Created
February 7, 2024 14:53
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Several ways of graphing an equation.
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MIN_X = -10 | |
MAX_X = 10 | |
MIN_Y = -10 | |
MAX_Y = 10 | |
RANGE_X = MAX_X - MIN_X + 1 | |
RANGE_Y = MAX_Y - MIN_Y + 1 | |
// Transform grid coordinates into screen coordinates. | |
transform = function(x, y) | |
y = (y + RANGE_Y / 2) * gfx.height / RANGE_Y | |
x = (x + RANGE_Y / 2) * gfx.width / RANGE_X | |
return { | |
"x": x, | |
"y": y, | |
} | |
end function | |
setPixel = function(x, y, c, size = 1) | |
pnt = transform(x, y) | |
if size == 1 then | |
gfx.setPixel pnt.x, pnt.y, c | |
else | |
gfx.fillEllipse pnt.x - size / 2, pnt.y - size / 2, size, size, c | |
end if | |
end function | |
line = function(x1, y1, x2, y2, lineColor, penSize) | |
start = transform(x1, y1) | |
finish = transform(x2, y2) | |
gfx.line(start.x, start.y, finish.x, finish.y, lineColor, penSize) | |
end function | |
lineColor = color.green | |
penSize = 2 | |
text.clear | |
gfx.clear | |
// Draw the grid. | |
line MIN_X, 0, MAX_X, 0, color.gray, 1 | |
line 0, MIN_Y, 0, MAX_Y, color.gray, 1 | |
for x in range(MIN_X, MAX_X) | |
line x, -0.1, x, 0.1, color.gray, 1 | |
end for | |
for y in range(MIN_Y, MAX_Y) | |
line -0.1, y, 0.1, y, color.gray, 1 | |
end for | |
for y in range(MIN_Y, MAX_Y) | |
for x in range(MIN_X, MAX_X) | |
setPixel x, y, color.gray | |
end for | |
end for | |
////////////////////////////////////////////////////////////////////////////////////////////////////////////// | |
// Graph a line with dots. | |
// m = 0.5 | |
// b = 2 | |
// for x in range(MIN_X, MAX_X) | |
// y = m * x + b | |
// setPixel x, y, lineColor, 3 | |
// end for | |
////////////////////////////////////////////////////////////////////////////////////////////////////////////// | |
// Graph a line with lines. | |
// for x0 in range(MIN_X, MAX_X) | |
// y0 = x0 ^ 2 - 2 | |
// x1 = x0 - 1 | |
// y1 = x1 ^ 2 - 2 | |
// line x0, y0, x1, y1, lineColor, 3 | |
// end for | |
////////////////////////////////////////////////////////////////////////////////////////////////////////////// | |
// Graph a circle with dots. | |
// x^2+y^2=r^2 | |
// --> if r=3, then y=+-sqrt(3^2-x^2) | |
// for x in range(MIN_X, MAX_X, 1) | |
// y = sqrt(3^2 - x^2) | |
// setPixel x, y, lineColor, 3 | |
// y = -sqrt(3^2 - x^2) | |
// setPixel x, y, lineColor, 3 | |
// end for | |
////////////////////////////////////////////////////////////////////////////////////////////////////////////// | |
// Graph a circle with lots of dots. | |
// x^2+y^2=r^2 | |
// --> if r=3, then y=+-sqrt(3^2-x^2) | |
// for x in range(MIN_X, MAX_X, 0.1) | |
// y = sqrt(3^2 - x^2) | |
// setPixel x, y, lineColor, 3 | |
// y = -sqrt(3^2 - x^2) | |
// setPixel x, y, lineColor, 3 | |
// end for | |
// You can never quite get enough dots to make the ends look complete. | |
////////////////////////////////////////////////////////////////////////////////////////////////////////////// | |
// Graph a circle with lines. | |
// Looks a little better, but goes nuts at the endpoints. | |
// Even so, how to programmatically solve x^2+y^2=r^2 for y? | |
// for x0 in range(MIN_X, MAX_X, 0.1) | |
// x1 = x0 - 0.1 | |
// y0 = sqrt(3^2 - x0^2) | |
// y1 = sqrt(3^2 - x1^2) | |
// line x0, y0, x1, y1, lineColor, 3 | |
// y0 = -sqrt(3^2 - x0^2) | |
// y1 = -sqrt(3^2 - x1^2) | |
// line x0, y0, x1, y1, lineColor, 3 | |
// end for | |
////////////////////////////////////////////////////////////////////////////////////////////////////////////// | |
// And now, let's try marching squares on the little bugger. | |
GRID_RESOLUTION = 0.5 | |
sample = function(x, y) | |
r = 5 | |
dx = -3 | |
dy = 2 | |
return r^2 / ((x - dx)^2 + (y - dy)^2) | |
// return r^2 / (x^2 + cos(y)) | |
end function | |
lerp = function(x, x0, x1, y0 = 0, y1 = 1) | |
return y0 + ((y1 - y0) * (x - x0)) / (x1 - x0) | |
end function | |
c = color.green | |
for y in range(MIN_Y, MAX_Y, GRID_RESOLUTION) | |
for x in range(MIN_Y, MAX_Y, GRID_RESOLUTION) | |
bl = sample(x, y) | |
br = sample(x + GRID_RESOLUTION, y) | |
tl = sample(x, y + GRID_RESOLUTION) | |
tr = sample(x + GRID_RESOLUTION, y + GRID_RESOLUTION) | |
a = [ | |
x * GRID_RESOLUTION + GRID_RESOLUTION * lerp(1, tl, tr), | |
y * GRID_RESOLUTION + GRID_RESOLUTION, | |
] | |
b = [ | |
x * GRID_RESOLUTION + GRID_RESOLUTION, | |
y * GRID_RESOLUTION + GRID_RESOLUTION * lerp(1, br, tr), | |
] | |
c = [ | |
x * GRID_RESOLUTION + GRID_RESOLUTION * lerp(1, bl, br), | |
y * GRID_RESOLUTION, | |
] | |
d = [ | |
x * GRID_RESOLUTION, | |
y * GRID_RESOLUTION + GRID_RESOLUTION * lerp(1, bl, tl), | |
] | |
bl = bl >= 1 | |
br = br >= 1 | |
tl = tl >= 1 | |
tr = tr >= 1 | |
case = bl + br * 2 + tr * 4 + tl * 8 | |
if case == 0 or case == 15 then | |
continue | |
else if case == 1 or case == 14 then | |
line d[0], d[1], c[0], c[1], lineColor, penSize | |
else if case == 2 or case == 13 then | |
line b[0], b[1], c[0], c[1], lineColor, penSize | |
else if case == 3 or case == 12 then | |
line d[0], d[1], b[0], b[1], lineColor, penSize | |
else if case == 4 or case == 11 then | |
line a[0], a[1], b[0], b[1], lineColor, penSize | |
else if case == 5 then | |
line d[0], d[1], a[0], a[1], lineColor, penSize | |
line c[0], c[1], b[0], b[1], lineColor, penSize | |
else if case == 6 or case == 9 then | |
line c[0], c[1], a[0], a[1], lineColor, penSize | |
else if case == 7 or case == 8 then | |
line d[0], d[1], a[0], a[1], lineColor, penSize | |
else if case == 10 then | |
line a[0], a[1], b[0], b[1], lineColor, penSize | |
line c[0], c[1], d[0], d[1], lineColor, penSize | |
end if | |
end for | |
end for |
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