Ads
related to: perfect circleebay.com has been visited by 1M+ users in the past month
Search results
Results from the WOW.Com Content Network
People often play around with the word "perfect circle" but I have always been curious as to what exactly is a "perfect circle". It is easy to imagine, but to me, even when given precise geometrical equipment, it seems impossible to verify that a circle is perfect unless you have infinite time. The way I understand a "perfect circle" is as follows:
In the same sense as you think a circle is impossible, a square with truly perfect sides can never exist because the lines would have to have infinitesimal width, and we can never measure a perfect right angle, etc. You say that you think a square is physically possible to represent with 4 points, though.
A real circle is exactly what you normally think of as a circle; it has a radius that is a real number (not imaginary). A point "circle" is just a point; it's a circle with a radius of zero (hence a degenerate circle). An imaginary circle is one in which the radius is the square root of a negative number—i.e., imaginary.
Take a piece of rigid cardboard. Draw a perfect circle on it. Hold it up, and take a picture, with the cardboard held perpendicular to the direction we're looking. You get a photo that looks like this: Notice: it looks like a perfect circle in the photograph.
Given The radius of Circle A is 1/3 the radius of Circle B. Circle A rolls around Circle B one trip back to its starting point. Question How many times will Circle A rotate about its center *** Solution, Part 1 Begin by drawing (1) Circle B (2) Circle A where it initially contacts Circle B (3) Circle A where it contacts Circle B after rolling 1 ...
Without using rational Bezier curves, drawing a circle is impossible. I remember I had to prove that once for some class I had, and the proof isn't pretty. However, drawing the circle using rational bezier curves is quite easy, as I recall.
The standard circle is drawn with the 0 degree starting point at the intersection of the circle and the x-axis with a positive angle going in the counter-clockwise direction. Thus, the standard textbook parameterization is: x=cos t y=sin t. In your drawing you have a different scenario.
$\begingroup$ @MoebiusCorzer Well, I don't think so :) but probably you have some grounds for stating that. In fact a line has no thickness so ... as you draw it, you already know it's not perfect i.e. it's not really a line, it's a rectangle in the best case, and even that rectangle is not perfect :) because in some of its parts this rectangle is surely thicker (assuming you can measure it ...
However, if you're willing to consider a Bézier curve in 3D which forms a perfect circular arc when viewed from the correct point (i.e. with a perspective projection; this is also known as "rational Bézier curves"). E.g. these notes show how to construct any conic section with rational quadratic Béziers.[Now 404s and not in archive.org].
First of all, you haven't defined a circle. Sure, you can define a circle, but a circle will not be a regular polygon, at least not by the definition of a regular polygon. OK, that may be a problem you can overcome. We can say that a circle is some sort of curve, just like a polygon. However, there is another problem:
Ads
related to: perfect circleebay.com has been visited by 1M+ users in the past month