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https://github.com/revarbat/BOSL2.git
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Implemented solution for issue #159
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Revar Desmera
183
geometry.scad
183
geometry.scad
@@ -84,6 +84,23 @@ function collinear_indexed(points, a, b, c, eps=EPSILON) =
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) collinear(p1, p2, p3, eps);
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// Function: points_are_collinear()
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// Usage:
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// points_are_collinear(points);
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// Description:
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// Given a list of points, returns true if all points in the list are collinear.
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// Arguments:
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// points = The list of points to test.
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// eps = How much variance is allowed in testing that each point is on the same line. Default: `EPSILON` (1e-9)
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function points_are_collinear(points, eps=EPSILON) =
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let(
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a = furthest_point(points[0], points),
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b = furthest_point(points[a], points),
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pa = points[a],
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pb = points[b]
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) all([for (pt = points) collinear(pa, pb, pt, eps=eps)]);
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// Function: distance_from_line()
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// Usage:
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// distance_from_line(line, pt);
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@@ -584,38 +601,14 @@ function plane3pt_indexed(points, i1, i2, i3) =
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) plane3pt(p1,p2,p3);
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// Function: plane_intersection()
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// Usage:
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// plane_intersection(plane1, plane2, [plane3])
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// Description:
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// Compute the point which is the intersection of the three planes, or the line intersection of two planes.
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// If you give three planes the intersection is returned as a point. If you give two planes the intersection
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// is returned as a list of two points on the line of intersection. If any of the input planes are parallel
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// then returns undef.
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function plane_intersection(plane1,plane2,plane3) =
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is_def(plane3)? let(
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matrix = [for(p=[plane1,plane2,plane3]) select(p,0,2)],
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rhs = [for(p=[plane1,plane2,plane3]) p[3]]
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) linear_solve(matrix,rhs) :
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let(
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normal = cross(plane_normal(plane1), plane_normal(plane2))
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) approx(norm(normal),0) ? undef :
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let(
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matrix = [for(p=[plane1,plane2]) select(p,0,2)],
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rhs = [for(p=[plane1,plane2]) p[3]],
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point = linear_solve(matrix,rhs)
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) is_undef(point)? undef :
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[point, point+normal];
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// Function: plane_from_normal()
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// Usage:
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// plane_from_normal(normal, pt)
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// plane_from_normal(normal, [pt])
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// Description:
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// Returns a plane defined by a normal vector and a point.
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// Example:
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// plane_from_normal([0,0,1], [2,2,2]); // Returns the xy plane passing through the point (2,2,2)
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function plane_from_normal(normal, pt) =
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function plane_from_normal(normal, pt=[0,0,0]) =
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concat(normal, [normal*pt]);
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@@ -632,6 +625,12 @@ function plane_from_normal(normal, pt) =
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// points = The list of points to find the plane of.
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// fast = If true, don't verify that all points in the list are coplanar. Default: false
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// eps = How much variance is allowed in testing that each point is on the same plane. Default: `EPSILON` (1e-9)
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// Example:
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// xyzpath = rot(45, v=[-0.3,1,0], p=path3d(star(n=6,id=70,d=100), 70));
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// plane = plane_from_points(xyzpath);
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// #stroke(xyzpath,closed=true);
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// cp = centroid(xyzpath);
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// move(cp) rot(from=UP,to=plane_normal(plane)) anchor_arrow();
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function plane_from_points(points, fast=false, eps=EPSILON) =
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let(
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points = deduplicate(points),
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@@ -646,6 +645,39 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
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) all_coplanar? plane : undef;
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// Function: plane_from_polygon()
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// Usage:
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// plane_from_polygon(points, [fast], [eps]);
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// Description:
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// Given a 3D planar polygon, returns the cartesian equation of a plane.
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// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane.
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// If not all the points in the polygon are coplanar, then `undef` is returned.
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// If `fast` is true, then a polygon where not all points are coplanar will
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// result in an invalid plane value, as all coplanar checks are skipped.
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// Arguments:
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// poly = The planar 3D polygon to find the plane of.
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// fast = If true, don't verify that all points in the polygon are coplanar. Default: false
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// eps = How much variance is allowed in testing that each point is on the same plane. Default: `EPSILON` (1e-9)
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// Example:
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// xyzpath = rot(45, v=[0,1,0], p=path3d(star(n=5,step=2,d=100), 70));
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// plane = plane_from_polygon(xyzpath);
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// #stroke(xyzpath,closed=true);
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// cp = centroid(xyzpath);
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// move(cp) rot(from=UP,to=plane_normal(plane)) anchor_arrow();
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function plane_from_polygon(poly, fast=false, eps=EPSILON) =
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let(
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poly = deduplicate(poly),
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n = polygon_normal(poly),
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plane = [n.x, n.y, n.z, n*poly[0]]
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) fast? plane : let(
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all_coplanar = [
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for (pt = poly)
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if (!coplanar(plane,pt,eps=eps)) 1
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] == []
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) all_coplanar? plane :
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undef;
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// Function: plane_normal()
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// Usage:
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// plane_normal(plane);
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@@ -654,6 +686,48 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
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function plane_normal(plane) = unit([for (i=[0:2]) plane[i]]);
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// Function: plane_offset()
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// Usage:
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// d = plane_offset(plane);
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// Description:
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// Returns D, or the scalar offset of the plane from the origin. This can be a negative value.
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// The absolute value of this is the distance of the plane from the origin at its closest approach.
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function plane_offset(plane) = plane[3];
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// Function: plane_transform()
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// Usage:
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// mat = plane_transform(plane);
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// Description:
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// Given a plane definition `[A,B,C,D]`, where `Ax+By+Cz=D`, returns a 3D affine
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// transformation matrix that will rotate and translate from points on that plane
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// to points on the XY plane. You can generally then use `path2d()` to drop the
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// Z coordinates, so you can work with the points in 2D.
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// Arguments:
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// plane = The `[A,B,C,D]` plane definition where `Ax+By+Cz=D` is the formula of the plane.
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// Example:
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// xyzpath = move([10,20,30], p=yrot(25, p=path3d(circle(d=100))));
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// plane = plane_from_points(xyzpath);
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// mat = plane_transform(plane);
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// xypath = path2d(apply(mat, xyzpath));
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// #stroke(xyzpath,closed=true);
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// stroke(xypath,closed=true);
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function plane_transform(plane) =
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let(
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n = plane_normal(plane),
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cp = n * plane[3]
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) rot(from=n, to=UP) * move(-cp);
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// Function: plane_point_nearest_origin()
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// Usage:
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// pt = plane_point_nearest_origin(plane);
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// Description:
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// Returns the point on the plane that is closest to the origin.
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function plane_point_nearest_origin(plane) =
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plane_normal(plane) * plane[3];
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// Function: distance_from_plane()
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// Usage:
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// distance_from_plane(plane, point)
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@@ -808,21 +882,28 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
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res[0];
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// Function: points_are_collinear()
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// Function: plane_intersection()
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// Usage:
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// points_are_collinear(points);
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// plane_intersection(plane1, plane2, [plane3])
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// Description:
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// Given a list of points, returns true if all points in the list are collinear.
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// Arguments:
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// points = The list of points to test.
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// eps = How much variance is allowed in testing that each point is on the same line. Default: `EPSILON` (1e-9)
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function points_are_collinear(points, eps=EPSILON) =
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// Compute the point which is the intersection of the three planes, or the line intersection of two planes.
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// If you give three planes the intersection is returned as a point. If you give two planes the intersection
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// is returned as a list of two points on the line of intersection. If any of the input planes are parallel
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// then returns undef.
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function plane_intersection(plane1,plane2,plane3) =
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is_def(plane3)? let(
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matrix = [for(p=[plane1,plane2,plane3]) select(p,0,2)],
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rhs = [for(p=[plane1,plane2,plane3]) p[3]]
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) linear_solve(matrix,rhs) :
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let(
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a = furthest_point(points[0], points),
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b = furthest_point(points[a], points),
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pa = points[a],
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pb = points[b]
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) all([for (pt = points) collinear(pa, pb, pt, eps=eps)]);
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normal = cross(plane_normal(plane1), plane_normal(plane2))
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) approx(norm(normal),0) ? undef :
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let(
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matrix = [for(p=[plane1,plane2]) select(p,0,2)],
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rhs = [for(p=[plane1,plane2]) p[3]],
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point = linear_solve(matrix,rhs)
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) is_undef(point)? undef :
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[point, point+normal];
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// Function: coplanar()
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@@ -1289,7 +1370,7 @@ function centroid(poly) =
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// Usage:
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// point_in_polygon(point, path, [eps])
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// Description:
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// This function tests whether the given point is inside, outside or on the boundary of
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// This function tests whether the given 2D point is inside, outside or on the boundary of
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// the specified 2D polygon using the Winding Number method.
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// The polygon is given as a list of 2D points, not including the repeated end point.
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// Returns -1 if the point is outside the polyon.
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@@ -1299,7 +1380,7 @@ function centroid(poly) =
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// But the polygon cannot have holes (it must be simply connected).
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// Rounding error may give mixed results for points on or near the boundary.
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// Arguments:
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// point = The point to check position of.
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// point = The 2D point to check position of.
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// path = The list of 2D path points forming the perimeter of the polygon.
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// eps = Acceptable variance. Default: `EPSILON` (1e-9)
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function point_in_polygon(point, path, eps=EPSILON) =
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@@ -1334,7 +1415,7 @@ function polygon_is_clockwise(path) =
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// Usage:
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// clockwise_polygon(path);
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// Description:
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// Given a polygon path, returns the clockwise winding version of that path.
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// Given a 2D polygon path, returns the clockwise winding version of that path.
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function clockwise_polygon(path) =
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polygon_is_clockwise(path)? path : reverse_polygon(path);
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@@ -1343,7 +1424,7 @@ function clockwise_polygon(path) =
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// Usage:
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// ccw_polygon(path);
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// Description:
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// Given a polygon path, returns the counter-clockwise winding version of that path.
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// Given a 2D polygon path, returns the counter-clockwise winding version of that path.
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function ccw_polygon(path) =
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polygon_is_clockwise(path)? reverse_polygon(path) : path;
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@@ -1357,5 +1438,23 @@ function reverse_polygon(poly) =
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let(lp=len(poly)) [for (i=idx(poly)) poly[(lp-i)%lp]];
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// Function: polygon_normal()
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// Usage:
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// n = polygon_normal(poly);
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// Description:
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// Given a 3D planar polygon, returns a unit-length normal vector for the
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// clockwise orientation of the polygon.
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// Example:
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function polygon_normal(poly) =
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let(
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poly = path3d(cleanup_path(poly)),
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p0 = poly[0],
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n = sum([
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for (i=[1:1:len(poly)-2])
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cross(poly[i+1]-p0, poly[i]-p0)
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])
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) unit(n);
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// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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