3 function vecdiff2d(a,b) = [b[0]-a[0], b[1]-a[1]];
4 function vecdiff(a,b) = [b[0]-a[0], b[1]-a[1], b[2]-a[2]];
6 #define dsq(i) (a[i]-b[i])*(a[i]-b[i])
7 function dist2d(a,b) = sqrt(dsq(0) + dsq(1));
8 function dist(a,b) = sqrt(dsq(0) + dsq(1) + dsq(2));
11 #define vsq(i) (v[i]*v[i])
12 function vectorlen2d(v) = sqrt(vsq(0) + vsq(1));
13 function vectorlen(v) = sqrt(vsq(0) + vsq(1) + vsq(2));
16 function unitvector2d(v) = v / vectorlen2d(v);
17 function unitvector(v) = v / vectorlen(v);
19 function atan2vector(v) = atan2(v[1], v[0]);
21 // | m[0][0] m[0][1] |
22 // | m[1][0] m[1][1] |
23 function determinant2(m) = (m[0][0] * m[1][1] - m[0][1] * m[1][0]);
25 function clockwise2d(v) = [v[1], -v[0]];
27 function rotate2d(theta, v) = [ v[0] * cos(theta) - v[1] * sin(theta),
28 v[1] * cos(theta) + v[0] * sin(theta) ];
30 // intersection of lines p1..p2 and p3..p4
31 function line_intersection_2d(p1,p2,p3,p4) = [
32 // from https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection#Given_two_points_on_each_line
33 #define XY12 determinant2([p1,p2])
34 #define XY34 determinant2([p3,p4])
35 #define XU12 QU(0,1,2)
36 #define XU34 QU(0,3,4)
37 #define YU12 QU(1,1,2)
38 #define YU34 QU(1,3,4)
39 #define QU(c,i,j) determinant2([[ p##i[c], 1 ], \
42 determinant2([[ XU12, YU12 ], \
45 determinant2([[ XY12, XU12 ],
46 [ XY34, XU34 ]]) / DENOM,
47 determinant2([[ XY12, YU12 ],
48 [ XY34, YU34 ]]) / DENOM,
60 function circle_point(c, r, alpha) = [ c[0] + r * cos(alpha),
61 c[1] + r * sin(alpha) ];
63 #define d (dist2d(a,c))
64 #define alpha (atan2(a[1]-c[1],a[0]-c[0]))
65 #define gamma (asin(r / d))
66 #define beta (alpha + 90 - gamma)
68 function tangent_intersect_beta(c,r,a) =
71 function tangent_intersect_b(c,r,a) =
72 circle_point(c, r, beta);
78 function tangents_intersect_beta(cbig,rbig,csmall,rsmall) =
79 tangent_intersect_beta(cbig,rbig-rsmall,csmall);
81 function reflect_in_y(p) = [-p[0], p[1]];
83 function angle_map_range(in,base) =
84 in < base ? in + 360 :
85 in >= base + 360 ? in - 360 :