Curve that touches three points: Difference between revisions
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Center : (105.0, 81.3)
Radius : 118.8
</pre>
=={{header|ALGOL 68}}==
{{Trans|Ada}}
As with the Ada and FreeBASIC translation of it, finds the centre and radius of a circle through the points.
<syntaxhighlight lang="algol68">
BEGIN # draw a curve that passes through 3 points - translated from the Ada #
# sample - finds the centre and radius of a circle through the points #
REAL x1 = 10; # Point P1 #
REAL y1 = 10;
REAL x2 = 100 # Point P2 #;
REAL y2 = 200;
REAL x3 = 200; # Point P3 #
REAL y3 = 10;
REAL x4 = ( x1 + x2 ) / 2; # Point P4 - midpoint between P1 and P2 #
REAL y4 = ( y1 + y2 ) / 2;
REAL s4 = ( y2 - y1 ) / ( x2 - x1 ); # Slope P1-P2 #
REAL a4 = -1 / s4; # Slope P4-Centre #
# Y4 = A4 * X4 + B4 <=> B4 = Y4 - A4 * X4 #
REAL b4 = y4 - a4 * x4;
REAL x5 = ( x2 + x3 ) / 2; # Point P5 - midpoint between P2 and P3 #
REAL y5 = ( y2 + y3 ) / 2;
REAL s5 = ( y3 - y2 ) / ( x3 - x2 ); # Slope P2-P3 #
REAL a5 = -1.0 / s5; # Slope P5-Centre #
# Y5 = A5 * X5 + B5 <=> B5 = Y5 - A5 * X5 #
REAL b5 = y5 - a5 * x5;
# Find centre #
# 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) #
REAL xc = ( b5 - b4 ) / ( a4 - a5 );
REAL yc = a4 * xc + b4;
# Radius #
REAL r = sqrt( ( x1 - xc ) ^ 2 + ( y1 - yc ) ^ 2 );
print( ( "Centre : (", fixed( xc, -6, 1 ), ", ", fixed( yc, -6, 1 ), " )", newline ) );
print( ( "Radius : ", fixed( r, -6, 1 ), newline ) )
END
</syntaxhighlight>
{{out}}
<pre>
Centre : ( 105.0, 81.3 )
Radius : 118.8
</pre>
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