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at its most basic level you are simply drawing objects that are independent of each other and can be manipulated separately. There is a stacking order for them and there are also named layers they can be on. At its most basic, an object is simply a path defined by endpoints, and whether the path is curved or straight depends on the "handles" at the endpoints. A square is just four endpoints with no handles. A circle is also just four enpoints, but they have handles that define the curves between the points. You can manipulate the shape of an object either by moving individual points or by just moving the handles. Or a complete object can be moved or altered using tools such as scale, rotate, shear, distort, etc. You can duplicate and group objects easily. An object can have properties such as fill (filling in the interior of the boundaries with a color, shade, pattern, etc.), stroke (the line itself defined by the object can have thickness, color, shade, pattern, etc.) and transparency. Different combinations of these properties including transparency, working with the stacking order and layering, can produce different effects. The advantage of object-oriented artwork is that it can be easily resized without losing any quality or detail, since the objects are resolution-independent until the moment they are displayed or printed. At that moment the result is resolution-dependent, at whatever the resolution of the device showing it is (72 dpi for a monitor, 300 or 600 dpi for a laser printer, 1200 dpi or more for an imagesetter for printing on a press, etc.) But the objects within the Illustrator file are resolution-independent as far as Illustrator is concerned. This makes Illustrator ideal for logos, which may be used at different sizes in the course of their uses. This is the fundamental concept with Illustrator and was about all there was at the beginning 20 years ago. Since then many bells and whistles have been added to the program and complex operations are possible now. Some of them include masking effects, such as making a photo appear only within the outlines of an object, or type and typography effects, 3-D drawing and more. But the fundamental element of an Illustrator file is an object, which is defined by the points and the handles associated with those points. The actual shape of the object is defined by complex mathematical formulas called Bezier curves, but you don't have to do any math. You just draw with the various tools, and the Bezier curves are created for you automatcially by the program. Just take the pen tool and draw some lines and curves for a while to get a feel for it.
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