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added circle_circle_tangents

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Adrian Mariano 2020-05-23 17:25:46 -04:00
parent 4fc24ef939
commit 4eda2c701e
1 changed files with 64 additions and 0 deletions
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geometry.scad
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@ -1106,6 +1106,70 @@ function find_circle_tangents(r, d, cp, pt) =
// Function: circle_circle_tangents()
// Usage: circle_circle_tangents(c1, r1|d1, c2, r2|d2)
// Description:
// Computes lines tangents to a pair of circles. Returns a list of line endpoints [p1,p2] where
// p2 is the tangent point on circle 1 and p2 is the tangent point on circle 2.
// If four tangents exist then the first one the left hand exterior tangent as regarded looking from
// circle 1 toward circle 2. The second value is the right hand exterior tangent. The third entry
// gives the interior tangent that starts on the left of circle 1 and crosses to the right side of
// circle 2. And the fourth entry is the last interior tangent that starts on the right side of
// circle 1. If the circles intersect then the interior tangents don't exist and the function
// returns only two entries. If one circle is inside the other one then no tangents exist
// so the function returns the empty set. When the circles are tangent a degenerate tangent line
// passes through the point of tangency of the two circles: this degenerate line is NOT returned.
// Example(2D): Four tangents, first in green, second in black, third in blue, last in red.
// $fn=32;
// c1 = [3,4]; r1 = 2;
// c2 = [7,10]; r2 = 3;
// pts = circle_circle_tangents(c1,r1,c2,r2);
// stroke(move(c1,p=circle(r=r1)),width=.1,closed=true);
// stroke(move(c2,p=circle(r=r2)),width=.1,closed=true);
// colors = ["green","black","blue","red"];
// for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=.1);
// Example(2D): Circles overlap so only exterior tangents exist.
// $fn=32;
// c1 = [4,4]; r1 = 3;
// c2 = [7,7]; r2 = 2;
// pts = circle_circle_tangents(c1,r1,c2,r2);
// stroke(move(c1,p=circle(r=r1)),width=.1,closed=true);
// stroke(move(c2,p=circle(r=r2)),width=.1,closed=true);
// colors = ["green","black","blue","red"];
// for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=.1);
// Example(2D): Circles are tangent. Only exterior tangents are returned. The degenerate internal tangent is not returned.
// $fn=32;
// c1 = [4,4]; r1 = 4;
// c2 = [4,10]; r2 = 2;
// pts = circle_circle_tangents(c1,r1,c2,r2);
// stroke(move(c1,p=circle(r=r1)),width=.1,closed=true);
// stroke(move(c2,p=circle(r=r2)),width=.1,closed=true);
// colors = ["green","black","blue","red"];
// for(i=[0:1:len(pts)-1]) color(colors[i]) stroke(pts[i],width=.1);
// Example(2D): One circle is inside the other: no tangents exist. If the interior circle is tangent the single degenerate tangent will not be returned.
// $fn=32;
// c1 = [4,4]; r1 = 4;
// c2 = [5,5]; r2 = 2;
// pts = circle_circle_tangents(c1,r1,c2,r2);
// stroke(move(c1,p=circle(r=r1)),width=.1,closed=true);
// stroke(move(c2,p=circle(r=r2)),width=.1,closed=true);
// echo(pts); // Returns []
function circle_circle_tangents(c1,r1,c2,r2,d1,d2) =
let(
r1 = get_radius(r1=r1,d1=d1),
r2 = get_radius(r1=r2,d1=d2),
Rvals = [r2-r1, r2-r1, -r2-r1, -r2-r1]/norm(c1-c2),
kvals = [-1,1,-1,1],
ext = [1,1,-1,-1],
N = 1-sqr(Rvals[2])>=0 ? 4 :
1-sqr(Rvals[0])>=0 ? 2 : 0,
coef= [for(i=[0:1:N-1]) [[Rvals[i], -kvals[i]*sqrt(1-sqr(Rvals[i]))],
[kvals[i]*sqrt(1-sqr(Rvals[i])), Rvals[i]]]*unit(c2-c1)]
)
[for(i=[0:1:N-1]) let(pt=[c1-r1*coef[i], c2-ext[i]*r2*coef[i]]) if (pt[0]!=pt[1]) pt];
// Section: Pointlists
// Function: first_noncollinear()