linear perspective is the perspective grid. The perspective grid is used to derive the geometric formulas for the 3D to 2D coordinate conversions used in computer graphics programs.
Descriptive geometry, like linear perspective, is used in computer graphics to construct a three-dimensional object on a two-dimensional computer screen. However, descriptive geometry does not produce a true perspective rendering like a camera would. A computer graphic based on descriptive geometry methods results in a drawing such that all lines that are parallel in three-dimensions are drawn parallel on the two-dimensional screen. Because a parallel grid is used instead of a perspective grid, the true dimensions of the object can be directly measured on the computer screen.