Bernstein basis polynomials: Difference between revisions
Added Wren
m (Clarify what sort of polynomial we care can be cast into Bernstein form.) |
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bern (1, 1.0, 1) --> bern (1, 1.0, 1.0, 1)
bern (1, 2.0, 6) --> bern (1, 1.6666666666666665, 3.333333333333333, 6)</pre>
=={{header|Wren}}==
{{trans|Algol 60}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascript">import "./fmt" for Fmt
var toBern2 = Fn.new { |a| [a[0], a[0] + a[1] / 2, a[0] + a[1] + a[2]] }
// uses de Casteljau's algorithm
var evalBern2 = Fn.new { |b, t|
var s = 1 - t
var b01 = s * b[0] + t * b[1]
var b12 = s * b[1] + t * b[2]
return s * b01 + t * b12
}
var toBern3 = Fn.new { |a|
var b = List.filled(4, 0)
b[0] = a[0]
b[1] = a[0] + a[1] / 3
b[2] = a[0] + a[1] * 2/3 + a[2] / 3
b[3] = a[0] + a[1] + a[2] + a[3]
return b
}
// uses de Casteljau's algorithm
var evalBern3 = Fn.new { |b, t|
var s = 1 - t
var b01 = s * b[0] + t * b[1]
var b12 = s * b[1] + t * b[2]
var b23 = s * b[2] + t * b[3]
var b012 = s * b01 + t * b12
var b123 = s * b12 + t * b23
return s * b012 + t * b123
}
var bern2to3 = Fn.new { |q|
var c = List.filled(4, 0)
c[0] = q[0]
c[1] = q[0] / 3 + q[1] * 2/3
c[2] = q[1] * 2/3 + q[2] / 3
c[3] = q[2]
return c
}
var pm = [1, 0, 0]
var qm = [1, 2, 3]
var rm = [1, 2, 3, 4]
var x
var y
System.print("Subprogram(1) examples:")
var pb2 = toBern2.call(pm)
var qb2 = toBern2.call(qm)
Fmt.print("mono$n --> bern$n", pm, pb2)
Fmt.print("mono$n --> bern$n", qm, qb2)
System.print("\nSubprogram(2) examples:")
x = 0.25
y = evalBern2.call(pb2, x)
Fmt.print("p($4.2f) = $j", x, y)
x = 7.5
y = evalBern2.call(pb2, x)
Fmt.print("p($4.2f) = $j", x, y)
x = 0.25
y = evalBern2.call(qb2, x)
Fmt.print("q($4.2f) = $j", x, y)
x = 7.5
y = evalBern2.call(qb2, x)
Fmt.print("q($4.2f) = $j", x, y)
System.print("\nSubprogram(3) examples:")
pm.add(0)
qm.add(0)
var pb3 = toBern3.call(pm)
var qb3 = toBern3.call(qm)
var rb3 = toBern3.call(rm)
Fmt.print("mono$n --> bern$n", pm, pb3)
Fmt.print("mono$n --> bern$n", qm, qb3)
Fmt.print("mono$n --> bern$n", rm, rb3)
System.print("\nSubprogram(4) examples:")
x = 0.25
y = evalBern3.call(pb3, x)
Fmt.print("p($4.2f) = $j", x, y)
x = 7.5
y = evalBern3.call(pb3, x)
Fmt.print("p($4.2f) = $j", x, y)
x = 0.25
y = evalBern3.call(qb3, x)
Fmt.print("q($4.2f) = $j", x, y)
x = 7.5
y = evalBern3.call(qb3, x)
Fmt.print("q($4.2f) = $j", x, y)
x = 0.25
y = evalBern3.call(rb3, x)
Fmt.print("r($4.2f) = $j", x, y)
x = 7.5
y = evalBern3.call(rb3, x)
Fmt.print("r($4.2f) = $j", x, y)
System.print("\nSubprogram(5) examples:")
var pc = bern2to3.call(pb2)
var qc = bern2to3.call(qb2)
Fmt.print("mono$n --> bern$n", pb2, pc)
Fmt.print("mono$n --> bern$n", qb2, qc)</syntaxhighlight>
{{out}}
<pre>
Subprogram(1) examples:
mono[1, 0, 0] --> bern[1, 1, 1]
mono[1, 2, 3] --> bern[1, 2, 6]
Subprogram(2) examples:
p(0.25) = 1
p(7.50) = 1
q(0.25) = 1.6875
q(7.50) = 184.75
Subprogram(3) examples:
mono[1, 0, 0, 0] --> bern[1, 1, 1, 1]
mono[1, 2, 3, 0] --> bern[1, 1.6666666666667, 3.3333333333333, 6]
mono[1, 2, 3, 4] --> bern[1, 1.6666666666667, 3.3333333333333, 10]
Subprogram(4) examples:
p(0.25) = 1
p(7.50) = 1
q(0.25) = 1.6875
q(7.50) = 184.75
r(0.25) = 1.75
r(7.50) = 1872.25
Subprogram(5) examples:
mono[1, 1, 1] --> bern[1, 1, 1, 1]
mono[1, 2, 6] --> bern[1, 1.6666666666667, 3.3333333333333, 6]
</pre>
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