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B-spline: Difference between revisions
Added Lua.
SqrtNegInf (talk | contribs) (Added Perl) |
(Added Lua.) |
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plt = plot(map(a -> a.x, controlpoints), map(a -> a.y, controlpoints))
savefig(plt, "BSplineplot.png")</lang>
=={{header|Lua}}==
{{trans|Wren}}
<lang Lua>local function Range(from, to)
local range = {}
for n = from, to do table.insert(range, n) end
return range
end
local function Bspline(controlPoints, k)
return {
controlPoints = controlPoints,
n = #controlPoints,
k = k,
t = Range(1, #controlPoints+k), -- Use a uniform knot vector, delta=1.
}
end
local function helper(bspline, i, k, x)
return (bspline.t[i+k] ~= bspline.t[i])
and (x - bspline.t[i]) / (bspline.t[i+k] - bspline.t[i])
or 0
end
local function calculateBspline(bspline, i, k, x)
if k == 1 then
return (bspline.t[i] <= x and x < bspline.t[i+1]) and 1 or 0
end
return ( helper(bspline, i , k-1, x)) * calculateBspline(bspline, i , k-1, x)
+ (1-helper(bspline, i+1, k-1, x)) * calculateBspline(bspline, i+1, k-1, x)
end
local function round(n)
return math.floor(n+.5)
end
local function getBsplinePoints(bspline)
local points = {}
for x = bspline.t[bspline.k], bspline.t[bspline.n+1]-1 do
local sumX = 0
local sumY = 0
for i = 1, bspline.n do
local f = calculateBspline(bspline, i, bspline.k, x)
sumX = sumX + f * bspline.controlPoints[i].x
sumY = sumY + f * bspline.controlPoints[i].y
end
table.insert(points, {x=round(sumX), y=round(sumY)})
end
return points
end
local function Plot(unscaledWidth,unscaledHeight, scaleX,scaleY)
local plot = {
width = round(unscaledWidth * scaleX),
height = round(unscaledHeight * scaleY),
scaleX = scaleX,
scaleY = scaleY,
}
for row = 1, plot.height do
plot[row] = {}
end
return plot
end
local function raytrace(x,y, x2,y2, visit)
local dx = math.abs(x2 - x)
local dy = math.abs(y2 - y)
local n = 1 + dx + dy
local dirX = (x2 > x) and 1 or -1
local dirY = (y2 > y) and 1 or -1
local err = dx - dy
dx, dy = 2*dx, 2*dy
for n = 1, n do
visit(x, y)
if err > 0 then x, err = x+dirX, err-dy
else y, err = y+dirY, err+dx end
end
end
local function plotLine(plot, x1,y1, x2,y2)
raytrace(x1,y1, x2,y2, function(x, y)
if x >= 0 and y >= 0 and x < plot.width and y < plot.height then
plot[y+1][x+1] = true
end
end)
end
local function plotBspline(bspline, plot)
if bspline.k > bspline.n or bspline.k < 1 then
error("k (= "..bspline.k..") can't be more than "..bspline.n.." or less than 1.")
end
local points = getBsplinePoints(bspline)
-- Plot the curve.
for i = 1, #points-1 do
local p1 = points[i]
local p2 = points[i+1]
plotLine(plot,
round(p1.x*plot.scaleX), round(p1.y*plot.scaleY),
round(p2.x*plot.scaleX), round(p2.y*plot.scaleY)
)
end
end
local function printPlot(plot)
for row = 1, plot.height do
for column = 1, plot.width do
io.write(plot[row][column] and "@" or " ")
end
io.write("\n")
end
end
local controlPoints = {
{x=171, y=171}, {x=185, y=111}, {x=202, y=109}, {x=202, y=189}, {x=328, y=160}, {x=208, y=254},
{x=241, y=330}, {x=164, y=252}, {x= 69, y=278}, {x=139, y=208}, {x= 72, y=148}, {x=168, y=172},
}
local k = 4 -- Polynomial degree is one less than this i.e. cubic.
local bspline = Bspline(controlPoints, k)
local scaleX = .4 -- Since we print the plot to the console as text let's scale things appropriately.
local scaleY = .2
local plot = Plot(350,350, scaleX,scaleY)
plotBspline(bspline, plot)
printPlot(plot)</lang>
{{out}}
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
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