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Added find_circle_tangents()

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Revar Desmera 2019-10-21 18:59:35 -07:00
parent bee132d175
commit c0a131549f
1 changed files with 41 additions and 5 deletions
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46
geometry.scad
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@ -315,6 +315,42 @@ function find_circle_3points(pt1, pt2, pt3) =
// Function: find_circle_tangents()
// Usage:
// tangents = find_circle_tangents(r|d, cp, pt);
// Description:
// Given a circle and a point outside that circle, finds the tangent point(s) on the circle for a
// line passing through the point. Returns list of zero or more sublists of [ANG, TANGPT]
// Arguments:
// r = Radius of the circle.
// d = Diameter of the circle.
// cp = The coordinates of the circle centerpoint.
// pt = The coordinates of the external point.
// Example(2D):
// cp = [-10,-10]; r = 30; pt = [30,10];
// tanpts = subindex(find_circle_tangents(r=r, cp=cp, pt=pt),1);
// color("yellow") translate(cp) circle(r=r);
// color("cyan") for(tp=tanpts) {stroke([tp,pt]); stroke([tp,cp]);}
// color("red") place_copies(tanpts) circle(d=3,$fn=12);
// color("blue") place_copies([cp,pt]) circle(d=3,$fn=12);
function find_circle_tangents(r, d, cp, pt) =
assert(is_num(r) || is_num(d))
assert(is_vector(cp))
assert(is_vector(pt))
let(
r = get_radius(r=r, d=d, dflt=1),
delta = pt - cp,
dist = norm(delta),
baseang = atan2(delta.y,delta.x)
) dist < r? [] :
approx(dist,r)? [[baseang, pt]] :
let(
relang = acos(r/dist),
angs = [baseang + relang, baseang - relang]
) [for (ang=angs) [ang, cp + r*[cos(ang),sin(ang)]]];
// Function: tri_calc()
// Usage:
// tri_calc(ang,ang2,adj,opp,hyp);
@ -421,7 +457,7 @@ function plane3pt(p1, p2, p3) =
// Usage:
// plane3pt_indexed(points, i1, i2, i3);
// Description:
// Given a list of points, and the indexes of three of those points,
// Given a list of points, and the indices of three of those points,
// generates the cartesian equation of a plane that those points all
// lie on. Requires that the three indexed points be non-collinear.
// Returns [A,B,C,D] where Ax+By+Cz+D=0 is the equation of a plane.
@ -442,7 +478,7 @@ function plane3pt_indexed(points, i1, i2, i3) =
// Usage:
// plane_from_pointslist(points);
// Description:
// Given a list of coplanar points, returns the cartesian equation of a plane.
// Given a list of 3 or more coplanar points, returns the cartesian equation of a plane.
// Returns [A,B,C,D] where Ax+By+Cz+D=0 is the equation of the plane.
function plane_from_pointslist(points) =
let(
@ -731,7 +767,7 @@ function first_noncollinear(i1, i2, points, _i) =
// Usage:
// find_noncollinear_points(points);
// Description:
// Finds the indexes of three good points in the points list `points` that are not collinear.
// Finds the indices of three good non-collinear points from the points list `points`.
function find_noncollinear_points(points) =
let(
a = 0,
@ -893,13 +929,13 @@ function simplify_path(path, eps=EPSILON) =
// Function: simplify_path_indexed()
// Description:
// Takes a list of points, and a path as a list of indexes into `points`,
// Takes a list of points, and a path as a list of indices into `points`,
// and removes all path points that are unecessarily collinear.
// Usage:
// simplify_path_indexed(path, eps)
// Arguments:
// points = A list of points.
// path = A list of indexes into `points` that forms a path.
// path = A list of indices into `points` that forms a path.
// eps = Largest angle variance allowed. Default: EPSILON (1-e9) degrees.
function simplify_path_indexed(points, path, eps=EPSILON) =
len(path)<=2? path : let(