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Bezier Curve in JS, includes arc-length parameterization stuff
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function Bezier(a, b, c, d) { | |
this.a = a; | |
this.b = b; | |
this.c = c; | |
this.d = d; | |
this.len = 100; | |
this.arcLengths = new Array(this.len + 1); | |
this.arcLengths[0] = 0; | |
var ox = this.x(0), oy = this.y(0), clen = 0; | |
for(var i = 1; i <= this.len; i += 1) { | |
var x = this.x(i * 0.01), y = this.y(i * 0.01); | |
var dx = ox - x, dy = oy - y; | |
clen += Math.sqrt(dx * dx + dy * dy); | |
this.arcLengths[i] = clen; | |
ox = x, oy = y; | |
} | |
this.length = clen; | |
} | |
Bezier.prototype = { | |
map: function(u) { | |
var targetLength = u * this.arcLengths[this.len]; | |
var low = 0, high = this.len, index = 0; | |
while (low < high) { | |
index = low + (((high - low) / 2) | 0); | |
if (this.arcLengths[index] < targetLength) { | |
low = index + 1; | |
} else { | |
high = index; | |
} | |
} | |
if (this.arcLengths[index] > targetLength) { | |
index--; | |
} | |
var lengthBefore = this.arcLengths[index]; | |
if (lengthBefore === targetLength) { | |
return index / this.len; | |
} else { | |
return (index + (targetLength - lengthBefore) / (this.arcLengths[index + 1] - lengthBefore)) / this.len; | |
} | |
}, | |
mx: function (u) { | |
return this.x(this.map(u)); | |
}, | |
my: function (u) { | |
return this.y(this.map(u)); | |
}, | |
x: function (t) { | |
return ((1 - t) * (1 - t) * (1 - t)) * this.a.x | |
+ 3 * ((1 - t) * (1 - t)) * t * this.b.x | |
+ 3 * (1 - t) * (t * t) * this.c.x | |
+ (t * t * t) * this.d.x; | |
}, | |
y: function (t) { | |
return ((1 - t) * (1 - t) * (1 - t)) * this.a.y | |
+ 3 * ((1 - t) * (1 - t)) * t * this.b.y | |
+ 3 * (1 - t) * (t * t) * this.c.y | |
+ (t * t * t) * this.d.y; | |
} | |
}; |
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