Lêer:Harmonic partials on strings.svg

Page contents not supported in other languages.
in Wikipedia, die vrye ensiklopedie

Oorspronklike lêer ‎(SVG-lêer, normaalweg 620 × 590 piksels, lêergrootte: 10 KG)

Hierdie lêer kom vanaf Wikimedia Commons en kan ook in ander projekte gebruik word. Die beskrywing op die lêer se inligtingsblad word hieronder weergegee.

Opsomming

Beskrywing
English: Illustration of harmonic overtones on the wave set up along a string when it is held steady in certain places, as when a guitar string is plucked while lightly held exactly half way along its length.
Datum
Bron Own work by uploader, based on design of bitmap image Image:Overtone.jpg
Outeur Qef / Houtlijm
Ander weergawes Massive JPEG bitmap version: Image:Overtone.jpg

Source code

Created by a specially written program in the Lua programming language. To recreate the image just run the program, and it will write the SVG into a file. There are various parameters that can be adjusted at the start of the code. The sine-wave approximation using Bezier curves is derived from Bezier curve sinewave approximation (PDF) by Jim Fitzsimmons. 

local MARGIN = 10
local AMPLITUDE, WAVE_WIDTH = 30, 600
local GAP_BETWEEN_WAVES = 25
local NUM_WAVES = 7
local FONT_SIZE, FONT_FUDGE = 20, 5

local WAVE_STYLE = ' stroke="#000" stroke-width="1.5" fill="none"'

local img_wd = 2 * MARGIN + WAVE_WIDTH
local img_ht = 2 * MARGIN + NUM_WAVES * AMPLITUDE * 2 +
               (NUM_WAVES - 1) * GAP_BETWEEN_WAVES

local PI = math.asin(1) * 2
local XD = PI / 12
local SQRT2 = math.sqrt(2)
local Y1 = (2 * SQRT2) / 7 - 1 / 7
local Y2 = (4 * SQRT2) / 7 - 2 / 7
local Y3 = SQRT2 / 2
local Y4 = (3 * SQRT2) / 7 + 2 / 7

function sine_wave_path (x, y, width, amp, num_half_waves)
    local xmul = width / (num_half_waves * PI)
    local xd = XD * xmul
    local path = 'M' .. coords(x, y)
    for _ = 1, num_half_waves do
        path = path .. ' C' .. coords(x + xd,   y + amp * Y1)
                    ..  ' ' .. coords(x + 2*xd, y + amp * Y2)
                    ..  ' ' .. coords(x + 3*xd, y + amp * Y3)
                    .. ' C' .. coords(x + 4*xd, y + amp * Y4)
                    ..  ' ' .. coords(x + 5*xd, y + amp)
                    ..  ' ' .. coords(x + 6*xd, y + amp)
                    .. ' C' .. coords(x + 7*xd, y + amp)
                    ..  ' ' .. coords(x + 8*xd, y + amp * Y4)
                    ..  ' ' .. coords(x + 9*xd, y + amp * Y3)
                    .. ' C' .. coords(x + 10*xd, y + amp * Y2)
                    ..  ' ' .. coords(x + 11*xd, y + amp * Y1)
                    ..  ' ' .. coords(x + 12*xd, y)
        x = x + width / num_half_waves
        amp = amp * -1  -- flip over vertically every half wave
    end
    return path
end

function coords (x, y)
    return string.format('%g,%g', x, y)
end

local fh = assert(io.open("Harmonic_partials_on_strings.svg", "wb"))
fh:write('<?xml version="1.0" encoding="UTF-8"?>\n' ..
         '<svg version="1.0" width="', img_wd, '" height="', img_ht,
         '" xmlns="http://www.w3.org/2000/svg">\n')

local y_origin = MARGIN + AMPLITUDE
local wave_labels, pick_circles = '', ''
for n = 1, NUM_WAVES do
    local amp = AMPLITUDE - (n - 1) * AMPLITUDE * 0.1
    fh:write(' <path', WAVE_STYLE, ' d="',
             sine_wave_path(MARGIN, y_origin, WAVE_WIDTH, amp, n), ' ',
             sine_wave_path(MARGIN, y_origin, WAVE_WIDTH, -amp, n),
             '"/>\n')
    if n > 1 then
        local pick_x = MARGIN + WAVE_WIDTH / n
        local pick_r = AMPLITUDE * 0.2
        pick_circles = pick_circles .. '  <circle cx="' .. pick_x ..
                       '" cy="' .. y_origin + pick_r ..
                       '" r="' .. pick_r .. '"/>\n'
        wave_labels = wave_labels .. '  <text x="' .. pick_x ..
                      '" y="' .. y_origin - FONT_SIZE + 2 * FONT_FUDGE ..
                      '">1/' .. n .. '</text>\n'
    end
    y_origin = y_origin + 2 * AMPLITUDE + GAP_BETWEEN_WAVES
end

fh:write(' <g stroke="#000" fill="#bbb">\n', pick_circles, ' </g>\n',
         ' <g font-family="Bitstream Vera Sans" font-size="', FONT_SIZE, 'px"',
         ' text-anchor="middle">\n',
         '  <text x="', MARGIN + FONT_FUDGE,
         '" y="', MARGIN + AMPLITUDE - FONT_SIZE + 2 * FONT_FUDGE,
         '">0</text>\n',
         '  <text x="', MARGIN + WAVE_WIDTH - FONT_FUDGE,
         '" y="', MARGIN + AMPLITUDE - FONT_SIZE + 2 * FONT_FUDGE,
         '">1</text>\n',
         wave_labels,
         ' </g>\n',
         '</svg>\n')

Lisensiëring

Public domain This work has been released into the public domain by its author, Qef. This applies worldwide.

In sommige lande is dit dalk nie wettiglik moontlik nie. Indien so:
Qef grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

uitbeelding

Lêergeskiedenis

Klik op die datum/tyd om te sien hoe die lêer destyds gelyk het.

Datum/TydDuimnaelsketsDimensiesGebruikerOpmerking
huidig14:46, 8 Julie 2008Duimnaelskets vir weergawe vanaf 14:46, 8 Julie 2008620 × 590 (10 KG)Qef{{Information |Description={{en|1=Illustration of harmonic overtones on the wave set up along a string when it is held steady in certain places, as when a guitar string is plucked while lightly held exactly half way along its length. }} |Source=Own work

Die volgende bladsy gebruik dié lêer:

Globale lêergebruik

Die volgende ander wiki's gebruik hierdie lêer:

Wys meer globale gebruik van die lêer.

Ontsluit van "https://af.wikipedia.org/wiki/Lêer:Harmonic_partials_on_strings.svg"