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Line circle intersection: Difference between revisions
→{{header|REXX}}: added the REXX computer programming language for this task.
SqrtNegInf (talk | contribs) m (→{{header|Raku}}: Fix code: Perl 6 --> Raku) |
(→{{header|REXX}}: added the REXX computer programming language for this task.) |
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For data set: [(5 2 −2.26) (0.77 2 4) (1 4 0) 4]
Solution(s) is/are: [(4.2615520237084015 2 -1.1671668246843006) (1.13386504516801 2 3.461514141193441)]
</pre>
=={{header|REXX}}==
The formulae used for this REXX version were taken from the MathWorld
webpage: [https://mathworld.wolfram.com/Circle-LineIntersection.html circle line intersection].
<lang rexx>/*REXX program calculates where (or if) a line intersects (or tengents) a cirle. */
/*───────────────────────────────────── line= x1,y1 x2,y2; circle is at 0,0, radius=r*/
parse arg x1 y1 x2 y2 cx cy r . /*obtain optional arguments from the CL*/
if x1=='' | x1=="," then x1= 0 /*Not specified? Then use the default.*/
if y1=='' | y1=="," then y1= -3 /* " " " " " " */
if x2=='' | x2=="," then x2= 0 /* " " " " " " */
if y2=='' | y2=="," then y2= 6 /* " " " " " " */
if cx=='' | cx=="," then cx= 0 /* " " " " " " */
if cy=='' | cy=="," then cy= 0 /* " " " " " " */
if r =='' | r =="," then r = 4 /* " " " " " " */
x_1= x1; x1= x1 + cx
x_2= x2; x2= x2 + cx
y_1= y1; y1= y1 + cy
y_2= y2; y2= y2 + cy
dx= x2 - x1; dy= y2 - y1
dr= sqrt(dx**2 + dy**2)
D= x1 * y2 - x2 * y1
ix1= ( D * dy + sgn(dy) * dx * sqrt(r**2 * dr**2 - D**2) ) / dr**2
ix2= ( D * dy - sgn(dy) * dx * sqrt(r**2 * dr**2 - D**2) ) / dr**2
iy1= (-D * dx + abs(dy) * sqrt(r**2 * dr**2 - D**2) ) / dr**2
iy2= (-D * dx - abs(dy) * sqrt(r**2 * dr**2 - D**2) ) / dr**2
incidence= (r**2 * dr**2 - D**2) / 1
say 'incidence=' incidence
@potla= 'points on the line are: '
if incidence<0 then do
say @potla ' ('||x_1","y_1') and ('||x_2","y_2') are: ' ix1","iy1
say "The line doesn't intersect the circle with radius: " r
end
if incidence=0 then do
say @potla ' ('||x_1","y_1') and ('||x_2","y_2') are: ' ix1","iy1
say "The line is tangent to circle with radius: " r
end
if incidence>0 then do
say @potla ' ('||x_1","y_1') and ('||x_2","y_2') are: ' ix1","iy1
say "The line is secant to circle with radius: " r
end
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
sgn: procedure; if arg(1)<0 then return -1; return 1
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; h=d+6
numeric form; m.=9; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g=g *.5'e'_ %2
do j=0 while h>9; m.j= h; h= h%2 + 1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g= (g+x/g) *.5; end /*k*/
numeric digits d; return g/1</lang>
{{out|output|text= when using the default inputs:}}
<pre>
incidence= 1296
points on the line are: (0,-3) and (0,6) are: 0,4
The line is secant to circle with radius: 4
</pre>
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