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plane_intersection() bugfix. plane_line_intersection() and polygon_line_intersection() can now detect on-plane intersections.
This commit is contained in:
Revar Desmera
parent
9257c74236
commit
412dd9e260
2 changed files with 53 additions and 25 deletions
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@ -592,23 +592,19 @@ function plane3pt_indexed(points, i1, i2, i3) =
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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) ?
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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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)
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linear_solve(matrix,rhs)
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:
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let(
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normal = cross(plane_normal(plane1), plane_normal(plane2))
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)
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approx(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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)
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[point, point+normal];
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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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@ -653,8 +649,8 @@ function plane_from_pointslist(points, fast=false, eps=EPSILON) =
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// Usage:
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// plane_normal(plane);
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// Description:
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// Returns the normal vector for the given plane.
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function plane_normal(plane) = [for (i=[0:2]) plane[i]];
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// Returns the unit length normal vector for the given plane.
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function plane_normal(plane) = unit([for (i=[0:2]) plane[i]]);
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// Function: distance_from_plane()
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@ -690,6 +686,9 @@ function closest_point_on_plane(plane, point) =
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) point - n*d;
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// Returns [POINT, U] if line intersects plane at one point.
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// Returns [LINE, undef] if the line is on the plane.
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// Returns undef if line is parallel to, but not on the given plane.
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function _general_plane_line_intersection(plane, line, eps=EPSILON) =
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let(
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p0 = line[0],
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@ -698,6 +697,7 @@ function _general_plane_line_intersection(plane, line, eps=EPSILON) =
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u = p1 - p0,
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d = n * u
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) abs(d)<eps? (
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coplanar(plane, p0)? [line,undef] : // Line on plane
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undef // Line parallel to plane
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) : let(
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v0 = closest_point_on_plane(plane, [0,0,0]),
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@ -726,20 +726,24 @@ function plane_line_angle(plane, line) =
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// pt = plane_line_intersection(plane, line, [eps]);
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// Description:
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// Takes a line, and a plane [A,B,C,D] where the equation of that plane is `Ax+By+Cz=D`.
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// Returns the coordinates of the where the given `line` intersects the given `plane`.
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// Returns `undef` if the line is parallel to the plane.
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// If `line` intersects `plane` at one point, then that intersection point is returned.
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// If `line` lies on `plane`, then the original given `line` is returned.
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// If `line` is parallel to, but not on `plane`, then `undef` is returned.
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// Arguments:
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// plane = The [A,B,C,D] values for the equation of the plane.
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// line = A list of two 3D points that are on the line.
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// bounded = If false, the line is considered unbounded. If true, it is treated as a bounded line segment. If given as `[true, false]` or `[false, true]`, the boundedness of the points are specified individually, allowing the line to be treated as a half-bounded ray. Default: false (unbounded)
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// eps = The epsilon error value to determine whether the line is too close to parallel to the plane. Default: `EPSILON` (1e-9)
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function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
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assert(is_vector(plane)&&len(plane)==4)
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assert(is_path(line)&&len(line)==2)
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assert(is_vector(plane)&&len(plane)==4, "Invalid plane value.")
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assert(is_path(line)&&len(line)==2, "Invalid line value.")
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assert(!approx(line[0],line[1]), "The two points defining the line must not be the same point.")
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let(
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bounded = is_list(bounded)? bounded : [bounded, bounded],
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res = _general_plane_line_intersection(plane, line, eps=eps)
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)
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is_undef(res)? undef :
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is_undef(res[1])? res[0] :
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bounded[0]&&res[1]<0? undef :
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bounded[1]&&res[1]>1? undef :
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res[0];
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@ -750,7 +754,10 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
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// pt = polygon_line_intersection(poly, line, [bounded], [eps]);
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// Description:
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// Takes a possibly bounded line, and a 3D planar polygon, and finds their intersection point.
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// Returns the 3D coordinates of the intersection point, or `undef` if they do not intersect.
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// If the line is on the plane as the polygon, and intersects, then a list of 3D line
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// segments is returned, one for each section of the line that is inside the polygon.
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// If the line is not on the plane of the polygon, but intersects, then the 3D intersection
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// point is returned. If the line does not intersect the polygon, then `undef` is returned.
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// Arguments:
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// poly = The 3D planar polygon to find the intersection with.
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// line = A list of two 3D points that are on the line.
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@ -770,6 +777,27 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
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res = _general_plane_line_intersection(plane, line, eps=eps)
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)
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is_undef(res)? undef :
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is_undef(res[1])? (
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let(
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// Line is on polygon plane.
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linevec = unit(line[1] - line[0]),
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lp1 = line[0] + (bounded[0]? 0 : -1000000) * linevec,
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lp2 = line[1] + (bounded[1]? 0 : 1000000) * linevec,
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poly2d = clockwise_polygon(project_plane(poly, p1, p2, p3)),
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line2d = project_plane([lp1,lp2], p1, p2, p3),
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parts = split_path_at_region_crossings(line2d, [poly2d], closed=false),
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inside = [
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for (part = parts)
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if (point_in_polygon(mean(part), poly2d)>0) part
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]
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) !inside? undef :
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let(
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isegs = [
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for (seg = inside)
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lift_plane(seg, p1, p2, p3)
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]
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) isegs
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) :
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bounded[0]&&res[1]<0? undef :
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bounded[1]&&res[1]>1? undef :
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let(
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@ -8,7 +8,7 @@
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//////////////////////////////////////////////////////////////////////
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BOSL_VERSION = [2,0,196];
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BOSL_VERSION = [2,0,197];
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// Section: BOSL Library Version Functions
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