@RobDraw wrote:
Agreed with everything except for these:
...
@apatterson2APPDE wrote:
the vector geometry will be converted to look like actual curves on the print.
The curves output to the print are vector geometry. Now, what the printer driver does with that information I would expect to vary depending on the printer. I'm just not familiar enough with what happens with the driver to know if they can actually print the vector data or there is a conversion to segmented arcs.
The process of drawing a circle on paper with a compass is an analog, as opposed to digital, process. The curve produced is smooth and continuous.
Computer printers of graphics rely on one of two methods to make a print. They are either raster printers that use a series of dots to make an image or they are what is often referred to as XY plotters. Raster printers may make lines other than horizontal and vertical appear like a step of stairs. This is especially true with lines of small angles. To reduce the "jaggies" cause by this stair stepping antialiasing is used. A simple form of anti-aliasing makes the dot (or pixel) at the beginning of a step half the intensity of the line. This softens the appearance of the step. I feel the effect is more akin to making the image slightly out of focus. XY plotters in contrast can move a pen from one location on directly to anther location on the paper in a perfectly straight line. XY plotters use stepping motors to precisely position a pen on paper. A stepping motor can be considered a digital device in that there is a finite size to the step. To draw a circle, arc or spline, the XY plotter is given a series of positions it should move to in order to create the curve. Therefore the curve is draw by moving the pen to specific coordinates. A circle is thus interpreted as a series of points along its circumference although the data for the circle may be just its center location and radius. Mathematically, the location of the pen is simply:
x = x_center + radius * cos(theta) and y = y_center + radius * sin(theta)
To draw the circle theta must go from 0° to 360°. If you incremented theta by 45° (0, 45, 90,...) then the result would look like an octagon IF THE SIZE OF THE PLOTTED CIRCLE WERE LARGE ENOUGH TO SEE THE EIGHT SIDES. Typically it would be large enough so a step size much smaller than 45° is used. The increment value for theta that is used when plotting is a function of the radius of the printed circle and the minimum step size for the stepping motors. Bigger circles will use smaller angle steps. Similarly splines will be drawn by determining the step size for the independent variable of the parametric spline definition whether they are Bezier, B-splines or NURBS. These splines store the curve not as a series of points that are along the curve but as a series of points that define Control Vertices. Just like the circle, points along the curve are calculated on-the-fly as it is printed (or displayed). One nice feature of these splines is that for a given value of delta_t (the step size of the independent variable) the length of the line segments used to draw the spline are shorter where the radius of curvature is small and longer where the spline flattens out. This yields the same degree of perceived smoothness for the entire spline.
Bottom line? Whether printed with a raster printer (e.g. laser printer) or XY plotter, at some level a curve will not be smooth. The question is, will it be smooth enough. This leads me to the age old question, "what's the difference between a scientist and an engineer?" 😀
lee.minardi
