User:Wongyanyan/sandbox

Helix Drawing
Helix Drawing is the art of drawing helices, which are curves in three-dimensional space, such that the way they curve causes them to “stack” on top of themselves in layers. The path of a helix is that created by a point travelling along the circumference of a circle as that circle moves in a straight line perpendicular to its surface. This creates the shape that looks like a winding staircase. Drawing a helix by hand is not as complicated as one would think. There are standard steps to follow to achieve a properly drawn helix.

We first draw a circle with a diameter the same length as the width of the helix desired. Then draw a square that encases this circle. Draw in the diagonals of this square. Mark the intersections of the circle with the diagonals. Extend the lines of the square to the length of the desired helix. Divide the extension lines into sections as long as one period of the helix. Then divide each of these sections into eight equal parts. Take the intersections marked earlier and draw lines from them, parallel to the square extension lines. Work with the original circle is now done. Moving on to the grid that has been set up as a frame, draw a sinusoidal curve, using the intersections of the grid lines as guides (intersections are the values of the function at 0, π/4, π/2, 3 π/4, π, 5π/4, 3π/2, 7 π/4, and 2π. After drawing this curve in lightly, shift one gridline to the right, and draw the same sinusoidal curve again, but shifted over.  These two curves form the basis for the single helix.	With the two sinusoidal curves drawn, darkening the appropriate lines will make the helix ribbon three-dimensional.  In every period, darken the lines that travel from π/2 to 3π/2 on a sine curve.  These are the sides of the helix that are facing you.  Afterward darkening these front lines, the slightly hidden ones on the far side of the helix need to be drawn.  This is done by darkening all lines that are still light, while not crossing over any existing lines.  This creates the illusion of depth in the helix.

More Complex Helices
The single ribbon helix, albeit simple, begs elaboration. There are several ways to do this. The helix can be made into a solid piece, instead of a planar ribbon. This is done by drawing a smaller circle inside of the circle originally drawn as a guide for the single helix. Using the same guiding techniques described above, an internal helix is created. This time, however, before darkening the far edges of the helix, darken the front internal lines. Then darken the appropriate far edges, creating a ribbon helix that has a thickness. Another variation of the single helix is the double helix. This shape is most commonly seen in the structure of DNA. To prepare to draw a double helix, use the same process of setting up a single helix, and repeat the process, but shifted half a period, or π units to one side. Now darkening the appropriate lines uses a similar process to that of drawing a single helix. First darken the lines travelling from π/2 to 3π/2 on the sine curves, then darken the remaining lines, without crossing over existing lines. The final product is two single helices intertwined into each other.