Curve that touches three points: Difference between revisions
added RPL
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[100, 200.000000]
[200, 10.000000]</pre>
=={{header|F_Sharp|F#}}==
This task uses [[Lagrange_Interpolation#F#]]
<syntaxhighlight lang="fsharp">
// Curve that touches three points. Nigel Galloway: September 13th., 2023
open Plotly.NET
let points=let a=LIF([10;100;200],[10;200;10]).Expression in [10.0..200.0]|>List.map(fun n->(n,(Evaluate.evaluate (Map.ofList ["x",n]) a).RealValue))
Chart.Point(points)|>Chart.show
</syntaxhighlight>
{{out}}
[[File:C3p.png]]
=={{header|FreeBASIC}}==
{{trans|Ada}}
<syntaxhighlight lang="vb">' Point P1
Dim As Double X1 = 10.0
Dim As Double Y1 = 10.0
' Point P2
Dim As Double X2 = 100.0
Dim As Double Y2 = 200.0
' Point P3
Dim As Double X3 = 200.0
Dim As Double Y3 = 10.0
' Point P4 - midpoint between P1 and P2
Dim As Double X4 = (X1 + X2) / 2.0
Dim As Double Y4 = (Y1 + Y2) / 2.0
Dim As Double S4 = (Y2 - Y1) / (X2 - X1) ' Slope P1-P2
Dim As Double A4 = -1.0 / S4 ' Slope P4-Center
' Y4 = A4 * X4 + B4 <=> B4 = Y4 - A4 * X4
Dim As Double B4 = Y4 - A4 * X4
' Point P5 - midpoint between P2 and P3
Dim As Double X5 = (X2 + X3) / 2.0
Dim As Double Y5 = (Y2 + Y3) / 2.0
Dim As Double S5 = (Y3 - Y2) / (X3 - X2) ' Slope P2-P3
Dim As Double A5 = -1.0 / S5 ' Slope P5-Center
' Y5 = A5 * X5 + B5 <=> B5 = Y5 - A5 * X5
Dim As Double B5 = Y5 - A5 * X5
' Find center
' Y = A4 * X + B4 ' Line 1
' Y = A5 * X + B5 ' Line 2
' Solve for X:
' A4 * X + B4 = A5 * X + B5
' A4 * X - A5 * X = B5 - B4
' X * (A4 - A5) = B5 - B4
' X = (B5 - B4) / (A4 - A5)
Dim As Double Xc = (B5 - B4) / (A4 - A5)
Dim As Double Yc = A4 * Xc + B4
' Radius
Dim As Double R = Sqr((X1 - Xc) ^ 2 + (Y1 - Yc) ^ 2)
Print Using "Center : (###.#, ###.#)"; Xc; Yc
Print Using "Radius : ###.#"; R
Sleep</syntaxhighlight>
=={{header|Go}}==
Line 327 ⟶ 386:
=={{header|Julia}}==
To make things more specific,
<syntaxhighlight lang="julia">using
struct Point; x::Float64; y::Float64; end
Line 353 ⟶ 412:
x = a-r:0.25:a+r
y0 = sqrt.(r^2 .- (x .- a).^2)
scatter!(
</syntaxhighlight>{{out}}
<pre>
The circle with center at x = 105.0, y = 81.31578947368422 and radius 118.78948534384199.
</pre>
[[File:Circle3points.png]]
=={{header|Lambdatalk}}==
Line 1,340 ⟶ 1,400:
=={{header|Perl}}==
[[File:Curve-3-points-perl.svg|300px|thumb|right]]
Hilbert '''curve''' task code repeated here, with the addition that the 3 task-required points are marked. Satisfies the letter-of-the-law of task specification while (all in good fun) subverting the spirit of the thing.
<syntaxhighlight lang="perl">use SVG;
use List::Util qw(max min);
Line 1,385 ⟶ 1,446:
print $fh $svg->xmlify(-namespace=>'svg');
close $fh;</syntaxhighlight>
=={{header|Phix}}==
Line 1,572 ⟶ 1,632:
}</syntaxhighlight>
See [https://github.com/thundergnat/rc/blob/master/img/Curve-3-points-perl6.png Curve-3-points-perl6.png] (offsite .png image)
=={{header|RPL}}==
HP-49+ RPL has a built-in function named <code>LAGRANGE</code> that returns the curve equation from the 3 points, but let's consider it as belonging to a library.
{{works with|HP|48G}}
[[File:Parabol.png|thumb|right|alt=HP-48G emulator screenshot|HP-48G emulator screenshot]]
« → a b c
« { 0 0 0 }
c a - C→R SWAP / c b - RE /
b a - C→R SWAP / c b - RE / -
1 SWAP PUT
b a - C→R SWAP / OVER 1 GET b a + RE * -
2 SWAP PUT
a IM OVER 1 GET a RE SQ * - OVER 2 GET a RE * -
3 SWAP PUT
{ 'X^2' 'X' 1 } * ∑LIST
» » '<span style="color:blue">PAREQ</span>' STO
« # 131d # 64d PDIM 0 210 DUP2 XRNG YRNG
FUNCTION
(10,10) (100,200) (200,10)
3 DUPN <span style="color:blue">PAREQ</span> STEQ
ERASE DRAW
1 3 '''START''' PIXOFF '''NEXT''' <span style="color:grey">''@ switch off the 3 points on the curve''</span>
{ } PVIEW
{ PPAR EQ } PURGE
» '<span style="color:blue">TASK</span>' STO
=={{header|Wren}}==
{{trans|Go}}
{{libheader|DOME}}
<syntaxhighlight lang="
import "dome" for Window
Line 1,622 ⟶ 1,708:
}
}</syntaxhighlight>
=={{header|XPL0}}==
[[File:XPL0_Curve.gif|200px|thumb|right]]
<syntaxhighlight lang "XPL0">def X0=10., Y0=10., X1=100., Y1=200., X2=200., Y2=10.;
func real Lagrange(X);
real X;
return (X-X1) * (X-X2) / (X0-X1) / (X0-X2) * Y0 +
(X-X0) * (X-X2) / (X1-X0) / (X1-X2) * Y1 +
(X-X0) * (X-X1) / (X2-X0) / (X2-X1) * Y2;
def Offset = 205;
real X;
[SetVid($13); \VGA 320x200x8 graphics
X:= X0;
Move(fix(X), Offset-fix(Y0));
repeat X:= X + 1.;
Line(fix(X), Offset-fix(Lagrange(X)), 3\cyan\);
until X >= X2;
Point(fix(X0), Offset-fix(Y0), 14\yellow\);
Point(fix(X1), Offset-fix(Y1), 14);
Point(fix(X2), Offset-fix(Y2), 14);
]</syntaxhighlight>
=={{header|zkl}}==
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