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Added find_circle_3points()

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Revar Desmera 2019-07-15 16:41:01 -07:00
parent c5a2197e3c
commit 958786daf6
1 changed files with 45 additions and 0 deletions
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45
geometry.scad
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@ -207,6 +207,51 @@ function find_circle_2tangents(pt1, pt2, pt3, r=undef, d=undef) =
) [cp, n];
// Function: find_circle_3points()
// Usage:
// find_circle_3points(pt1, pt2, pt3);
// Description:
// Returns the [CENTERPOINT, RADIUS, NORMAL] of the circle that passes through three non-collinear
// points. The centerpoint will be a 2D or 3D vector, depending on the points input. If all three
// points are 2D, then the resulting centerpoint will be 2D, and the normal will be UP ([0,0,1]).
// If any of the points are 3D, then the resulting centerpoint will be 3D. If the three points are
// collinear, then `[undef,undef,undef]` will be returned. The normal will be a normalized 3D
// vector with a non-negative Z axis.
// Arguments:
// pt1 = The first point.
// pt2 = The second point.
// pt3 = The third point.
function find_circle_3points(pt1, pt2, pt3) =
collinear(pt1,pt2,pt3)? [undef,undef,undef] :
let(
v1 = pt1-pt2,
v2 = pt3-pt2,
n = vector_axis(v1,v2),
n2 = n.z<0? -n : n
) len(pt1)+len(pt2)+len(pt3)>6? (
let(
a = project_plane(pt1, pt1, pt2, pt3),
b = project_plane(pt2, pt1, pt2, pt3),
c = project_plane(pt3, pt1, pt2, pt3),
res = find_circle_3points(a, b, c)
) res[0]==undef? [undef,undef,undef] : let(
cp = lift_plane(res[0], pt1, pt2, pt3),
r = norm(p2-cp)
) [cp, r, n2]
) : let(
mp1 = pt2 + v1/2,
mp2 = pt2 + v2/2,
mpv1 = rot(90, v=n, p=v1),
mpv2 = rot(90, v=n, p=v2),
l1 = [mp1, mp1+mpv1],
l2 = [mp2, mp2+mpv2],
isect = line_intersection(l1,l2)
) is_undef(isect)? [undef,undef,undef] : let(
r = norm(p2-isect)
) [isect, r, n2];
// Function: triangle_area()
// Usage:
// triangle_area(a,b,c);