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1 changed files with 135 additions and 56 deletions
191
geometry.scad
191
geometry.scad
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@ -10,7 +10,8 @@
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// Function: point_on_segment2d()
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// Usage:
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// point_on_segment2d(point, edge);
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// pt = point_on_segment2d(point, edge);
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// Topics: Geometry, Points, Segments
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// Description:
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// Determine if the point is on the line segment between two points.
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// Returns true if yes, and false if not.
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@ -45,7 +46,8 @@ function _valid_plane(p, eps=EPSILON) = is_vector(p,4) && ! approx(norm(p),0,eps
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// Function: point_left_of_line2d()
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// Usage:
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// point_left_of_line2d(point, line);
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// pt = point_left_of_line2d(point, line);
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// Topics: Geometry, Points, Lines
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// Description:
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// Return >0 if point is left of the line defined by `line`.
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// Return =0 if point is on the line.
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@ -60,7 +62,8 @@ function point_left_of_line2d(point, line) =
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// Function: collinear()
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// Usage:
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// collinear(a, [b, c], [eps]);
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// test = collinear(a, [b, c], [eps]);
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// Topics: Geometry, Points, Collinearity
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// Description:
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// Returns true if the points `a`, `b` and `c` are co-linear or if the list of points `a` is collinear.
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// Arguments:
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@ -80,7 +83,8 @@ function collinear(a, b, c, eps=EPSILON) =
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// Function: point_line_distance()
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// Usage:
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// point_line_distance(line, pt);
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// pt = point_line_distance(line, pt);
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// Topics: Geometry, Points, Lines, Distance
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// Description:
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// Finds the perpendicular distance of a point `pt` from the line `line`.
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// Arguments:
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@ -97,6 +101,7 @@ function point_line_distance(pt, line) =
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// Function: point_segment_distance()
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// Usage:
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// dist = point_segment_distance(pt, seg);
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// Topics: Geometry, Points, Segments, Distance
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// Description:
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// Returns the closest distance of the given point to the given line segment.
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// Arguments:
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@ -115,6 +120,8 @@ function point_segment_distance(pt, seg) =
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// Function: segment_distance()
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// Usage:
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// dist = segment_distance(seg1, seg2);
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// Topics: Geometry, Segments, Distance
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// See Also: convex_collision(), convex_distance()
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// Description:
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// Returns the closest distance of the two given line segments.
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// Arguments:
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@ -131,8 +138,9 @@ function segment_distance(seg1, seg2) =
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// Function: line_normal()
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// Usage:
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// line_normal([P1,P2])
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// line_normal(p1,p2)
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// vec = line_normal([P1,P2])
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// vec = line_normal(p1,p2)
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// Topics: Geometry, Lines
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// Description:
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// Returns the 2D normal vector to the given 2D line. This is otherwise known as the perpendicular vector counter-clockwise to the given ray.
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// Arguments:
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@ -172,7 +180,8 @@ function _general_line_intersection(s1,s2,eps=EPSILON) =
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// Function: line_intersection()
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// Usage:
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// line_intersection(l1, l2);
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// pt = line_intersection(l1, l2);
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// Topics: Geometry, Lines, Intersections
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// Description:
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// Returns the 2D intersection point of two unbounded 2D lines.
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// Returns `undef` if the lines are parallel.
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@ -190,7 +199,8 @@ function line_intersection(l1,l2,eps=EPSILON) =
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// Function: line_ray_intersection()
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// Usage:
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// line_ray_intersection(line, ray);
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// pt = line_ray_intersection(line, ray);
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// Topics: Geometry, Lines, Rays, Intersections
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// Description:
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// Returns the 2D intersection point of an unbounded 2D line, and a half-bounded 2D ray.
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// Returns `undef` if they do not intersect.
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@ -210,7 +220,8 @@ function line_ray_intersection(line,ray,eps=EPSILON) =
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// Function: line_segment_intersection()
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// Usage:
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// line_segment_intersection(line, segment);
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// pt = line_segment_intersection(line, segment);
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// Topics: Geometry, Lines, Segments, Intersections
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// Description:
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// Returns the 2D intersection point of an unbounded 2D line, and a bounded 2D line segment.
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// Returns `undef` if they do not intersect.
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@ -231,7 +242,8 @@ function line_segment_intersection(line,segment,eps=EPSILON) =
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// Function: ray_intersection()
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// Usage:
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// ray_intersection(s1, s2);
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// pt = ray_intersection(s1, s2);
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// Topics: Geometry, Lines, Rays, Intersections
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// Description:
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// Returns the 2D intersection point of two 2D line rays.
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// Returns `undef` if they do not intersect.
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@ -251,7 +263,8 @@ function ray_intersection(r1,r2,eps=EPSILON) =
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// Function: ray_segment_intersection()
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// Usage:
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// ray_segment_intersection(ray, segment);
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// pt = ray_segment_intersection(ray, segment);
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// Topics: Geometry, Rays, Segments, Intersections
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// Description:
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// Returns the 2D intersection point of a half-bounded 2D ray, and a bounded 2D line segment.
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// Returns `undef` if they do not intersect.
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@ -272,7 +285,8 @@ function ray_segment_intersection(ray,segment,eps=EPSILON) =
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// Function: segment_intersection()
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// Usage:
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// segment_intersection(s1, s2);
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// pt = segment_intersection(s1, s2);
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// Topics: Geometry, Segments, Intersections
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// Description:
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// Returns the 2D intersection point of two 2D line segments.
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// Returns `undef` if they do not intersect.
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@ -293,7 +307,8 @@ function segment_intersection(s1,s2,eps=EPSILON) =
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// Function: line_closest_point()
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// Usage:
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// line_closest_point(line,pt);
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// pt = line_closest_point(line,pt);
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// Topics: Geometry, Lines, Distance
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// Description:
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// Returns the point on the given 2D or 3D `line` that is closest to the given point `pt`.
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// The `line` and `pt` args should either both be 2D or both 3D.
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@ -351,7 +366,8 @@ function line_closest_point(line,pt) =
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// Function: ray_closest_point()
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// Usage:
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// ray_closest_point(seg,pt);
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// pt = ray_closest_point(seg,pt);
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// Topics: Geometry, Rays, Distance
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// Description:
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// Returns the point on the given 2D or 3D ray `ray` that is closest to the given point `pt`.
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// The `ray` and `pt` args should either both be 2D or both 3D.
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@ -414,7 +430,8 @@ function ray_closest_point(ray,pt) =
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// Function: segment_closest_point()
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// Usage:
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// segment_closest_point(seg,pt);
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// pt = segment_closest_point(seg,pt);
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// Topics: Geometry, Segments, Distance
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// Description:
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// Returns the point on the given 2D or 3D line segment `seg` that is closest to the given point `pt`.
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// The `seg` and `pt` args should either both be 2D or both 3D.
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@ -471,7 +488,8 @@ function segment_closest_point(seg,pt) =
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// Function: line_from_points()
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// Usage:
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// line_from_points(points, [fast], [eps]);
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// line = line_from_points(points, [fast], [eps]);
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// Topics: Geometry, Lines, Points
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// Description:
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// Given a list of 2 or more collinear points, returns a line containing them.
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// If `fast` is false and the points are coincident or non-collinear, then `undef` is returned.
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@ -496,6 +514,7 @@ function line_from_points(points, fast=false, eps=EPSILON) =
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// Usage:
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// C = law_of_cosines(a, b, c);
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// c = law_of_cosines(a, b, C);
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// Topics: Geometry, Triangles
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// Description:
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// Applies the Law of Cosines for an arbitrary triangle. Given three side lengths, returns the
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// angle in degrees for the corner opposite of the third side. Given two side lengths, and the
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@ -529,6 +548,7 @@ function law_of_cosines(a, b, c, C) =
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// Usage:
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// B = law_of_sines(a, A, b);
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// b = law_of_sines(a, A, B);
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// Topics: Geometry, Triangles
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// Description:
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// Applies the Law of Sines for an arbitrary triangle. Given two triangle side lengths and the
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// angle between them, returns the angle of the corner opposite of the second side. Given a side
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@ -561,7 +581,8 @@ function law_of_sines(a, A, b, B) =
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// Function: tri_calc()
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// Usage:
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// tri_calc(ang,ang2,adj,opp,hyp);
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// triangle = tri_calc(ang,ang2,adj,opp,hyp);
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// Topics: Geometry, Triangles
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// Description:
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// Given a side length and an angle, or two side lengths, calculates the rest of the side lengths
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// and angles of a right triangle. Returns [ADJACENT, OPPOSITE, HYPOTENUSE, ANGLE, ANGLE2] where
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@ -633,6 +654,7 @@ function tri_calc(ang,ang2,adj,opp,hyp) =
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// Function: hyp_opp_to_adj()
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// Usage:
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// adj = hyp_opp_to_adj(hyp,opp);
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// Topics: Geometry, Triangles
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// Description:
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// Given the lengths of the hypotenuse and opposite side of a right triangle, returns the length
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// of the adjacent side.
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@ -650,6 +672,7 @@ function hyp_opp_to_adj(hyp,opp) =
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// Function: hyp_ang_to_adj()
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// Usage:
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// adj = hyp_ang_to_adj(hyp,ang);
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// Topics: Geometry, Triangles
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// Description:
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// Given the length of the hypotenuse and the angle of the primary corner of a right triangle,
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// returns the length of the adjacent side.
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@ -667,6 +690,7 @@ function hyp_ang_to_adj(hyp,ang) =
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// Function: opp_ang_to_adj()
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// Usage:
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// adj = opp_ang_to_adj(opp,ang);
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// Topics: Geometry, Triangles
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// Description:
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// Given the angle of the primary corner of a right triangle, and the length of the side opposite of it,
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// returns the length of the adjacent side.
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@ -684,6 +708,7 @@ function opp_ang_to_adj(opp,ang) =
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// Function: hyp_adj_to_opp()
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// Usage:
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// opp = hyp_adj_to_opp(hyp,adj);
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// Topics: Geometry, Triangles
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// Description:
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// Given the length of the hypotenuse and the adjacent side, returns the length of the opposite side.
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// Arguments:
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@ -700,6 +725,7 @@ function hyp_adj_to_opp(hyp,adj) =
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// Function: hyp_ang_to_opp()
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// Usage:
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// opp = hyp_ang_to_opp(hyp,adj);
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// Topics: Geometry, Triangles
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// Description:
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// Given the length of the hypotenuse of a right triangle, and the angle of the corner, returns the length of the opposite side.
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// Arguments:
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@ -716,6 +742,7 @@ function hyp_ang_to_opp(hyp,ang) =
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// Function: adj_ang_to_opp()
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// Usage:
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// opp = adj_ang_to_opp(adj,ang);
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// Topics: Geometry, Triangles
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// Description:
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// Given the length of the adjacent side of a right triangle, and the angle of the corner, returns the length of the opposite side.
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// Arguments:
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@ -732,6 +759,7 @@ function adj_ang_to_opp(adj,ang) =
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// Function: adj_opp_to_hyp()
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// Usage:
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// hyp = adj_opp_to_hyp(adj,opp);
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// Topics: Geometry, Triangles
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// Description:
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// Given the length of the adjacent and opposite sides of a right triangle, returns the length of thee hypotenuse.
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// Arguments:
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@ -748,6 +776,7 @@ function adj_opp_to_hyp(adj,opp) =
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// Function: adj_ang_to_hyp()
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// Usage:
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// hyp = adj_ang_to_hyp(adj,ang);
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// Topics: Geometry, Triangles
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// Description:
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// For a right triangle, given the length of the adjacent side, and the corner angle, returns the length of the hypotenuse.
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// Arguments:
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@ -764,6 +793,7 @@ function adj_ang_to_hyp(adj,ang) =
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// Function: opp_ang_to_hyp()
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// Usage:
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// hyp = opp_ang_to_hyp(opp,ang);
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// Topics: Geometry, Triangles
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// Description:
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// For a right triangle, given the length of the opposite side, and the corner angle, returns the length of the hypotenuse.
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// Arguments:
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@ -796,6 +826,7 @@ function hyp_adj_to_ang(hyp,adj) =
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// Function: hyp_opp_to_ang()
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// Usage:
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// ang = hyp_opp_to_ang(hyp,opp);
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// Topics: Geometry, Triangles
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// Description:
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// For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the angle of the corner.
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// Arguments:
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@ -812,6 +843,7 @@ function hyp_opp_to_ang(hyp,opp) =
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// Function: adj_opp_to_ang()
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// Usage:
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// ang = adj_opp_to_ang(adj,opp);
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// Topics: Geometry, Triangles
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// Description:
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// For a right triangle, given the lengths of the adjacent and opposite sides, returns the angle of the corner.
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// Arguments:
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@ -827,7 +859,8 @@ function adj_opp_to_ang(adj,opp) =
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// Function: triangle_area()
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// Usage:
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// triangle_area(a,b,c);
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// area = triangle_area(a,b,c);
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// Topics: Geometry, Triangles, Area
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// Description:
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// Returns the area of a triangle formed between three 2D or 3D vertices.
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// Result will be negative if the points are 2D and in clockwise order.
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@ -851,7 +884,8 @@ function triangle_area(a,b,c) =
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// Function: plane3pt()
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// Usage:
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// plane3pt(p1, p2, p3);
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// plane = plane3pt(p1, p2, p3);
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// Topics: Geometry, Planes
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// Description:
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// Generates the normalized cartesian equation of a plane from three 3d points.
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// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
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@ -873,7 +907,8 @@ function plane3pt(p1, p2, p3) =
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// Function: plane3pt_indexed()
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// Usage:
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// plane3pt_indexed(points, i1, i2, i3);
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// plane = plane3pt_indexed(points, i1, i2, i3);
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// Topics: Geometry, Planes
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// Description:
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// Given a list of 3d points, and the indices of three of those points,
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// generates the normalized cartesian equation of a plane that those points all
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@ -899,7 +934,8 @@ function plane3pt_indexed(points, i1, i2, i3) =
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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 = plane_from_normal(normal, [pt])
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// Topics: Geometry, Planes
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// Description:
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// Returns a plane defined by a normal vector and a point.
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// Arguments:
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@ -957,7 +993,8 @@ function _covariance_evec_eval(points) =
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// Function: plane_from_points()
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// Usage:
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// plane_from_points(points, <fast>, <eps>);
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// plane = plane_from_points(points, <fast>, <eps>);
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// Topics: Geometry, Planes, Points
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// Description:
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// Given a list of 3 or more coplanar 3D points, returns the coefficients of the normalized cartesian equation of a plane,
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// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane and norm([A,B,C])=1.
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@ -991,7 +1028,8 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
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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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// plane = plane_from_polygon(points, [fast], [eps]);
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// Topics: Geometry, Planes, Polygons
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// Description:
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// Given a 3D planar polygon, returns the normalized cartesian equation of its plane.
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// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1.
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@ -1020,7 +1058,8 @@ function plane_from_polygon(poly, fast=false, eps=EPSILON) =
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// Function: plane_normal()
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// Usage:
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// plane_normal(plane);
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// vec = plane_normal(plane);
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// Topics: Geometry, Planes
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// Description:
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// Returns the unit length normal vector for the given plane.
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// Arguments:
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@ -1033,6 +1072,7 @@ function plane_normal(plane) =
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// Function: plane_offset()
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// Usage:
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// d = plane_offset(plane);
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// Topics: Geometry, Planes
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// Description:
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// Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin.
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// This value may be negative.
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@ -1048,6 +1088,7 @@ function plane_offset(plane) =
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// Function: projection_on_plane()
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// Usage:
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// pts = projection_on_plane(plane, points);
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// Topics: Geometry, Planes, Projection
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// Description:
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// Given a plane definition `[A,B,C,D]`, where `Ax+By+Cz=D`, and a list of 2d or
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// 3d points, return the 3D orthogonal projection of the points on the plane.
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@ -1083,6 +1124,7 @@ function projection_on_plane(plane, points) =
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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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// Topics: Geometry, Planes, Distance
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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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// Arguments:
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@ -1094,7 +1136,8 @@ function plane_point_nearest_origin(plane) =
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|
||||
// Function: point_plane_distance()
|
||||
// Usage:
|
||||
// point_plane_distance(plane, point)
|
||||
// dist = point_plane_distance(plane, point)
|
||||
// Topics: Geometry, Planes, Distance
|
||||
// Description:
|
||||
// Given a plane as [A,B,C,D] where the cartesian equation for that plane
|
||||
// is Ax+By+Cz=D, determines how far from that plane the given point is.
|
||||
|
|
@ -1130,6 +1173,7 @@ function _general_plane_line_intersection(plane, line, eps=EPSILON) =
|
|||
// Function: normalize_plane()
|
||||
// Usage:
|
||||
// nplane = normalize_plane(plane);
|
||||
// Topics: Geometry, Planes
|
||||
// Description:
|
||||
// Returns a new representation [A,B,C,D] of `plane` where norm([A,B,C]) is equal to one.
|
||||
function normalize_plane(plane) =
|
||||
|
|
@ -1140,6 +1184,7 @@ function normalize_plane(plane) =
|
|||
// Function: plane_line_angle()
|
||||
// Usage:
|
||||
// angle = plane_line_angle(plane,line);
|
||||
// Topics: Geometry, Planes, Lines, Angle
|
||||
// Description:
|
||||
// Compute the angle between a plane [A, B, C, D] and a 3d line, specified as a pair of 3d points [p1,p2].
|
||||
// The resulting angle is signed, with the sign positive if the vector p2-p1 lies on
|
||||
|
|
@ -1159,6 +1204,7 @@ function plane_line_angle(plane, line) =
|
|||
// Function: plane_line_intersection()
|
||||
// Usage:
|
||||
// pt = plane_line_intersection(plane, line, [bounded], [eps]);
|
||||
// Topics: Geometry, Planes, Lines, Intersection
|
||||
// Description:
|
||||
// Takes a line, and a plane [A,B,C,D] where the equation of that plane is `Ax+By+Cz=D`.
|
||||
// If `line` intersects `plane` at one point, then that intersection point is returned.
|
||||
|
|
@ -1187,6 +1233,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
|
|||
// Function: polygon_line_intersection()
|
||||
// Usage:
|
||||
// pt = polygon_line_intersection(poly, line, [bounded], [eps]);
|
||||
// Topics: Geometry, Polygons, Lines, Intersection
|
||||
// Description:
|
||||
// Takes a possibly bounded line, and a 3D planar polygon, and finds their intersection point.
|
||||
// If the line and the polygon are on the same plane then returns a list, possibly empty, of 3D line
|
||||
|
|
@ -1246,7 +1293,9 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
|
|||
|
||||
// Function: plane_intersection()
|
||||
// Usage:
|
||||
// plane_intersection(plane1, plane2, [plane3])
|
||||
// line = plane_intersection(plane1, plane2)
|
||||
// pt = plane_intersection(plane1, plane2, plane3)
|
||||
// Topics: Geometry, Planes, Intersection
|
||||
// Description:
|
||||
// Compute the point which is the intersection of the three planes, or the line intersection of two planes.
|
||||
// If you give three planes the intersection is returned as a point. If you give two planes the intersection
|
||||
|
|
@ -1277,7 +1326,8 @@ function plane_intersection(plane1,plane2,plane3) =
|
|||
|
||||
// Function: coplanar()
|
||||
// Usage:
|
||||
// coplanar(points,<eps>);
|
||||
// test = coplanar(points,<eps>);
|
||||
// Topics: Geometry, Coplanarity
|
||||
// Description:
|
||||
// Returns true if the given 3D points are non-collinear and are on a plane.
|
||||
// Arguments:
|
||||
|
|
@ -1304,7 +1354,8 @@ function _pointlist_greatest_distance(points,plane) =
|
|||
|
||||
// Function: points_on_plane()
|
||||
// Usage:
|
||||
// points_on_plane(points, plane, <eps>);
|
||||
// test = points_on_plane(points, plane, <eps>);
|
||||
// Topics: Geometry, Planes, Points
|
||||
// Description:
|
||||
// Returns true if the given 3D points are on the given plane.
|
||||
// Arguments:
|
||||
|
|
@ -1320,7 +1371,8 @@ function points_on_plane(points, plane, eps=EPSILON) =
|
|||
|
||||
// Function: in_front_of_plane()
|
||||
// Usage:
|
||||
// in_front_of_plane(plane, point);
|
||||
// test = in_front_of_plane(plane, point);
|
||||
// Topics: Geometry, Planes
|
||||
// Description:
|
||||
// Given a plane as [A,B,C,D] where the cartesian equation for that plane
|
||||
// is Ax+By+Cz=D, determines if the given 3D point is on the side of that
|
||||
|
|
@ -1339,6 +1391,7 @@ function in_front_of_plane(plane, point) =
|
|||
// Function&Module: circle_2tangents()
|
||||
// Usage: As Function
|
||||
// circ = circle_2tangents(pt1, pt2, pt3, r|d, <tangents>);
|
||||
// Topics: Geometry, Circles, Tangents
|
||||
// Usage: As Module
|
||||
// circle_2tangents(pt1, pt2, pt3, r|d, <h>, <center>);
|
||||
// Description:
|
||||
|
|
@ -1449,6 +1502,7 @@ module circle_2tangents(pt1, pt2, pt3, r, d, h, center=false) {
|
|||
// Usage: As Function
|
||||
// circ = circle_3points(pt1, pt2, pt3);
|
||||
// circ = circle_3points([pt1, pt2, pt3]);
|
||||
// Topics: Geometry, Circles
|
||||
// Usage: As Module
|
||||
// circle_3points(pt1, pt2, pt3, <h>, <center>);
|
||||
// circle_3points([pt1, pt2, pt3], <h>, <center>);
|
||||
|
|
@ -1527,6 +1581,7 @@ module circle_3points(pt1, pt2, pt3, h, center=false) {
|
|||
// Function: circle_point_tangents()
|
||||
// Usage:
|
||||
// tangents = circle_point_tangents(r|d, cp, pt);
|
||||
// Topics: Geometry, Circles, Tangents
|
||||
// Description:
|
||||
// Given a 2d circle and a 2d point outside that circle, finds the 2d tangent point(s) on the circle for a
|
||||
// line passing through the point. Returns a list of zero or more 2D tangent points.
|
||||
|
|
@ -1561,6 +1616,7 @@ function circle_point_tangents(r, d, cp, pt) =
|
|||
// Function: circle_circle_tangents()
|
||||
// Usage:
|
||||
// segs = circle_circle_tangents(c1, r1|d1, c2, r2|d2);
|
||||
// Topics: Geometry, Circles, Tangents
|
||||
// Description:
|
||||
// Computes 2d lines tangents to a pair of circles in 2d. Returns a list of line endpoints [p1,p2] where
|
||||
// p2 is the tangent point on circle 1 and p2 is the tangent point on circle 2.
|
||||
|
|
@ -1643,6 +1699,7 @@ function circle_circle_tangents(c1,r1,c2,r2,d1,d2) =
|
|||
// Function: circle_line_intersection()
|
||||
// Usage:
|
||||
// isect = circle_line_intersection(c,<r|d>,<line>,<bounded>,<eps>);
|
||||
// Topics: Geometry, Circles, Lines, Intersection
|
||||
// Description:
|
||||
// Find intersection points between a 2d circle and a line, ray or segment specified by two points.
|
||||
// By default the line is unbounded.
|
||||
|
|
@ -1683,7 +1740,8 @@ function circle_line_intersection(c,r,d,line,bounded=false,eps=EPSILON) =
|
|||
|
||||
// Function: noncollinear_triple()
|
||||
// Usage:
|
||||
// noncollinear_triple(points);
|
||||
// test = noncollinear_triple(points);
|
||||
// Topics: Geometry, Noncollinearity
|
||||
// Description:
|
||||
// Finds the indices of three good non-collinear points from the pointlist `points`.
|
||||
// If all points are collinear returns [] when `error=true` or an error otherwise .
|
||||
|
|
@ -1715,7 +1773,8 @@ function noncollinear_triple(points,error=true,eps=EPSILON) =
|
|||
|
||||
// Function: pointlist_bounds()
|
||||
// Usage:
|
||||
// pointlist_bounds(pts);
|
||||
// pt_pair = pointlist_bounds(pts);
|
||||
// Topics: Geometry, Bounding Boxes, Bounds
|
||||
// Description:
|
||||
// Finds the bounds containing all the points in `pts` which can be a list of points in any dimension.
|
||||
// Returns a list of two items: a list of the minimums and a list of the maximums. For example, with
|
||||
|
|
@ -1734,7 +1793,8 @@ function pointlist_bounds(pts) =
|
|||
|
||||
// Function: closest_point()
|
||||
// Usage:
|
||||
// closest_point(pt, points);
|
||||
// index = closest_point(pt, points);
|
||||
// Topics: Geometry, Points, Distance
|
||||
// Description:
|
||||
// Given a list of `points`, finds the index of the closest point to `pt`.
|
||||
// Arguments:
|
||||
|
|
@ -1748,7 +1808,8 @@ function closest_point(pt, points) =
|
|||
|
||||
// Function: furthest_point()
|
||||
// Usage:
|
||||
// furthest_point(pt, points);
|
||||
// index = furthest_point(pt, points);
|
||||
// Topics: Geometry, Points, Distance
|
||||
// Description:
|
||||
// Given a list of `points`, finds the index of the furthest point from `pt`.
|
||||
// Arguments:
|
||||
|
|
@ -1766,6 +1827,7 @@ function furthest_point(pt, points) =
|
|||
// Function: polygon_area()
|
||||
// Usage:
|
||||
// area = polygon_area(poly);
|
||||
// Topics: Geometry, Polygons, Area
|
||||
// Description:
|
||||
// Given a 2D or 3D planar polygon, returns the area of that polygon.
|
||||
// If the polygon is self-crossing, the results are undefined. For non-planar 3D polygon the result is `undef`.
|
||||
|
|
@ -1784,16 +1846,17 @@ function polygon_area(poly, signed=false) =
|
|||
let(
|
||||
n = plane_normal(plane),
|
||||
total =
|
||||
sum([ for(i=[1:1:len(poly)-2])
|
||||
cross(poly[i]-poly[0], poly[i+1]-poly[0])
|
||||
]) * n/2
|
||||
sum([ for(i=[1:1:len(poly)-2])
|
||||
cross(poly[i]-poly[0], poly[i+1]-poly[0])
|
||||
]) * n/2
|
||||
)
|
||||
signed ? total : abs(total);
|
||||
|
||||
|
||||
// Function: polygon_shift()
|
||||
// Usage:
|
||||
// polygon_shift(poly, i);
|
||||
// newpoly = polygon_shift(poly, i);
|
||||
// Topics: Geometry, Polygons
|
||||
// Description:
|
||||
// Given a polygon `poly`, rotates the point ordering so that the first point in the polygon path is the one at index `i`.
|
||||
// Arguments:
|
||||
|
|
@ -1808,7 +1871,8 @@ function polygon_shift(poly, i) =
|
|||
|
||||
// Function: polygon_shift_to_closest_point()
|
||||
// Usage:
|
||||
// polygon_shift_to_closest_point(path, pt);
|
||||
// newpoly = polygon_shift_to_closest_point(path, pt);
|
||||
// Topics: Geometry, Polygons
|
||||
// Description:
|
||||
// Given a polygon `poly`, rotates the point ordering so that the first point in the path is the one closest to the given point `pt`.
|
||||
// Arguments:
|
||||
|
|
@ -1827,6 +1891,7 @@ function polygon_shift_to_closest_point(poly, pt) =
|
|||
// Function: reindex_polygon()
|
||||
// Usage:
|
||||
// newpoly = reindex_polygon(reference, poly);
|
||||
// Topics: Geometry, Polygons
|
||||
// Description:
|
||||
// Rotates and possibly reverses the point order of a 2d or 3d polygon path to optimize its pairwise point
|
||||
// association with a reference polygon. The two polygons must have the same number of vertices and be the same dimension.
|
||||
|
|
@ -1877,6 +1942,7 @@ function reindex_polygon(reference, poly, return_error=false) =
|
|||
// Function: align_polygon()
|
||||
// Usage:
|
||||
// newpoly = align_polygon(reference, poly, angles, <cp>);
|
||||
// Topics: Geometry, Polygons
|
||||
// Description:
|
||||
// Tries the list or range of angles to find a rotation of the specified 2D polygon that best aligns
|
||||
// with the reference 2D polygon. For each angle, the polygon is reindexed, which is a costly operation
|
||||
|
|
@ -1913,7 +1979,8 @@ function align_polygon(reference, poly, angles, cp) =
|
|||
|
||||
// Function: centroid()
|
||||
// Usage:
|
||||
// cp = centroid(poly);
|
||||
// cpt = centroid(poly);
|
||||
// Topics: Geometry, Polygons, Centroid
|
||||
// Description:
|
||||
// Given a simple 2D polygon, returns the 2D coordinates of the polygon's centroid.
|
||||
// Given a simple 3D planar polygon, returns the 3D coordinates of the polygon's centroid.
|
||||
|
|
@ -1948,7 +2015,8 @@ function centroid(poly, eps=EPSILON) =
|
|||
|
||||
// Function: point_in_polygon()
|
||||
// Usage:
|
||||
// point_in_polygon(point, poly, <eps>)
|
||||
// test = point_in_polygon(point, poly, <eps>)
|
||||
// Topics: Geometry, Polygons
|
||||
// Description:
|
||||
// This function tests whether the given 2D point is inside, outside or on the boundary of
|
||||
// the specified 2D polygon using either the Nonzero Winding rule or the Even-Odd rule.
|
||||
|
|
@ -2008,7 +2076,8 @@ function point_in_polygon(point, poly, nonzero=true, eps=EPSILON) =
|
|||
|
||||
// Function: polygon_is_clockwise()
|
||||
// Usage:
|
||||
// polygon_is_clockwise(poly);
|
||||
// test = polygon_is_clockwise(poly);
|
||||
// Topics: Geometry, Polygons, Clockwise
|
||||
// Description:
|
||||
// Return true if the given 2D simple polygon is in clockwise order, false otherwise.
|
||||
// Results for complex (self-intersecting) polygon are indeterminate.
|
||||
|
|
@ -2021,7 +2090,8 @@ function polygon_is_clockwise(poly) =
|
|||
|
||||
// Function: clockwise_polygon()
|
||||
// Usage:
|
||||
// clockwise_polygon(poly);
|
||||
// newpoly = clockwise_polygon(poly);
|
||||
// Topics: Geometry, Polygons, Clockwise
|
||||
// Description:
|
||||
// Given a 2D polygon path, returns the clockwise winding version of that path.
|
||||
// Arguments:
|
||||
|
|
@ -2033,7 +2103,8 @@ function clockwise_polygon(poly) =
|
|||
|
||||
// Function: ccw_polygon()
|
||||
// Usage:
|
||||
// ccw_polygon(poly);
|
||||
// newpoly = ccw_polygon(poly);
|
||||
// Topics: Geometry, Polygons, Clockwise
|
||||
// Description:
|
||||
// Given a 2D polygon poly, returns the counter-clockwise winding version of that poly.
|
||||
// Arguments:
|
||||
|
|
@ -2045,7 +2116,8 @@ function ccw_polygon(poly) =
|
|||
|
||||
// Function: reverse_polygon()
|
||||
// Usage:
|
||||
// reverse_polygon(poly)
|
||||
// newpoly = reverse_polygon(poly)
|
||||
// Topics: Geometry, Polygons, Clockwise
|
||||
// Description:
|
||||
// Reverses a polygon's winding direction, while still using the same start point.
|
||||
// Arguments:
|
||||
|
|
@ -2057,7 +2129,8 @@ function reverse_polygon(poly) =
|
|||
|
||||
// Function: polygon_normal()
|
||||
// Usage:
|
||||
// n = polygon_normal(poly);
|
||||
// vec = polygon_normal(poly);
|
||||
// Topics: Geometry, Polygons
|
||||
// Description:
|
||||
// Given a 3D planar polygon, returns a unit-length normal vector for the
|
||||
// clockwise orientation of the polygon. If the polygon points are collinear, returns `undef`.
|
||||
|
|
@ -2165,6 +2238,7 @@ function _split_polygon_at_z(poly, z) =
|
|||
// Function: split_polygons_at_each_x()
|
||||
// Usage:
|
||||
// splitpolys = split_polygons_at_each_x(polys, xs);
|
||||
// Topics: Geometry, Polygons, Intersections
|
||||
// Description:
|
||||
// Given a list of 3D polygons, splits all of them wherever they cross any X value given in `xs`.
|
||||
// Arguments:
|
||||
|
|
@ -2185,6 +2259,7 @@ function split_polygons_at_each_x(polys, xs, _i=0) =
|
|||
// Function: split_polygons_at_each_y()
|
||||
// Usage:
|
||||
// splitpolys = split_polygons_at_each_y(polys, ys);
|
||||
// Topics: Geometry, Polygons, Intersections
|
||||
// Description:
|
||||
// Given a list of 3D polygons, splits all of them wherever they cross any Y value given in `ys`.
|
||||
// Arguments:
|
||||
|
|
@ -2205,6 +2280,7 @@ function split_polygons_at_each_y(polys, ys, _i=0) =
|
|||
// Function: split_polygons_at_each_z()
|
||||
// Usage:
|
||||
// splitpolys = split_polygons_at_each_z(polys, zs);
|
||||
// Topics: Geometry, Polygons, Intersections
|
||||
// Description:
|
||||
// Given a list of 3D polygons, splits all of them wherever they cross any Z value given in `zs`.
|
||||
// Arguments:
|
||||
|
|
@ -2228,7 +2304,8 @@ function split_polygons_at_each_z(polys, zs, _i=0) =
|
|||
|
||||
// Function: is_convex_polygon()
|
||||
// Usage:
|
||||
// is_convex_polygon(poly);
|
||||
// test = is_convex_polygon(poly);
|
||||
// Topics: Geometry, Convexity, Test
|
||||
// Description:
|
||||
// Returns true if the given 2D or 3D polygon is convex.
|
||||
// The result is meaningless if the polygon is not simple (self-intersecting) or non coplanar.
|
||||
|
|
@ -2237,11 +2314,11 @@ function split_polygons_at_each_z(polys, zs, _i=0) =
|
|||
// poly = Polygon to check.
|
||||
// eps = Tolerance for the collinearity test. Default: EPSILON.
|
||||
// Example:
|
||||
// is_convex_polygon(circle(d=50)); // Returns: true
|
||||
// is_convex_polygon(rot([50,120,30], p=path3d(circle(1,$fn=50)))); // Returns: true
|
||||
// test1 = is_convex_polygon(circle(d=50)); // Returns: true
|
||||
// test2 = is_convex_polygon(rot([50,120,30], p=path3d(circle(1,$fn=50)))); // Returns: true
|
||||
// Example:
|
||||
// spiral = [for (i=[0:36]) let(a=-i*10) (10+i)*[cos(a),sin(a)]];
|
||||
// is_convex_polygon(spiral); // Returns: false
|
||||
// test = is_convex_polygon(spiral); // Returns: false
|
||||
function is_convex_polygon(poly,eps=EPSILON) =
|
||||
assert(is_path(poly), "The input should be a 2D or 3D polygon." )
|
||||
let( lp = len(poly),
|
||||
|
|
@ -2260,9 +2337,10 @@ function is_convex_polygon(poly,eps=EPSILON) =
|
|||
|
||||
// Function: convex_distance()
|
||||
// Usage:
|
||||
// convex_distance(pts1, pts2,<eps=>);
|
||||
// dist = convex_distance(pts1, pts2,<eps=>);
|
||||
// Topics: Geometry, Convexity, Distance
|
||||
// See also:
|
||||
// convex_collision
|
||||
// convex_collision(), hull()
|
||||
// Description:
|
||||
// Returns the smallest distance between a point in convex hull of `points1`
|
||||
// and a point in the convex hull of `points2`. All the points in the lists
|
||||
|
|
@ -2320,9 +2398,10 @@ function _GJK_distance(points1, points2, eps=EPSILON, lbd, d, simplex=[]) =
|
|||
|
||||
// Function: convex_collision()
|
||||
// Usage:
|
||||
// convex_collision(pts1, pts2,<eps=>);
|
||||
// test = convex_collision(pts1, pts2,<eps=>);
|
||||
// Topics: Geometry, Convexity, Collision, Intersection
|
||||
// See also:
|
||||
// convex_distance
|
||||
// convex_distance(), hull()
|
||||
// Description:
|
||||
// Returns `true` if the convex hull of `points1` intercepts the convex hull of `points2`
|
||||
// otherwise, `false`.
|
||||
|
|
@ -2383,7 +2462,7 @@ function _closest_simplex(s,eps=EPSILON) =
|
|||
: _closest_s3(s,eps);
|
||||
|
||||
|
||||
// find the closest to a 1-simplex
|
||||
// find the point of a 1-simplex closest to the origin
|
||||
// Based on: http://uu.diva-portal.org/smash/get/diva2/FFULLTEXT01.pdf
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function _closest_s1(s,eps=EPSILON) =
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norm(s[1]-s[0])<eps*(norm(s[0])+norm(s[1]))/2 ? [ s[0], [s[0]] ] :
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@ -2396,7 +2475,7 @@ function _closest_s1(s,eps=EPSILON) =
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[ s[0]+t*c, s ];
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// find the closest to a 2-simplex
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// find the point of a 2-simplex closest to the origin
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// Based on: http://uu.diva-portal.org/smash/get/diva2/FFULLTEXT01.pdf
|
||||
function _closest_s2(s,eps=EPSILON) =
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||||
let(
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|
@ -2432,7 +2511,7 @@ function _closest_s2(s,eps=EPSILON) =
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c*(c-a)>0 ? _closest_s1([s[0],s[2]],eps) : _closest_s1([s[1],s[2]],eps);
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|
||||
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||||
// find the closest to a 3-simplex
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// find the point of a 3-simplex closest to the origin
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||||
// it seems that degenerate 3-simplices are correctly manage without extra code
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function _closest_s3(s,eps=EPSILON) =
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||||
assert( len(s[0])==3 && len(s)==4, "Internal error." )
|
||||
|
|
|
|||
Loading…
Reference in a new issue