2d cad/cam simplification example

hello :) a normal cad should allow drawing basic shapes ( 5 of them : points, lines, circles, elipses, beziers ), and formula driven ones ( less used, but still )

each one of the basic shapes is handled by its own code, and variations will occure, as one will have to create, for example, intersections

idea behind this thread is reducing variations, from the consideration that points lines circles and elipses, are nothing but restricted beziers:
... line = an analytical bezier
... ellipse = interpolated spline, within a given accuracy, that has to be corelated with cnc precision
*voila, basic shapes set just reduced from 5 to 1, and variations for intersections reduced from 15 to 1

how most machine operations are lines & circles, there can be used labels to identify that a bezier is a line, or a circle arch, in order to generate relevant g-code / kindly :)

when computing resources were poor the brief expression of drawing element was important: point has only coordinates and nothing else. Segment of straight line has coordinates of two points and nothing else. Circle has coordinates of the center point and radius and nothin else. And so on. Shapes produced consisted simple segments.
Today we want to have one complex element with desribed behaviour and parametrise it to whatever shape we want.

Quote:

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Circle has coordinates of the center point and radius and nothin else

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hy :) it may also have sense, like trigonometric or backwards, and also other parameters if it is considered a particular case of an arch, ellipse or whatever

Quote:

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Shapes produced consisted simple segments

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if i may, this is only for rough representations, in order to speed up processing speed; for smooth analytical ones. that take more time to compute, where segment size is scaled to fit screen pixels grid, a bit more simple math is involved, segments size being no longer equal, or equal at a resolution higher than the screen / kindly :)