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Rewrote line_closest_point() and segment_closest_point() to support 3D. Added ray_closest_point().

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Garth Minette 2020-07-19 23:07:49 -07:00
parent 375f1f2e3b
commit ae1a6d8d61
2 changed files with 173 additions and 14 deletions
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185
geometry.scad
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@ -133,8 +133,9 @@ function distance_from_line(line, pt) =
// color("green") stroke([p1,p1+10*n], endcap2="arrow2");
// color("blue") move_copies([p1,p2]) circle(d=2, $fn=12);
function line_normal(p1,p2) =
is_undef(p2)? line_normal(p1[0],p1[1]) :
unit([p1.y-p2.y,p2.x-p1.x]);
is_undef(p2)?
assert(is_path(p1,2)) line_normal(p1[0],p1[1]) :
assert(is_vector(p1,2)&&is_vector(p2,2)) unit([p1.y-p2.y,p2.x-p1.x]);
// 2D Line intersection from two segments.
@ -252,34 +253,192 @@ function segment_intersection(s1,s2,eps=EPSILON) =
// Usage:
// line_closest_point(line,pt);
// Description:
// Returns the point on the given `line` that is closest to the given point `pt`.
// Returns the point on the given 2D or 3D `line` that is closest to the given point `pt`.
// The `line` and `pt` args should either both be 2D or both 3D.
// Arguments:
// line = A list of two points that are on the unbounded line.
// pt = The point to find the closest point on the line to.
// Example(2D):
// line = [[-30,0],[30,30]];
// pt = [-32,-10];
// p2 = line_closest_point(line,pt);
// stroke(line, endcaps="arrow2");
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(2D):
// line = [[-30,0],[30,30]];
// pt = [-5,0];
// p2 = line_closest_point(line,pt);
// stroke(line, endcaps="arrow2");
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(2D):
// line = [[-30,0],[30,30]];
// pt = [40,25];
// p2 = line_closest_point(line,pt);
// stroke(line, endcaps="arrow2");
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(FlatSpin):
// line = [[-30,-15,0],[30,15,30]];
// pt = [5,5,5];
// p2 = line_closest_point(line,pt);
// stroke(line, endcaps="arrow2");
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
// Example(FlatSpin):
// line = [[-30,-15,0],[30,15,30]];
// pt = [-35,-15,0];
// p2 = line_closest_point(line,pt);
// stroke(line, endcaps="arrow2");
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
// Example(FlatSpin):
// line = [[-30,-15,0],[30,15,30]];
// pt = [40,15,25];
// p2 = line_closest_point(line,pt);
// stroke(line, endcaps="arrow2");
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
function line_closest_point(line,pt) =
assert(is_path(line)&&len(line)==2)
assert(same_shape(pt,line[0]))
assert(!approx(line[0],line[1]))
let(
n = line_normal(line),
isect = _general_line_intersection(line,[pt,pt+n])
) isect[0];
seglen = norm(line[1]-line[0]),
segvec = (line[1]-line[0])/seglen,
projection = (pt-line[0]) * segvec
)
line[0] + projection*segvec;
// Function: ray_closest_point()
// Usage:
// ray_closest_point(seg,pt);
// Description:
// Returns the point on the given 2D or 3D ray `ray` that is closest to the given point `pt`.
// The `ray` and `pt` args should either both be 2D or both 3D.
// Arguments:
// ray = The ray, given as a list `[START,POINT]` of the start-point START, and a point POINT on the ray.
// pt = The point to find the closest point on the ray to.
// Example(2D):
// ray = [[-30,0],[30,30]];
// pt = [-32,-10];
// p2 = ray_closest_point(ray,pt);
// stroke(ray, endcap2="arrow2");
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(2D):
// ray = [[-30,0],[30,30]];
// pt = [-5,0];
// p2 = ray_closest_point(ray,pt);
// stroke(ray, endcap2="arrow2");
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(2D):
// ray = [[-30,0],[30,30]];
// pt = [40,25];
// p2 = ray_closest_point(ray,pt);
// stroke(ray, endcap2="arrow2");
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(FlatSpin):
// ray = [[-30,-15,0],[30,15,30]];
// pt = [5,5,5];
// p2 = ray_closest_point(ray,pt);
// stroke(ray, endcap2="arrow2");
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
// Example(FlatSpin):
// ray = [[-30,-15,0],[30,15,30]];
// pt = [-35,-15,0];
// p2 = ray_closest_point(ray,pt);
// stroke(ray, endcap2="arrow2");
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
// Example(FlatSpin):
// ray = [[-30,-15,0],[30,15,30]];
// pt = [40,15,25];
// p2 = ray_closest_point(ray,pt);
// stroke(ray, endcap2="arrow2");
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
function ray_closest_point(ray,pt) =
assert(is_path(ray)&&len(ray)==2)
assert(same_shape(pt,ray[0]))
assert(!approx(ray[0],ray[1]))
let(
seglen = norm(ray[1]-ray[0]),
segvec = (ray[1]-ray[0])/seglen,
projection = (pt-ray[0]) * segvec
)
projection<=0 ? ray[0] :
ray[0] + projection*segvec;
// Function: segment_closest_point()
// Usage:
// segment_closest_point(seg,pt);
// Description:
// Returns the point on the given line segment `seg` that is closest to the given point `pt`.
// Returns the point on the given 2D or 3D line segment `seg` that is closest to the given point `pt`.
// The `seg` and `pt` args should either both be 2D or both 3D.
// Arguments:
// seg = A list of two points that are the endpoints of the bounded line segment.
// pt = The point to find the closest point on the segment to.
// Example(2D):
// seg = [[-30,0],[30,30]];
// pt = [-32,-10];
// p2 = segment_closest_point(seg,pt);
// stroke(seg);
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(2D):
// seg = [[-30,0],[30,30]];
// pt = [-5,0];
// p2 = segment_closest_point(seg,pt);
// stroke(seg);
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(2D):
// seg = [[-30,0],[30,30]];
// pt = [40,25];
// p2 = segment_closest_point(seg,pt);
// stroke(seg);
// color("blue") translate(pt) circle(r=1,$fn=12);
// color("red") translate(p2) circle(r=1,$fn=12);
// Example(FlatSpin):
// seg = [[-30,-15,0],[30,15,30]];
// pt = [5,5,5];
// p2 = segment_closest_point(seg,pt);
// stroke(seg);
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
// Example(FlatSpin):
// seg = [[-30,-15,0],[30,15,30]];
// pt = [-35,-15,0];
// p2 = segment_closest_point(seg,pt);
// stroke(seg);
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
// Example(FlatSpin):
// seg = [[-30,-15,0],[30,15,30]];
// pt = [40,15,25];
// p2 = segment_closest_point(seg,pt);
// stroke(seg);
// color("blue") translate(pt) sphere(r=1,$fn=12);
// color("red") translate(p2) sphere(r=1,$fn=12);
function segment_closest_point(seg,pt) =
assert(is_path(seg)&&len(seg)==2)
assert(same_shape(pt,seg[0]))
approx(seg[0],seg[1])? seg[0] :
let(
n = line_normal(seg),
isect = _general_line_intersection(seg,[pt,pt+n])
seglen = norm(seg[1]-seg[0]),
segvec = (seg[1]-seg[0])/seglen,
projection = (pt-seg[0]) * segvec
)
norm(n)==0? seg[0] :
isect[1]<=0? seg[0] :
isect[1]>=1? seg[1] :
isect[0];
projection<=0 ? seg[0] :
projection>=seglen ? seg[1] :
seg[0] + projection*segvec;
// Section: 2D Triangles

2
version.scad
View file

@ -8,7 +8,7 @@
//////////////////////////////////////////////////////////////////////
BOSL_VERSION = [2,0,395];
BOSL_VERSION = [2,0,396];
// Section: BOSL Library Version Functions