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