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Enhanced find_circle_2tangents()

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Revar Desmera 2020-04-18 18:38:22 -07:00
parent 7ebb83a81d
commit 1c06298f10
2 changed files with 31 additions and 14 deletions
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43
geometry.scad
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@ -875,17 +875,27 @@ function in_front_of_plane(plane, point) =
// Function: find_circle_2tangents()
// Usage:
// find_circle_2tangents(pt1, pt2, pt3, r|d);
// find_circle_2tangents(pt1, pt2, pt3, r|d, [tangents]);
// Description:
// Returns [centerpoint, normal] of a circle of known size that is between and tangent to two rays with the same starting point.
// Both rays start at `pt2`, and one passes through `pt1`, while the other passes through `pt3`.
// If the rays given are 180º apart, `undef` is returned. If the rays are 3D, the normal returned is the plane normal of the circle.
// Given a pair of rays with a common origin, and a known circle radius/diameter, finds
// the centerpoint for the circle of that size that touches both rays tangentally.
// Both rays start at `pt2`, one passing through `pt1`, and the other through `pt3`.
// If the rays given are collinear, `undef` is returned. Otherwise, if `tangents` is
// true, then `[CP,NORMAL]` is returned. If `tangents` is false, the more extended
// `[CP,NORMAL,TANPT1,TANPT2,ANG1,ANG2]` is returned
// - CP is the centerpoint of the circle.
// - NORMAL is the normal vector of the plane that the circle is on (UP or DOWN if the points are 2D).
// - TANPT1 is the point where the circle is tangent to the ray `[pt2,pt1]`.
// - TANPT2 is the point where the circle is tangent to the ray `[pt2,pt3]`.
// - ANG1 is the angle from the ray `[CP,pt2]` to the ray `[CP,TANPT1]`
// - ANG2 is the angle from the ray `[CP,pt2]` to the ray `[CP,TANPT2]`
// Arguments:
// pt1 = A point that the first ray passes though.
// pt2 = The starting point of both rays.
// pt3 = A point that the second ray passes though.
// r = The radius of the circle to find.
// d = The diameter of the circle to find.
// tangents = If true, extended information about the tangent points is calculated and returned. Default: false
// Example(2D):
// pts = [[60,40], [10,10], [65,5]];
// rad = 10;
@ -902,21 +912,28 @@ function in_front_of_plane(plane, point) =
// translate(circ[0]) color("red") circle(d=2, $fn=12);
// labels = [[pts[0], "pt1"], [pts[1],"pt2"], [pts[2],"pt3"], [circ[0], "CP"], [circ[0]+[cos(315),sin(315)]*rad*0.7, "r"]];
// for(l=labels) translate(l[0]+[0,2]) color("black") text(text=l[1], size=2.5, halign="center");
function find_circle_2tangents(pt1, pt2, pt3, r=undef, d=undef) =
function find_circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
let(r = get_radius(r=r, d=d, dflt=undef))
assert(r!=undef, "Must specify either r or d.")
(is_undef(pt2) && is_undef(pt3) && is_list(pt1))? find_circle_2tangents(pt1[0], pt1[1], pt1[2], r=r) :
collinear(pt1, pt2, pt3)? undef :
let(
v1 = unit(pt1 - pt2),
v2 = unit(pt3 - pt2)
) approx(norm(v1+v2))? undef :
v2 = unit(pt3 - pt2),
vmid = unit(mean([v1, v2])),
n = vector_axis(v1, v2),
a = vector_angle(v1, v2),
hyp = r / sin(a/2),
cp = pt2 + hyp * vmid
) !tangents? [cp, n] :
let(
a = vector_angle(v1,v2),
n = vector_axis(v1,v2),
v = unit(mean([v1,v2])),
s = r/sin(a/2),
cp = pt2 + s*v/norm(v)
) [cp, n];
x = hyp * cos(a/2),
tp1 = pt2 + x * v1,
tp2 = pt2 + x * v2,
fff=echo(tp1=tp1,cp=cp,pt2=pt2),
dang1 = vector_angle(tp1-cp,pt2-cp),
dang2 = vector_angle(tp2-cp,pt2-cp)
) [cp, n, tp1, tp2, dang1, dang2];
// Function: find_circle_3points()

2
version.scad
View file

@ -8,7 +8,7 @@
//////////////////////////////////////////////////////////////////////
BOSL_VERSION = [2,0,269];
BOSL_VERSION = [2,0,270];
// Section: BOSL Library Version Functions