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Fixed interior_fillet(). Refactored circle_* functions.
This commit is contained in:
Garth Minette
193
geometry.scad
193
geometry.scad
@@ -861,14 +861,14 @@ function _is_point_above_plane(plane, point) =
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// Function: circle_line_intersection()
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// Usage:
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// isect = circle_line_intersection(c, r|d=, line, [bounded], [eps=]);
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// pts = circle_line_intersection(r|d=, cp, line, [bounded], [eps=]);
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// Topics: Geometry, Circles, Lines, Intersection
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// Description:
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// Find intersection points between a 2d circle and a line, ray or segment specified by two points.
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// Find intersection points between a 2D circle and a line, ray or segment specified by two points.
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// By default the line is unbounded. Returns the list of zero or more intersection points.
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// Arguments:
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// c = Center of circle
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// r = Radius of circle
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// cp = Center of circle
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// line = Two points defining the line
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// bounded = False for unbounded line, true for a segment, or a vector [false,true] or [true,false] to specify a ray with the first or second end unbounded. Default: false
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// ---
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@@ -879,14 +879,14 @@ function _is_point_above_plane(plane, point) =
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// cp = [1,2]; r = 10;
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// translate(cp) circle(r=r);
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// color("black") stroke(line, endcaps="arrow2", width=0.5);
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// isects = circle_line_intersection(c=cp, r=r, line=line);
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// isects = circle_line_intersection(r=r, cp=cp, line=line);
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// color("red") move_copies(isects) circle(d=1);
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// Example(2D): Tangent intersection returns one point.
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// line = [[-10,12], [10,12]];
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// cp = [1,2]; r = 10;
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// translate(cp) circle(r=r);
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// color("black") stroke(line, endcaps="arrow2", width=0.5);
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// isects = circle_line_intersection(c=cp, r=r, line=line);
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// isects = circle_line_intersection(r=r, cp=cp, line=line);
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// color("#f44") move_copies(isects) circle(d=1);
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// Example(2D): A bounded ray might only intersect in one direction.
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// line = [[-5,2], [5,7]];
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@@ -895,30 +895,30 @@ function _is_point_above_plane(plane, point) =
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// translate(cp) circle(r=r);
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// color("gray") dashed_stroke(extended, width=0.2);
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// color("black") stroke(line, endcap2="arrow2", width=0.5);
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// isects = circle_line_intersection(c=cp, r=r, line=line, bounded=[true,false]);
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// isects = circle_line_intersection(r=r, cp=cp, line=line, bounded=[true,false]);
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// color("#f44") move_copies(isects) circle(d=1);
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// Example(2D): If they don't intersect at all, then an empty list is returned.
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// line = [[-12,12], [12,8]];
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// cp = [-5,-2]; r = 10;
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// translate(cp) circle(r=r);
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// color("black") stroke(line, endcaps="arrow2", width=0.5);
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// isects = circle_line_intersection(c=cp, r=r, line=line);
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// isects = circle_line_intersection(r=r, cp=cp, line=line);
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// color("#f44") move_copies(isects) circle(d=1);
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function circle_line_intersection(c,r,line,bounded=false,d,eps=EPSILON) =
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function circle_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
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assert(_valid_line(line,2), "Invalid 2d line.")
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assert(is_vector(c,2), "Circle center must be a 2-vector")
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_circle_or_sphere_line_intersection(c,r,line,bounded,d,eps);
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assert(is_vector(cp,2), "Circle center must be a 2-vector")
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_circle_or_sphere_line_intersection(r, cp, line, bounded, d, eps);
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function _circle_or_sphere_line_intersection(c,r,line,bounded=false,d,eps=EPSILON) =
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function _circle_or_sphere_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
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let(r=get_radius(r=r,d=d,dflt=undef))
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assert(is_num(r) && r>0, "Radius must be positive")
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assert(is_bool(bounded) || is_bool_list(bounded,2), "Invalid bound condition")
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let(
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bounded = force_list(bounded,2),
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closest = line_closest_point(line,c),
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d = norm(closest-c)
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closest = line_closest_point(line,cp),
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d = norm(closest-cp)
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)
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d > r ? [] :
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let(
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@@ -934,73 +934,74 @@ function _circle_or_sphere_line_intersection(c,r,line,bounded=false,d,eps=EPSILO
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// Function: circle_circle_intersection()
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// Usage:
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// pts = circle_circle_tangents(c1, r1|d1=, c2, r2|d2=, [eps]);
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// pts = circle_circle_intersection(r1|d1=, cp1, r2|d2=, cp2, [eps]);
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// Topics: Geometry, Circles
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// Description:
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// Compute the intersection points of two circles. Returns a list of the intersection points, which
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// will contain two points in the general case, one point for tangent circles, or will be empty
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// if the circles do not intersect.
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// Arguments:
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// c1 = Center of the first circle.
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// r1 = Radius of the first circle.
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// c2 = Center of the second circle.
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// cp1 = Centerpoint of the first circle.
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// r2 = Radius of the second circle.
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// cp2 = Centerpoint of the second circle.
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// eps = Tolerance for detecting tangent circles. Default: EPSILON
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// ---
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// d1 = Diameter of the first circle.
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// d2 = Diameter of the second circle.
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// Example(2D,NoAxes): Circles intersect in two points.
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// $fn=32;
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// c1 = [4,4]; r1 = 3;
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// c2 = [7,7]; r2 = 2;
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// pts = circle_circle_intersection(c1,r1,c2,r2);
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// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red")move_copies(pts) circle(r=.3);
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// cp1 = [4,4]; r1 = 3;
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// cp2 = [7,7]; r2 = 2;
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// pts = circle_circle_intersection(r1, cp1, r2, cp2);
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// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red") move_copies(pts) circle(r=.3);
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// Example(2D,NoAxes): Circles are tangent, so one intersection point:
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// $fn=32;
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// c1 = [4,4]; r1 = 4;
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// c2 = [4,10]; r2 = 2;
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// pts = circle_circle_intersection(c1,r1,c2,r2);
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// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red")move_copies(pts) circle(r=.3);
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// cp1 = [4,4]; r1 = 4;
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// cp2 = [4,10]; r2 = 2;
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// pts = circle_circle_intersection(r1, cp1, r2, cp2);
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// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red") move_copies(pts) circle(r=.3);
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// Example(2D,NoAxes): Another tangent example:
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// $fn=32;
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// c1 = [4,4]; r1 = 4;
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// c2 = [5,5]; r2 = 4-sqrt(2);
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// pts = circle_circle_intersection(c1,r1,c2,r2);
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// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red")move_copies(pts) circle(r=.3);
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// cp1 = [4,4]; r1 = 4;
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// cp2 = [5,5]; r2 = 4-sqrt(2);
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// pts = circle_circle_intersection(r1, cp1, r2, cp2);
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// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red") move_copies(pts) circle(r=.3);
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// Example(2D,NoAxes): Circles do not intersect. Returns empty list.
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// $fn=32;
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// c1 = [3,4]; r1 = 2;
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// c2 = [7,10]; r2 = 3;
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// pts = circle_circle_intersection(c1,r1,c2,r2);
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// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red")move_copies(pts) circle(r=.2); // pts is []
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function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
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assert( is_path([c1,c2],dim=2), "Invalid center point(s)." )
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// cp1 = [3,4]; r1 = 2;
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// cp2 = [7,10]; r2 = 3;
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// pts = circle_circle_intersection(r1, cp1, r2, cp2);
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// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
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// color("red") move_copies(pts) circle(r=.3);
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function circle_circle_intersection(r1, cp1, r2, cp2, eps=EPSILON, d1, d2) =
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assert( is_path([cp1,cp2],dim=2), "Invalid center point(s)." )
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let(
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r1 = get_radius(r1=r1,d1=d1),
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r2 = get_radius(r1=r2,d1=d2),
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d = norm(c2-c1),
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a = (c2-c1)/d,
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d = norm(cp2-cp1),
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a = (cp2-cp1)/d,
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b = [-a.y,a.x],
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L = (r1^2-r2^2+d^2)/2/d,
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hsqr = r1^2-L^2
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)
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approx(hsqr,0,eps) ? [L*a+c1]
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approx(hsqr,0,eps) ? [L*a+cp1]
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: hsqr<0 ? []
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: let(h=sqrt(hsqr))
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[L*a+h*b+c1, L*a-h*b+c1];
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[L*a+h*b+cp1, L*a-h*b+cp1];
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// Function: circle_2tangents()
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// Usage:
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// circ = circle_2tangents(pt1, pt2, pt3, r|d=, [tangents=]);
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// circ = circle_2tangents(r|d=, pt1, pt2, pt3, [tangents=]);
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// circ = circle_2tangents(r|d=, [PT1, PT2, PT3], [tangents=]);
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// Topics: Geometry, Circles, Tangents
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// Description:
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// Given a pair of rays with a common origin, and a known circle radius/diameter, finds
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@@ -1017,7 +1018,7 @@ function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
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// Figure(3D,Med,NoAxes,VPD=130,VPT=[29,19,3],VPR=[55,0,25]):
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// pts = [[45,10,-5], [10,5,10], [15,40,5]];
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// rad = 15;
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// circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad, tangents=true);
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// circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2], tangents=true);
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// cp = circ[0]; n = circ[1]; tp1 = circ[2]; tp2 = circ[3];
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// color("yellow") stroke(pts, endcaps="arrow2");
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// color("purple") move_copies([cp,tp1,tp2]) sphere(d=2, $fn=12);
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@@ -1034,32 +1035,32 @@ function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
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// ["TanPt2", "brown", 2.0, [-5, 0, 2], tp2],
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// ];
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// for(l=labels)
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// color(l[1]) move(l[4]+l[3]) rot($vpr)
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// color(l[1]) move(l[4]+l[3]) rot([55,0,25])
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// linear_extrude(height=0.1)
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// text(text=l[0], size=l[2], halign="center", valign="center");
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// color("green",0.5) move(cp) cyl(h=0.1, r=rad, orient=n, $fn=36);
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// Arguments:
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// r = The radius of the circle to find.
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// pt1 = A point that the first ray passes though.
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// pt2 = The starting point of both rays.
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// pt3 = A point that the second ray passes though.
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// r = The radius of the circle to find.
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// ---
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// d = The diameter of the circle to find.
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// tangents = If true, extended information about the tangent points is calculated and returned. Default: false
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// Example(2D):
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// pts = [[40,40], [10,10], [55,5]]; rad = 10;
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// circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
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// circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2]);
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// stroke(pts, endcaps="arrow2");
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// color("red") move(circ[0]) circle(r=rad);
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// Example(2D):
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// pts = [[20,40], [10,10], [55,20]]; rad = 10;
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// circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad, tangents=true);
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// circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2], tangents=true);
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// stroke(pts, endcaps="arrow2");
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// color("red") move(circ[0]) circle(r=rad);
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// color("blue") move_copies(select(circ,2,3)) circle(d=2);
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// Example(3D): Fit into 3D path corner.
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// pts = [[45,5,10], [10,10,15], [30,40,30]]; rad = 10;
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// circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
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// circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2]);
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// stroke(pts, endcaps="arrow2");
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// color("red") move(circ[0]) cyl(h=10, r=rad, orient=circ[1]);
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// Example(3D):
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@@ -1067,17 +1068,17 @@ function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
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// stroke(path, closed=true);
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// for (i = [0:1:5]) {
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// crn = select(path, i*2-1, i*2+1);
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// ci = circle_2tangents(crn[0], crn[1], crn[2], r=5);
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// ci = circle_2tangents(r=5, crn[0], crn[1], crn[2]);
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// move(ci[0]) cyl(h=10,r=5,,orient=ci[1]);
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// }
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function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
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function circle_2tangents(r, pt1, pt2, pt3, tangents=false, d) =
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let(r = get_radius(r=r, d=d, dflt=undef))
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assert(r!=undef, "Must specify either r or d.")
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assert( ( is_path(pt1) && len(pt1)==3 && is_undef(pt2) && is_undef(pt3))
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|| (is_matrix([pt1,pt2,pt3]) && (len(pt1)==2 || len(pt1)==3) ),
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"Invalid input points." )
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is_undef(pt2)
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? circle_2tangents(pt1[0], pt1[1], pt1[2], r=r, tangents=tangents)
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? circle_2tangents(r, pt1[0], pt1[1], pt1[2], tangents=tangents)
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: is_collinear(pt1, pt2, pt3)? undef :
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let(
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v1 = unit(pt1 - pt2),
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@@ -1100,7 +1101,7 @@ function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
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// Function: circle_3points()
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// Usage:
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// circ = circle_3points(pt1, pt2, pt3);
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// circ = circle_3points([pt1, pt2, pt3]);
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// circ = circle_3points([PT1, PT2, PT3]);
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// Topics: Geometry, Circles
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// Description:
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// Returns the [CENTERPOINT, RADIUS, NORMAL] of the circle that passes through three non-collinear
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@@ -1109,8 +1110,8 @@ function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
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// points are 2D, then the resulting centerpoint will be 2D, and the normal will be UP ([0,0,1]).
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// If any of the points are 3D, then the resulting centerpoint will be 3D. If the three points are
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// collinear, then `[undef,undef,undef]` will be returned. The normal will be a normalized 3D
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// vector with a non-negative Z axis.
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// Instead of 3 arguments, it is acceptable to input the 3 points in a list `pt1`, leaving `pt2`and `pt3` as undef.
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// vector with a non-negative Z axis. Instead of 3 arguments, it is acceptable to input the 3 points
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// as a list given in `pt1`, leaving `pt2`and `pt3` as undef.
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// Arguments:
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// pt1 = The first point.
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// pt2 = The second point.
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@@ -1186,7 +1187,7 @@ function circle_point_tangents(r, cp, pt, d) =
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// Function: circle_circle_tangents()
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// Usage:
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// segs = circle_circle_tangents(c1, r1|d1=, c2, r2|d2=);
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// segs = circle_circle_tangents(r1|d1=, cp1, r2|d2=, cp2);
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// Topics: Geometry, Circles, Tangents
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// Description:
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// Computes 2d lines tangents to a pair of circles in 2d. Returns a list of line endpoints [p1,p2] where
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@@ -1200,54 +1201,54 @@ function circle_point_tangents(r, cp, pt, d) =
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// so the function returns the empty set. When the circles are tangent a degenerate tangent line
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// passes through the point of tangency of the two circles: this degenerate line is NOT returned.
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// Arguments:
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// c1 = Center of the first circle.
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// r1 = Radius of the first circle.
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// c2 = Center of the second circle.
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// cp1 = Centerpoint of the first circle.
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// r2 = Radius of the second circle.
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// cp2 = Centerpoint of the second circle.
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// ---
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// d1 = Diameter of the first circle.
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// d2 = Diameter of the second circle.
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// Example(2D,NoAxes): Four tangents, first in green, second in black, third in blue, last in red.
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// $fn=32;
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// c1 = [3,4]; r1 = 2;
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// c2 = [7,10]; r2 = 3;
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// pts = circle_circle_tangents(c1,r1,c2,r2);
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// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
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// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
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// cp1 = [3,4]; r1 = 2;
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// cp2 = [7,10]; r2 = 3;
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// pts = circle_circle_tangents(r1, cp1, r2, cp2);
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// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// colors = ["green","black","blue","red"];
|
||||
// for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=0.2);
|
||||
// Example(2D,NoAxes): 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);
|
||||
// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// cp1 = [4,4]; r1 = 3;
|
||||
// cp2 = [7,7]; r2 = 2;
|
||||
// pts = circle_circle_tangents(r1, cp1, r2, cp2);
|
||||
// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// colors = ["green","black","blue","red"];
|
||||
// for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=0.2);
|
||||
// Example(2D,NoAxes): 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);
|
||||
// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// cp1 = [4,4]; r1 = 4;
|
||||
// cp2 = [4,10]; r2 = 2;
|
||||
// pts = circle_circle_tangents(r1, cp1, r2, cp2);
|
||||
// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// colors = ["green","black","blue","red"];
|
||||
// for(i=[0:1:len(pts)-1]) color(colors[i]) stroke(pts[i],width=0.2);
|
||||
// Example(2D,NoAxes): 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);
|
||||
// move(c1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(c2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// cp1 = [4,4]; r1 = 4;
|
||||
// cp2 = [5,5]; r2 = 2;
|
||||
// pts = circle_circle_tangents(r1, cp1, r2, cp2);
|
||||
// move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
|
||||
// move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
|
||||
// echo(pts); // Returns []
|
||||
function circle_circle_tangents(c1,r1,c2,r2,d1,d2) =
|
||||
assert( is_path([c1,c2],dim=2), "Invalid center point(s)." )
|
||||
function circle_circle_tangents(r1, cp1, r2, cp2, d1, d2) =
|
||||
assert( is_path([cp1,cp2],dim=2), "Invalid center point(s)." )
|
||||
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),
|
||||
Rvals = [r2-r1, r2-r1, -r2-r1, -r2-r1]/norm(cp1-cp2),
|
||||
kvals = [-1,1,-1,1],
|
||||
ext = [1,1,-1,-1],
|
||||
N = 1-sqr(Rvals[2])>=0 ? 4 :
|
||||
@@ -1256,13 +1257,13 @@ function circle_circle_tangents(c1,r1,c2,r2,d1,d2) =
|
||||
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)
|
||||
] * unit(cp2-cp1)
|
||||
]
|
||||
) [
|
||||
for(i=[0:1:N-1]) let(
|
||||
pt = [
|
||||
c1-r1*coef[i],
|
||||
c2-ext[i]*r2*coef[i]
|
||||
cp1-r1*coef[i],
|
||||
cp2-ext[i]*r2*coef[i]
|
||||
]
|
||||
) if (pt[0]!=pt[1]) pt
|
||||
];
|
||||
@@ -1311,15 +1312,15 @@ function _noncollinear_triple(points,error=true,eps=EPSILON) =
|
||||
|
||||
// Function: sphere_line_intersection()
|
||||
// Usage:
|
||||
// isect = sphere_line_intersection(c,r|d=,line,[bounded],[eps=]);
|
||||
// isect = sphere_line_intersection(r|d=, cp, line, [bounded], [eps=]);
|
||||
// Topics: Geometry, Spheres, Lines, Intersection
|
||||
// Description:
|
||||
// Find intersection points between a sphere and a line, ray or segment specified by two points.
|
||||
// By default the line is unbounded.
|
||||
// Arguments:
|
||||
// c = center of sphere
|
||||
// r = radius of sphere
|
||||
// line = two points defining the line
|
||||
// r = Radius of sphere
|
||||
// cp = Centerpoint of sphere
|
||||
// line = Two points defining the line
|
||||
// bounded = false for unbounded line, true for a segment, or a vector [false,true] or [true,false] to specify a ray with the first or second end unbounded. Default: false
|
||||
// ---
|
||||
// d = diameter of sphere
|
||||
@@ -1327,14 +1328,14 @@ function _noncollinear_triple(points,error=true,eps=EPSILON) =
|
||||
// Example(3D):
|
||||
// cp = [10,20,5]; r = 40;
|
||||
// line = [[-50,-10,25], [70,0,40]];
|
||||
// isects = sphere_line_intersection(c=cp, r=r, line=line);
|
||||
// isects = sphere_line_intersection(r=r, cp=cp, line=line);
|
||||
// color("cyan") stroke(line);
|
||||
// move(cp) sphere(r=r, $fn=72);
|
||||
// color("red") move_copies(isects) sphere(d=3, $fn=12);
|
||||
function sphere_line_intersection(c,r,line,bounded=false,d,eps=EPSILON) =
|
||||
function sphere_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
|
||||
assert(_valid_line(line,3), "Invalid 3d line.")
|
||||
assert(is_vector(c,3), "Sphere center must be a 3-vector")
|
||||
_circle_or_sphere_line_intersection(c,r,line,bounded,d,eps);
|
||||
assert(is_vector(cp,3), "Sphere center must be a 3-vector")
|
||||
_circle_or_sphere_line_intersection(r, cp, line, bounded, d, eps);
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user