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Merge pull request #266 from RonaldoCMP/master

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Solving bugs in plane operations; extending tests in test_geometry
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Revar Desmera 2020-09-09 16:35:56 -07:00 committed by GitHub
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4 changed files with 315 additions and 94 deletions
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22
coords.scad
View file

@ -142,24 +142,24 @@ function xy_to_polar(x,y=undef) = let(
// Function: project_plane()
// Usage: With 3 Points
// Usage: With the plane defined by 3 Points
// xyz = project_plane(point, a, b, c);
// Usage: With Pointlist
// Usage: With the plane defined by Pointlist
// xyz = project_plane(point, POINTLIST);
// Usage: With Plane Definition [A,B,C,D] Where Ax+By+Cz=D
// Usage: With the plane defined by Plane Definition [A,B,C,D] Where Ax+By+Cz=D
// xyz = project_plane(point, PLANE);
// Description:
// Converts the given 3D point from global coordinates to the 2D planar coordinates of the closest
// point on the plane. This coordinate system can be useful in taking a set of nearly coplanar
// Converts the given 3D points from global coordinates to the 2D planar coordinates of the closest
// points on the plane. This coordinate system can be useful in taking a set of nearly coplanar
// points, and converting them to a pure XY set of coordinates for manipulation, before converting
// them back to the original 3D plane.
// Can be called one of three ways:
// - Given three points, `a`, `b`, and `c`, the planar coordinate system will have `[0,0]` at point `a`, and the Y+ axis will be towards point `b`.
// - Given a list of points, finds three reasonably spaced non-collinear points in the list and uses them as points `a`, `b`, and `c` as above.
// - Given a plane definition `[A,B,C,D]` where `Ax+By+Cz=D`, the closest point on that plane to the global origin at `[0,0,0]` will be the planar coordinate origin `[0,0]`.
// them back to the original 3D plane. The parameter `point` may be a single point or a list of points
// The plane may be given in one of three ways:
// - by three points, `a`, `b`, and `c`, the planar coordinate system will have `[0,0]` at point `a`, and the Y+ axis will be towards point `b`.
// - by a list of points passed by `a`, finds three reasonably spaced non-collinear points in the list and uses them as points `a`, `b`, and `c` as above.
// - by a plane definition `[A,B,C,D]` passed by `a` where `Ax+By+Cz=D`, the closest point on that plane to the global origin at `[0,0,0]` will be the planar coordinate origin `[0,0]`.
// Arguments:
// point = The 3D point, or list of 3D points to project into the plane's 2D coordinate system.
// a = A 3D point that the plane passes through. Used to define the plane.
// a = A 3D point that the plane passes through or a list of points or a plane definition vector.
// b = A 3D point that the plane passes through. Used to define the plane.
// c = A 3D point that the plane passes through. Used to define the plane.
// Example:

99
geometry.scad
View file

@ -762,8 +762,8 @@ function triangle_area(a,b,c) =
// Usage:
// plane3pt(p1, p2, p3);
// Description:
// Generates the cartesian equation of a plane from three 3d points.
// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
// Generates the normalized cartesian equation of a plane from three 3d points.
// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
// Returns [], if the points are collinear.
// Arguments:
// p1 = The first point on the plane.
@ -777,7 +777,7 @@ function plane3pt(p1, p2, p3) =
nrm = norm(crx)
)
approx(nrm,0) ? [] :
concat(crx/nrm, [crx*p1]/nrm);
concat(crx, crx*p1)/nrm;
// Function: plane3pt_indexed()
@ -785,7 +785,7 @@ function plane3pt(p1, p2, p3) =
// plane3pt_indexed(points, i1, i2, i3);
// Description:
// Given a list of 3d points, and the indices of three of those points,
// generates the cartesian equation of a plane that those points all
// generates the normalized cartesian equation of a plane that those points all
// lie on. If the points are not collinear, returns [A,B,C,D] where Ax+By+Cz=D is the equation of a plane.
// If they are collinear, returns [].
// Arguments:
@ -816,15 +816,15 @@ function plane3pt_indexed(points, i1, i2, i3) =
function plane_from_normal(normal, pt=[0,0,0]) =
assert( is_matrix([normal,pt],2,3) && !approx(norm(normal),0),
"Inputs `normal` and `pt` should 3d vectors/points and `normal` cannot be zero." )
concat(normal, [normal*pt]);
concat(normal, normal*pt)/norm(normal);
// Function: plane_from_points()
// Usage:
// plane_from_points(points, <fast>, <eps>);
// Description:
// Given a list of 3 or more coplanar 3D points, returns the coefficients of the cartesian equation of a plane,
// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane.
// Given a list of 3 or more coplanar 3D points, returns the coefficients of the normalized cartesian equation of a plane,
// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1.
// If `fast` is false and the points in the list are collinear or not coplanar, then `undef` is returned.
// if `fast` is true, then the coplanarity test is skipped and a plane passing through 3 non-collinear arbitrary points is returned.
// Arguments:
@ -858,8 +858,8 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
// Usage:
// plane_from_polygon(points, [fast], [eps]);
// Description:
// Given a 3D planar polygon, returns the cartesian equation of its plane.
// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane.
// Given a 3D planar polygon, returns the normalized cartesian equation of its plane.
// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1.
// If not all the points in the polygon are coplanar, then [] is returned.
// If `fast` is true, the polygon coplanarity check is skipped and the plane may not contain all polygon points.
// Arguments:
@ -897,8 +897,9 @@ function plane_normal(plane) =
// Usage:
// d = plane_offset(plane);
// Description:
// Returns D, or the scalar offset of the plane from the origin. This can be a negative value.
// The absolute value of this is the distance of the plane from the origin at its closest approach.
// Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin.
// This value may be negative.
// The absolute value of this coefficient is the distance of the plane from the origin.
function plane_offset(plane) =
assert( _valid_plane(plane), "Invalid input plane." )
plane[3]/norm([plane.x, plane.y, plane.z]);
@ -923,7 +924,8 @@ function plane_offset(plane) =
// stroke(xypath,closed=true);
function plane_transform(plane) =
let(
n = plane_normal(plane),
plane = normalize_plane(plane),
n = point3d(plane),
cp = n * plane[3]
)
rot(from=n, to=UP) * move(-cp);
@ -949,8 +951,8 @@ function projection_on_plane(plane, points) =
p = len(points[0])==2
? [for(pi=points) point3d(pi) ]
: points,
plane = plane/norm([plane.x,plane.y,plane.z]),
n = [plane.x,plane.y,plane.z]
plane = normalize_plane(plane),
n = point3d(plane)
)
[for(pi=p) pi - (pi*n - plane[3])*n];
@ -961,7 +963,8 @@ function projection_on_plane(plane, points) =
// Description:
// Returns the point on the plane that is closest to the origin.
function plane_point_nearest_origin(plane) =
plane_normal(plane) * plane[3];
let( plane = normalize_plane(plane) )
point3d(plane) * plane[3];
// Function: distance_from_plane()
@ -980,8 +983,8 @@ function plane_point_nearest_origin(plane) =
function distance_from_plane(plane, point) =
assert( _valid_plane(plane), "Invalid input plane." )
assert( is_vector(point,3), "The point should be a 3D point." )
let( nrml = [plane.x, plane.y, plane.z] )
( nrml* point - plane[3])/norm(nrml);
let( plane = normalize_plane(plane) )
point3d(plane)* point - plane[3];
// Function: closest_point_on_plane()
@ -996,9 +999,9 @@ function distance_from_plane(plane, point) =
function closest_point_on_plane(plane, point) =
assert( _valid_plane(plane), "Invalid input plane." )
assert( is_vector(point,3), "Invalid point." )
let(
n = unit([plane.x, plane.y, plane.z]),
d = distance_from_plane(plane, point)
let( plane = normalize_plane(plane),
n = point3d(plane),
d = n*point - plane[3] // distance from plane
)
point - n*d;
@ -1008,23 +1011,29 @@ function closest_point_on_plane(plane, point) =
// Returns undef if line is parallel to, but not on the given plane.
function _general_plane_line_intersection(plane, line, eps=EPSILON) =
let(
l0 = line[0], // Ray start point
u = line[1] - l0, // Ray direction vector
n = plane_normal(plane),
p0 = n * plane[3], // A point on the plane
w = l0 - p0 // Vector from plane point to ray start
) approx(n*u, 0, eps=eps) ? (
// Line is parallel to plane.
approx(n*w, 0, eps=eps)
? [line, undef] // Line is on the plane.
: undef // Line never intersects the plane.
) : let(
t = (-n * w) / (n * u) // Distance ratio along ray
) [ l0 + u*t, t ];
a = plane*[each line[0],-1], // evaluation of the plane expression at line[0]
b = plane*[each(line[1]-line[0]),0] // difference between the plane expression evaluation at line[1] and at line[0]
)
approx(b,0,eps) // is (line[1]-line[0]) "parallel" to the plane ?
? approx(a,0,eps) // is line[0] on the plane ?
? [line,undef] // line is on the plane
: undef // line is parallel but not on the plane
: [ line[0]-a/b*(line[1]-line[0]), -a/b ];
// Function: normalize_plane()
// Usage:
// nplane = normalize_plane(plane);
// Description:
// Returns a new representation [A,B,C,D] of `plane` where norm([A,B,C]) is equal to one.
function normalize_plane(plane) =
assert( _valid_plane(plane), "Invalid plane." )
plane/norm(point3d(plane));
// Function: plane_line_angle()
// Usage: plane_line_angle(plane,line)
// Usage:
// angle = plane_line_angle(plane,line);
// Description:
// Compute the angle between a plane [A, B, C, D] and a line, specified as a pair of points [p1,p2].
// The resulting angle is signed, with the sign positive if the vector p2-p1 lies on
@ -1033,11 +1042,12 @@ function plane_line_angle(plane, line) =
assert( _valid_plane(plane), "Invalid plane." )
assert( _valid_line(line), "Invalid line." )
let(
vect = line[1]-line[0],
zplane = plane_normal(plane),
sin_angle = vect*zplane/norm(zplane)/norm(vect)
linedir = unit(line[1]-line[0]),
normal = plane_normal(plane),
sin_angle = linedir*normal,
cos_angle = norm(cross(linedir,normal))
)
asin(constrain(sin_angle,-1,1));
atan2(sin_angle,cos_angle);
// Function: plane_line_intersection()
@ -1085,7 +1095,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." )
assert(is_path(poly,dim=3), "Invalid polygon." )
assert(is_bool(bounded) || (is_list(bounded) && len(bounded)==2), "Invalid bound condition(s).")
assert(!is_list(bounded) || len(bounded)==2, "Invalid bound condition(s).")
assert(_valid_line(line,dim=3,eps=eps), "Invalid line." )
let(
bounded = is_list(bounded)? bounded : [bounded, bounded],
@ -1094,7 +1104,6 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
)
indices==[] ? undef :
let(
indices = sort(indices),
p1 = poly[indices[0]],
p2 = poly[indices[1]],
p3 = poly[indices[2]],
@ -1120,8 +1129,8 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
)
isegs
)
: bounded[0]&&res[1]<0? [] :
bounded[1]&&res[1]>1? [] :
: bounded[0] && res[1]<0? undef :
bounded[1] && res[1]>1? undef :
let(
proj = clockwise_polygon(project_plane(poly, p1, p2, p3)),
pt = project_plane(res[0], p1, p2, p3)
@ -1142,15 +1151,15 @@ function plane_intersection(plane1,plane2,plane3) =
"The input must be 2 or 3 planes." )
is_def(plane3)
? let(
matrix = [for(p=[plane1,plane2,plane3]) select(p,0,2)],
matrix = [for(p=[plane1,plane2,plane3]) point3d(p)],
rhs = [for(p=[plane1,plane2,plane3]) p[3]]
)
linear_solve(matrix,rhs)
: let( normal = cross(plane_normal(plane1), plane_normal(plane2)) )
approx(norm(normal),0) ? undef :
let(
matrix = [for(p=[plane1,plane2]) select(p,0,2)],
rhs = [for(p=[plane1,plane2]) p[3]],
matrix = [for(p=[plane1,plane2]) point3d(p)],
rhs = [plane1[3], plane2[3]],
point = linear_solve(matrix,rhs)
)
point==[]? undef: [point, point+normal];

5
regions.scad
View file

@ -180,8 +180,9 @@ function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON)
),
subpaths = [
for (p = pair(crossings))
deduplicate(eps=eps,
path_subselect(path, p[0][0], p[0][1], p[1][0], p[1][1], closed=closed)
deduplicate(
path_subselect(path, p[0][0], p[0][1], p[1][0], p[1][1], closed=closed),
eps=eps
)
]
)

283
tests/test_geometry.scad
View file

@ -4,6 +4,8 @@ include <../std.scad>
//the commented lines are for tests to be written
//the tests are ordered as they appear in geometry.scad
test_point_on_segment2d();
test_point_left_of_line2d();
test_collinear();
@ -35,33 +37,30 @@ test_tri_calc();
test_triangle_area();
test_plane3pt();
test_plane3pt_indexed();
//test_plane_from_normal();
test_plane_from_normal();
test_plane_from_points();
//test_plane_from_polygon();
test_plane_from_polygon();
test_plane_normal();
//test_plane_offset();
//test_plane_transform();
test_plane_offset();
test_plane_transform();
test_projection_on_plane();
//test_plane_point_nearest_origin();
test_plane_point_nearest_origin();
test_distance_from_plane();
test_find_circle_2tangents();
test_find_circle_3points();
test_circle_point_tangents();
test_tri_functions();
//test_closest_point_on_plane();
//test__general_plane_line_intersection();
//test_plane_line_angle();
//test_plane_line_intersection();
test_closest_point_on_plane();
test__general_plane_line_intersection();
test_plane_line_angle();
test_normalize_plane();
test_plane_line_intersection();
test_polygon_line_intersection();
//test_plane_intersection();
test_plane_intersection();
test_coplanar();
test_points_on_plane();
test_in_front_of_plane();
//test_find_circle_2tangents();
//test_find_circle_3points();
//test_circle_point_tangents();
//test_circle_circle_tangents();
test_find_circle_2tangents();
test_find_circle_3points();
test_circle_point_tangents();
test_noncollinear_triple();
test_pointlist_bounds();
test_closest_point();
@ -92,24 +91,204 @@ test_simplify_path();
test_simplify_path_indexed();
test_is_region();
// to be used when there are two alternative symmetrical outcomes
// from a function like a plane output.
// from a function like a plane output; v must be a vector
function standardize(v) =
v==[]? [] :
sign([for(vi=v) if( ! approx(vi,0)) vi,0 ][0])*v;
let( i = max_index([for(vi=v) abs(vi) ]),
s = sign(v[i]) )
v*s;
module assert_std(vc,ve,info) { assert_approx(standardize(vc),standardize(ve),info); }
function info_str(list,i=0,string=chr(10)) =
assert(i>=len(list) || (is_list(list[i])&&len(list[i])>=2), "Invalid list for info_str." )
i>=len(list)
? str(string)
: info_str(list,i+1,str(string,str(list[i][0],_valstr(list[i][1]),chr(10))));
module test_closest_point_on_plane(){
plane = rands(-5,5,4)+[10,0,0,0];
point = rands(-1,1,3);
point2 = closest_point_on_plane(plane,point);
assert_approx(norm(point-point2), abs(distance_from_plane(plane,point)));
}
*test_closest_point_on_plane();
module test_normalize_plane(){
plane = rands(-5,5,4)+[10,0,0,0];
plane2 = normalize_plane(plane);
assert_approx(norm(point3d(plane2)),1);
assert_approx(plane*plane2[3],plane2*plane[3]);
}
*test_normalize_plane();
module test_plane_line_intersection(){
line = [rands(-1,1,3),rands(-1,1,3)+[2,0,0]];
plane1 = plane_from_normal(line[1]-line[0],2*line[0]-line[1]); // plane disjoint from segment
plane2 = plane_from_normal(line[1]-line[0],(line[0]+line[1])/2); // through middle point of line
plane3 = plane3pt(line[1],line[0], rands(-1,1,3)+[0,3,0]); // containing line
plane4 = plane3pt(line[1],line[0], rands(-1,1,3)+[0,3,0])+[0,0,0,1]; // parallel to line
info1 = info_str([ ["line = ",line],["plane = ",plane1]]);
assert_approx(plane_line_intersection(plane1, line),2*line[0]-line[1],info1);
assert_approx(plane_line_intersection(plane1, line,[true,false]),undef,info1);
assert_approx(plane_line_intersection(plane1, line,[false,true]),2*line[0]-line[1],info1);
assert_approx(plane_line_intersection(plane1, line,[true, true]),undef,info1);
info2 = info_str([ ["line = ",line],["plane = ",plane2]]);
assert_approx(plane_line_intersection(plane2, line),(line[0]+line[1])/2,info2);
assert_approx(plane_line_intersection(plane2, line,[true,false]),(line[0]+line[1])/2,info2);
assert_approx(plane_line_intersection(plane2, line,[false,true]),(line[0]+line[1])/2,info2);
assert_approx(plane_line_intersection(plane2, line,[true, true]),(line[0]+line[1])/2,info2);
info3 = info_str([ ["line = ",line],["plane = ",plane3]]);
assert_approx(plane_line_intersection(plane3, line),line,info3);
assert_approx(plane_line_intersection(plane3, line,[true,false]),line,info3);
assert_approx(plane_line_intersection(plane3, line,[false,true]),line,info3);
assert_approx(plane_line_intersection(plane3, line,[true, true]),line,info3);
info4 = info_str([ ["line = ",line],["plane = ",plane4]]);
assert_approx(plane_line_intersection(plane4, line),undef,info4);
assert_approx(plane_line_intersection(plane4, line,[true,false]),undef,info4);
assert_approx(plane_line_intersection(plane4, line,[false,true]),undef,info4);
assert_approx(plane_line_intersection(plane4, line,[true, true]),undef,info4);
}
*test_plane_line_intersection();
module test_plane_intersection(){
line = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0] ]; // a valid line
pt0 = line[0]-[2,0,0]; // 2 points not on the line
pt1 = line[1]-[0,2,0];
plane01 = plane3pt(line[0],line[1],pt0);
plane02 = plane3pt(line[0],line[1],pt1);
plane03 = plane3pt(line[0],pt0,pt1);
info = info_str([["plane1 = ",plane01],["plane2 = ",plane02],["plane3 = ",plane03]]);
assert_approx(plane_intersection(plane01,plane02,plane03),line[0],info);
assert_approx(plane_intersection(plane01,2*plane01),undef,info);
lineInters = plane_intersection(plane01,plane02);
assert_approx(line_closest_point(lineInters,line[0]), line[0], info);
assert_approx(line_closest_point(lineInters,line[1]), line[1], info);
}
*test_plane_intersection();
module test_plane_point_nearest_origin(){
point = rands(-1,1,3)+[2,0,0]; // a non zero vector
plane = [ each point, point*point]; // a plane containing `point`
info = info_str([["point = ",point],["plane = ",plane]]);
assert_approx(plane_point_nearest_origin(plane),point,info);
assert_approx(plane_point_nearest_origin([each point,5]),5*unit(point)/norm(point),info);
}
test_plane_point_nearest_origin();
module test_plane_transform(){
normal = rands(-1,1,3)+[2,0,0];
offset = rands(-1,1,1)[0];
info = info_str([["normal = ",normal],["offset = ",offset]]);
assert_approx(plane_transform([0,0,1,offset]),move([0,0,-offset]),info );
assert_approx(plane_transform([0,1,0,offset]),xrot(90)*move([0,-offset,0]),info );
}
*test_plane_transform();
module test_plane_offset(){
plane = rands(-1,1,4)+[2,0,0,0]; // a valid plane
info = info_str([["plane = ",plane]]);
assert_approx(plane_offset(plane), normalize_plane(plane)[3],info);
assert_approx(plane_offset([1,1,1,1]), 1/sqrt(3),info);
}
*test_plane_offset();
module test_plane_from_polygon(){
poly1 = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0], rands(-1,1,3)+[0,2,2] ];
poly2 = concat(poly1, [sum(poly1)/3] );
info = info_str([["poly1 = ",poly1],["poly2 = ",poly2]]);
assert_std(plane_from_polygon(poly1),plane3pt(poly1[0],poly1[1],poly1[2]),info);
assert_std(plane_from_polygon(poly2),plane3pt(poly1[0],poly1[1],poly1[2]),info);
}
*test_plane_from_polygon();
module test_plane_from_normal(){
normal = rands(-1,1,3)+[2,0,0];
point = rands(-1,1,3);
displ = normal*point;
info = info_str([["normal = ",normal],["point = ",point],["displ = ",displ]]);
assert_approx(plane_from_normal(normal,point)*[each point,-1],0,info);
assert_std(plane_from_normal(normal,point),normalize_plane([each normal,displ]),info);
assert_std(plane_from_normal([1,1,1],[1,2,3]),[0.57735026919,0.57735026919,0.57735026919,3.46410161514]);
}
*test_plane_from_normal();
module test_plane_line_angle() {
angs = rands(0,360,3);
displ = rands(-1,1,1)[0];
info = info_str([["angs = ",angs],["displ = ",displ]]);
assert_approx(plane_line_angle([each rot(angs,p=[0,0,1]),displ],[[0,0,0],rot(angs,p=[0,0,1])]),90,info);
assert_approx(plane_line_angle([each rot(angs,p=[0,0,1]),displ],[[0,0,0],rot(angs,p=[0,1,1])]),45,info);
assert_approx(plane_line_angle([each rot(angs,p=[0,0,1]),0],[[0,0,0],rot(angs,p=[1,1,1])]),35.2643896828);
}
*test_plane_line_angle();
module test__general_plane_line_intersection() {
CRLF = chr(10);
// general line
plane1 = rands(-1,1,4)+[2,0,0,0]; // a random valid plane (normal!=0)
line1 = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0] ]; // a random valid line (line1[0]!=line1[1])
inters1 = _general_plane_line_intersection(plane1, line1);
info1 = info_str([["line = ",line1],["plane = ",plane1]]);
if(inters1==undef) { // parallel to the plane ?
assert_approx( point3d(plane1)*(line1[1]-line1[0]), 0, info1);
assert( point3d(plane1)*line1[0]== plane1[3], info1); // not on the plane
}
if( inters1[1]==undef) { // on the plane ?
assert_approx( point3d(plane1)*(line1[1]-line1[0]), 0, info1);
assert_approx(point3d(plane1)*line1[0],plane1[3], info1) ; // on the plane
}
else {
interspoint = line1[0]+inters1[1]*(line1[1]-line1[0]);
assert_approx(inters1[0],interspoint, info1);
assert_approx(point3d(plane1)*inters1[0], plane1[3], info1); // interspoint on the plane
assert_approx(distance_from_plane(plane1, inters1[0]), 0, info1); // inters1[0] on the plane
}
// line parallel to the plane
line2 = [ rands(-1,1,3)+[0,2,0], rands(-1,1,3)+[2,0,0] ]; // a random valid line2
// not containing the origin
plane0 = plane_from_points([line2[0], line2[1], [0,0,0]]); // plane cointaining the line
plane2 = plane_from_normal(plane_normal(plane0), [5,5,5]);
inters2 = _general_plane_line_intersection(plane2, line2);
info2 = info_str([["line = ",line2],["plane = ",plane2]]);
assert(inters2==undef, info2);
// line on the plane
line3 = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0] ]; // a random valid line
imax = max_index(line3[1]-line3[0]);
w = [for(j=[0:2]) imax==j? 0: 3 ];
p3 = line3[0] + cross(line3[1]-line3[0],w); // a point not on the line
plane3 = plane_from_points([line3[0], line3[1], p3]); // plane containing line
inters3 = _general_plane_line_intersection(plane3, line3);
info3 = info_str([["line = ",line3],["plane = ",plane3]]);
assert(!is_undef(inters3) && inters3[1]==undef, info3);
assert_approx(inters3[0], line3, info3);
}
*test__general_plane_line_intersection();
module assert_std(vc,ve) { assert(standardize(vc)==standardize(ve)); }
module test_points_on_plane() {
pts = [for(i=[0:40]) rands(-1,1,3) ];
dir = rands(-10,10,3);
normal0 = unit([1,2,3]);
normal0 = [1,2,3];
ang = rands(0,360,1)[0];
normal = rot(a=ang,p=normal0);
plane = [each normal, normal*dir];
prj_pts = projection_on_plane(plane,pts);
assert(points_on_plane(prj_pts,plane));
assert(!points_on_plane(concat(pts,[normal-dir]),plane));
info = info_str([["pts = ",pts],["dir = ",dir],["ang = ",ang]]);
assert(points_on_plane(prj_pts,plane),info);
assert(!points_on_plane(concat(pts,[normal-dir]),plane),info);
}
*test_points_on_plane();
@ -122,14 +301,15 @@ module test_projection_on_plane(){
plane = [each normal, 0];
planem = [each normal, normal*dir];
pts = [for(i=[1:10]) rands(-1,1,3)];
info = info_str([["ang = ",ang],["dir = ",dir]]);
assert_approx( projection_on_plane(plane,pts),
projection_on_plane(plane,projection_on_plane(plane,pts)));
projection_on_plane(plane,projection_on_plane(plane,pts)),info);
assert_approx( projection_on_plane(plane,pts),
rot(a=ang,p=projection_on_plane(plane0,rot(a=-ang,p=pts))));
rot(a=ang,p=projection_on_plane(plane0,rot(a=-ang,p=pts))),info);
assert_approx( move((-normal*dir)*normal,p=projection_on_plane(planem,pts)),
projection_on_plane(plane,pts));
projection_on_plane(plane,pts),info);
assert_approx( move((normal*dir)*normal,p=projection_on_plane(plane,pts)),
projection_on_plane(planem,pts));
projection_on_plane(planem,pts),info);
}
*test_projection_on_plane();
@ -543,12 +723,43 @@ module test_distance_from_plane() {
module test_polygon_line_intersection() {
poly1 = [[50,50,50], [50,-50,50], [-50,-50,50]];
assert_approx(polygon_line_intersection(poly1, [CENTER, UP]), [0,0,50]);
assert_approx(polygon_line_intersection(poly1, [CENTER, UP+RIGHT]), [50,0,50]);
assert_approx(polygon_line_intersection(poly1, [CENTER, UP+BACK+RIGHT]), [50,50,50]);
assert_approx(polygon_line_intersection(poly1, [[0,0,50], [1,0,50]]), [[[0,0,50], [50,0,50]]]);
assert_approx(polygon_line_intersection(poly1, [[0,0,0], [1,0,0]]), undef);
poly0 = [ [-10,-10, 0],[10,-10, 0],[10,10,0],[0,5,0],[-10,10,0] ];
line0 = [ [-3,7.5,0],[3,7.5,0] ]; // a segment on poly0 plane, out of poly0
angs = rands(0,360,3);
poly = rot(angs,p=poly0);
lineon = rot(angs,p=line0);
info = info_str([["angs = ",angs],["line = ",lineon],["poly = ",poly]]);
// line on polygon plane
assert_approx(polygon_line_intersection(poly,lineon,bounded=[true,true]),
undef, info);
assert_approx(polygon_line_intersection(poly,lineon,bounded=[true,false]),
[rot(angs,p=[[5,7.5,0],[10,7.5,0]])], info);
assert_approx(polygon_line_intersection(poly,lineon,bounded=[false,true]),
[rot(angs,p=[[-10,7.5,0],[-5,7.5,0]])], info);
assert_approx(polygon_line_intersection(poly,lineon,bounded=[false,false]),
rot(angs,p=[[[-10,7.5,0],[-5,7.5,0]],[[5,7.5,0],[10,7.5,0]]]), info);
// line parallel to polygon plane
linepll = move([0,0,1],lineon);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[true,true]),
undef, info);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[true,false]),
undef, info);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[false,true]),
undef, info);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[false,false]),
undef, info);
// general case
trnsl = [0,0,1];
linegnr = move(trnsl,rot(angs,p=[[5,5,5],[3,3,3]]));
polygnr = move(trnsl,rot(angs,p=poly0));
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[true,true]),
undef, info);
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[true,false]),
trnsl, info);
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[false,true]),
undef, info);
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[false,false]),
trnsl, info);
}
*test_polygon_line_intersection();
@ -576,6 +787,8 @@ module test_in_front_of_plane() {
module test_is_path() {
assert(is_path([[1,2,3],[4,5,6]]));
assert(is_path([[1,2,3],[4,5,6],[7,8,9]]));
assert(!is_path(123));
assert(!is_path("foo"));
assert(!is_path(true));
@ -584,8 +797,6 @@ module test_is_path() {
assert(!is_path([["foo","bar","baz"]]));
assert(!is_path([[1,2,3]]));
assert(!is_path([["foo","bar","baz"],["qux","quux","quuux"]]));
assert(is_path([[1,2,3],[4,5,6]]));
assert(is_path([[1,2,3],[4,5,6],[7,8,9]]));
}
*test_is_path();