Understand Vector Graphics

Vector graphics is a way of presenting images in computer graphics that is based on the use of mathematical equations to represent objects on a screen. Unlike raster graphics, where an image is made up of pixels, vector graphics use lines and shapes that scale losslessly, providing clean and crisp outlines regardless of size.

• Basic elements of vector graphics:
• Anchor Points: Specify the location on the plane.   
• Lines and curves: Connect anchor points to create shapes.          
• Properties Objects: Include color, transparency, and line thickness.

The listed elements are defined by coordinates and do not depend on resolution, making vector graphics ideal for creating logos, illustrations, advertising banners.

Popular vector graphics file formats:

•  AI (Adobe Illustrator)          
• SVG (Scalable Vector Graphics)    
• EPS (Encapsulated PostScript)     
• PDF (Portable Document Format)

Thanks to these formats, vector graphics are compatible with various programs and can be used in a wide range of applications.

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Objects and Transformations

In vector graphics, objects are mathematically written elements that are made up of primitives. Primitives are basic geometric figures such as circles, squares, triangles, curves, and segments.

Objects in vector graphics are created by specifying their mathematical parameters. For example, a circle is defined by the coordinates of the center and the length of the radius. To create an object:

• The type of primitive is chosen.        
• You specify its dimensions and location (for example, the center of the circle and the radius).         
• You add attributes such as color, stroke weight, and fill.

Object transformations

Vector graphics allow you to manipulate objects in a variety of ways, including scaling, which means resizing an object without losing its quality. It is also possible to rotate, which is to rotate an object around a specific axis, and translation, which involves changing the position of an object without affecting its shape. Additionally, vector graphics allow for beveling, which is a parallelepiped transformation that preserves the shape of an object but changes its angles. Advanced vector graphics editors also offer the ability to perform logical operations on objects, such as combining, which allows you to combine objects and turn off their intersections.

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Vector graphics and mathematics

Vector graphics are closely related to mathematics because it is based on the use of mathematical equations to define objects, which shows how mathematics enables the creation of vector graphics and influences the algorithms and processes used. In vector graphics, images consist of points defined in a mathematical coordinate system, where each point is precisely defined by pairs of coordinate values, allowing it to be accurately placed in the illustration. Shapes in vector graphics are described using straight lines and Bézier curves, which are represented by mathematical equations that allow images to be scaled without loss of quality. What's more, by using the mathematical properties of basic geometric figures such as squares, circles, and triangles, vector graphics allow for their precise description and transformation, further emphasizing the connection between vector graphics and mathematics.

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Form of notation

Vector graphics are characterized by storing images using mathematical equations that determine the coordinates of geometric objects in space. In vector graphics, the important elements are points, lines, curves, and shapes given by vectors. With this format, graphics are scalable without losing quality.

Shape and color information is saved in a vector file in a format that is compatible with vector graphics software, allowing you to edit and scale without loss of quality. Common file formats for vector graphics are SVG, EPS, AI, and PDF.

The file size of a vector graphic is typically smaller than that of a corresponding raster image with similar visual complexity, which is beneficial in terms of storage, sharing, and loading speed.

Vector graphics are an extremely valuable tool in the world of digital design, offering precision, scalability and efficiency. Thanks to its unique properties, such as the ability to scale without loss of quality and precisely define objects using mathematical equations, vector graphics are widely used in a variety of fields – from graphic design to illustration to advertising production.